USF Libraries
USF Digital Collections

Analysis of mass transfer by jet impingement and study of heat transfer in a trapezoidal microchannel

MISSING IMAGE

Material Information

Title:
Analysis of mass transfer by jet impingement and study of heat transfer in a trapezoidal microchannel
Physical Description:
Book
Language:
English
Creator:
Ojada, Ejiro Stephen
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Fully-confined fluid
Sherwood number
Rotating disk
Gadolinium
Heat sink
Dissertations, Academic -- Mechanical Engineering -- Masters -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: This thesis numerically studied mass transfer during fully confined liquid jet impingement on a rotating target disk of finite thickness and radius. The study involved laminar flow with jet Reynolds numbers from 650 to 1500. The nozzle to plate distance ratio was in the range of 0.5 to 2.0, the Schmidt number ranged from 1720 to 2513, and rotational speed was up to 325 rpm. In addition, the jet impingement to a stationary disk was also simulated for the purpose of comparison. The electrochemical fluid used was an electrolyte containing 0.005moles per liter potassium ferricyanide (K₃(Fe(CN₆)), 0.02moles per liter ferrocyanide (FeCN₆⁻⁴), and 0.5moles per liter potassium carbonate (K₂CO₃). The rate of mass transfer of this electrolyte was compared to Sodium Hydroxide (NaOH) and Hydrochloric acid (HCl) electrochemical solutions. The material of the rotating disk was made of 99.98% nickel and 0.02% of chromium, cobalt and aluminum.The rate of mass transfer was also examined for different geometrical shapes of conical, convex, and concave confinement plates over a spinning disk. The results obtained are found to be in agreement with previous experimental and numerical studies. The study of heat transfer involved a microchannel for a composite channel of trapezoidal cross-section fabricated by etching a silicon wafer and bonding it with a slab of gadolinium. Gadolinium is a magnetic material that exhibits high temperature rise during adiabatic magnetization around its transition temperature of 295K. Heat was generated in the substrate by the application of magnetic field. Water, ammonia, and FC-77 were studied as the possible working fluids. Thorough investigation for velocity and temperature distribution was performed by varying channel aspect ratio, Reynolds number, and the magnetic field. The thickness of gadolinium slab, spacing between channels in the heat exchanger, and fluid flow rate were varied.To check the validity of simulation, the results were compared with existing results for single material channels. Results showed that Nusselt number is larger near the inlet and decreases downstream. Also, an increase in Reynolds number increases the total Nusselt number of the system.
Thesis:
Thesis (M.S.M.E.)--University of South Florida, 2009.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Ejiro Stephen Ojada.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 104 pages.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 002069519
oclc - 608550466
usfldc doi - E14-SFE0003297
usfldc handle - e14.3297
System ID:
SFS0027613:00001


This item is only available as the following downloads:


Full Text

PAGE 1

i Analysis of Mass Transfer by Jet Impingement and Study of Heat Transfe r in a Trapezoidal Microchannel b y Ejiro Stephen Ojada A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering De partment of Mechanical Engineering University of South Florida Major Professor: Muhammad M. Rahman, Ph.D Frank Pyrtle, III, Ph.D Rasim Guldiken, Ph.D Date of Approval: November 5 2009 Keywords: Fully Confined Fluid, Sherwood number Rotating Disk, Gadolinium Heat Sink Cop yright 2009, Ejiro Stephen Ojada

PAGE 2

i TABLE OF CONTENT S LIST OF FIGURES ii LIST OF SYMBOLS v ABSTRACT viii CHAPTER 1 : INTRODUCTION AND LITERATURE REVIEW 1 1.1 Introduction (Mass Transfer by Jet Impingement ) 1 1.2 Literature Review (Mass Transfer by Jet Impingement) 2 1.3 Introduction (He at Transfer in a Microchannel) 7 1.4 Literature Review (He at Transfer in a Microchannel) 8 CHAPTER 2 : ANA LYSIS OF MASS TRANSF ER BY JET IMPINGEMENT 15 2.1 Mathematical Model 15 2.2 Numerical Simulation 19 2.3 Results and Discussion 21 CHAPTER 3 : ANALYSIS OF HEAT TRANSFER IN A TRAPEZOIDAL MICROCHANNEL 42 3.1 Modeling and Simulation 42 3.2 Result s and Discussion 48 CHAPTER 4 : CONCLUSION 6 5 REFERENCES 67 APPENDICES 79 Appendix A : FIDAP Code for Analysis of Mass Transfer by Jet Impingement 80 Appendix B : FIDAP Code for Fluid Flow and Heat Transfer in a Composite Trapezoidal Microchannel 8 6

PAGE 3

ii LIST OF FIGURES Figure 2 .1 a Confined liquid jet impingement be tween a rotating disk and an impingement plate, two dimensional schematic. 18 Figure 2.1b Confined liquid jet impingement between a rotating disk and an impingement plate three dimensional schematic. 18 Figure 2. 2 Mesh plot for a grid spacing of 20 x 500 in the axial and radial directions. 21 Figure 2. 3 Dimensionless interface temperature distributions for different number of elements in r and z directions (Re j =1000, Re r =2310, =1.0, and Sc=2315). 22 Figure 2. 4 Local Sherwood number and dimensi onless concentration for different jet Reynolds numbers ( =1.0, Re r =2310, nickel disk, and Sc=2315). 26 Figure 2. 5 Local Sherwood number and dimensionless concentration for different rotational Reynolds numbers ( =1.0, nickel disk, Re j =800, and Sc=2315) 27 Figure 2. 6 Local Sherwood number and dimensionless concentration for different dimensionless heights (Re j =1500, Re r =2310, and Sc=2315). 28 Figure 2. 7 Average Sherwood numbers with jet Reynolds numbers at various rotational Reynolds numbers ( =1. 0, nickel disk, and ferricyanide electrolyte and Sc=2315). 29 Figure 2. 8 Average Sherwood number with jet Reynolds number at different dimensionless nozzle to target spacing (Re r =2310, and Sc=2315). 32 Figure 2. 9 Average Sherwood number with jet Reyn olds number at different Schmidt number ( =1.15, nickel disk, ferricyanide electrolyte, and Re r =5082). 33

PAGE 4

iii Figure 2. 10 Dimensionless concentration for different electrolytes NaOH, HCl, (Re j =650, Re r =0, and =1.0). 34 Figure 2. 1 1 Local Sherwood number and d imensionless c oncentration over d imensionless r adial d istance for different impingement plate geometries, nickel disk with ferricyanide electrolyte (Re j =1000, Re r =5082, =1.15, and Sc=2315). 35 Figure 2. 1 2 Average Sherwood n umber comparison with the experimental results obtained by Arzutu et al. [13] under various jet Reynolds and Schmidt numbers (left: =1.0, Sc=2315, Re r =2310; right: ( =1.0, Re j =1000, and Re r =5082). 37 Figure 2. 1 3 Average Sherwood number comparison with other studies within the core region for various Schmidt numbers ( =1.0, Re j =800, Re r =2310). 38 Figure 2. 1 4 Comparison of predicted average Sherwood number using Equation 17 with present numerical data. 39 Figure 3.1 Schematic of the trapezoidal microchannel. 46 Figure 3.2 Average dimensionless interface temp erature over the dimensionless axial coordinate for different grid sizes ) 49 Figure 3.3 Variation of peripheral average Nusselt number along the channel dimensionless axial coordinate for different Rey nolds 50 Figure 3.4 Variation of peripheral average dimensionless interface temperature along the channel dimensionless axial coordinate for different Reynolds number and different magnetic fields (D=150 51 Figure 3.5 Variation of Nusselt number along the channel dimensionless axial coordinate for different heat generation rates (Re = 1600, 52 Figure 3.6 Variation of peripheral average dimensionless in terface temperature along the channel dimensionless axial coordinate for different thickness of the magnetic slab (Re= 1600, 54

PAGE 5

iv Figure 3.7 Variation of Nusselt number along the channel dimensionless axial coordin ate for different depths of the channel (Magnetic field =5T, Constant velocity). 55 Figure 3.8 Average dimensionless interface temperature numbers with Reynolds numbers at various channel depths (Magnetic field =5T, 1000 < Re < 3000). 56 Figure 3.9 V ariation of Nusselt number over the dimensionless axial coordinate for different spacing between the channels (Re = 57 Figure 3.10 Comparison between simulation and standard convection cm). 59 Figure 3.11 Variation of dimensionless pressure difference between inlet and outlet of the channel with Reynolds number (Magnetic field = 5T, L=2.3 cm). 60 Figure 3.12 Variation of the Nusselt numbers for different working fluids 61 Figure 3.13 Variation of dimensionless pumping power for different Reynolds numbers (Magnetic field = 5T, L=2.3 cm). 63 Figure 3.14 Average Nusselt number comparison with the expe rimental results obtained by Wu and Chen [38] under various jet 64

PAGE 6

v LIST OF SYMBOLS b Height of gadolinium slab, m B Substrate width, m B c Channel width, m B s Half of channel width (at botto m), m C avg A verage interface concentration, k g /m 3 C p Constant pressure specific heat, J/ k g K C Solute c oncentration, k g /m 3 d n Diameter of n ozzle, m d d Diameter of rotating disk, m D Diffusion c oefficient, m 2 /s Dp Dimensionless pump power D h Hydraulic diameter m g Acceleration due to gravity, m/s 2 go Heat generation rate within the solid, W/m 3 G Mass f lux, k g/m 2 .s h Heat transfer coefficient, q int / (T int b ) W/m 2 K H Distance of the nozzle from the rotating disk, m H Height of substrate, m k Thermal conductivity, W/m K; or Turbulent kinetic energy, m 2 /s 2 K Mass transfer c oefficient G / ( C int C j ) m/s L Channel length, m Nu Nusselt number P Pre ssure, N/m 2

PAGE 7

vi P d Dimensionless pressure P p Pumping power Pr t Turbulent Prandtl number q Heat flux, W/m 2 Q Dimensionless Concentration, 2 (C int C j ) / ( G d n ) r Radial coordinate, m R Radius of rotating disk, m Re Reynolds number, (V j d n )/ or Sh Sherwood n umber, (k d n )/D S Spacing between channels, m T Temperature, C Temperature difference between inlet and outlet, C V j Jet velocity, m/s V r, z, Velocity component in the r, z and direction, m/s, in cylindrical coordinate u Velocity component in x direction, m/s v Velocity component in y direction, m/s w V elocity component in z direction, m/s z Axial coordinate, m Greek Symbols Thermal diffusivity, m 2 /s Dimensionless nozzle to target spacing, H/d n Dissipation rate of turbulent kinetic energy, m 2 /s 3 Dynamic viscosity, kg/m s Kinematic viscosity, m 2 /s t Eddy diffusivity, m 2 /s Angular coordinate, rad Dimensionless interface temperature Density, kg/m 3 Angular velocity, rad/s

PAGE 8

vii Subscripts b Bulk avg. Average f Fluid g Gadolinium i Species i in Inlet int Interface j jet inlet max Maximum s si Silicon s Solid

PAGE 9

viii Analysis of Mass Transfer by Jet Impingement and Study of Heat Transfe r in a Trapezoidal Microchannel Ejiro S Ojada ABSTRACT This thesis numerically studie d mass transfer during fully confined liquid jet impingement on a rotating target disk of finite thickness and radius. The study involved laminar flow with jet Reynolds numbers from 650 to 1500. The nozzle to plate distance ratio was in the range of 0.5 to 2.0, the Schmidt number ranged from 1720 to 2513, and rotational speed was up to 325 rpm. In addition, the jet impingement to a stationary disk was also simulated for the purpose of comparison. The electrochemical fluid used was an electrolyte containing 0.005 moles per liter potassium ferricyanide (K 3 (Fe(CN 6 )), 0.02 mol es per liter ferrocyanide (FeCN 6 4 ), and 0.5 moles per liter potassium carbonate (K 2 CO 3 ). The rate of mass transfer of this electrolyte was compared to Sodium Hydroxide (NaOH) and Hydrochloric acid (HCl) electrochemical solutions. The material of the rota ting disk was made of 99 .98 % nickel and 0.02% of chromium, cobalt and aluminum T he rate of mass transfer was also examine d for different geometrical shapes of conical, convex, and concave confinement plates over a spinning disk. The results obtained are f ound to be in agreement with previous experimental and numerical studies.

PAGE 10

ix The study of heat transfer involved a microchanne l for a composite channel of trapezoidal cross section fabricated by etching a silic on <100> wafer and bonding it with a slab of gado linium. Gadolinium is a magnetic material that exhibits high temperature rise during adiabatic magnetization around its transition temperature of 295K. Heat was generated in the substrate by the application of magnetic field. Water, ammonia, and FC 77 were studied as the possible working fluids T horough investigation for velocity and temperature distribution was performed by varying channel aspect ratio, Reynolds number, and the magnetic field. The thickness of gadolinium slab, spacing between channels in the heat exchanger, and fluid flow rate were varied. To check the validity of simulation, the results were compared with existing results for single material channels. Results showed that Nusselt number is larger near the inlet and decreas es downstream. A lso, an increase in Reynolds number increases the total Nusselt number of the system.

PAGE 11

1 CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW 1.1 Introduction ( Mass Transfer by Jet Impingement) Jet impingement is a technique used in the industry to enhance heat a nd /or mass transfer processes. It provides the opportunity to control temperature and/or concentration to the desired needs. A few examples are paper drying process, material removal in steel mills, tempering of glass, cooling of high temperature gas turb ines and electronic fabrication of printed wiring board components. The rotation of a disk also plays a role in enhancing the heat and mass transfer by inducing a secondary flow. The rotating disk enhances the wall jet effect at the interface which adds mo re complexity to the flow field and more mixing with the impinging jet flow.

PAGE 12

2 1.2 Literature Review (Mass Transfer by Jet Impingement) An e arly research work on mass transfer from a rotating disk was performed by Kreith et al. [1] who studied the effect of a shroud on the mass transfer rate from a rotating disk in the laminar regime, hav ing rotational Reynolds numbers ranging from 70000 140000 T he correlation obtained did not account for the distance between the disk and the shroud. Nakoryakov et al. [2] studied theoretically and experimentally the hydrodynamics and mass transfer of a submerged liquid jet impinging onto a horizontal plane. They measured the wall shear stress and local mass transfer coefficients by an electro diffusion method for a wide range of liquid flow rates. Chin and Tsang [3] studied t he mass transfer from an impi nging jet to the stagnation region on a circular disk electrode using the method of perturbation. They found out that within the radius, r/d d from 0.1 to 1.0 turbulent nozzle flow and from 0.1 to 0.5 for laminar nozzle flow, the to decrease beyond the uniform accessibility region. The impingement of two dimensional slot jet flows for high speed selective electroplating was studied by Alkire and Ju [4]. They measu re local mass transfer coefficient for the system when it is submerged and when it is not. They also developed correlations for three regions: impingement, transition and wall jet flow regions. Chin and Agarwal [5] studied the local mass transfer rate of a submerged oblique impinging slot jet by electrochemical limiting current technique for the reduction of ferricyanide ion at isolated microelectrodes on the impinged surface. An electrochemical probe was used to measure the mass transfer coefficient. Mo reno et al. [6] studied t he mass transfer of an impinging liquid jet

PAGE 13

3 confined between two parallel plates theoretically and by experiments. The mass transfer rate was characterized by an etching method in a cupric chloride etching solution and jet instabi lity on the etching rate within the central impingement zone was discussed Chen et al. [7] investigated experimentally the mass transfer between an impinging jet and a rotating disk The naphthalene sublimation technique was used in the experiment. The experimental results showed that heat/mass transfer are divided into three regions which are the impingement dominated region, the mixed region and the rotation dominated region. It was concluded that the Sherwood number of a rotating disk with jet impin gement was the sum of two components governed by the impinging jet and the rotating disk. Pekdemir and Davies [8] studied t he mass transfer behavior of an isothermal system when a rotating circular cylinder is exposed to a two dimensional slot jet of air w ith a laminar flow. In the impingement dominated regime, they observed that the rotation of disk did not influence heat transfer characteristics of the system, while the jet impingement had a strong effect on the local heat transfer of the rotating disk. Chen and Modi [9] investigated the mass transfer characteristics of a turbulent slot jet impinging normally on a target wall with a confinement plate placed parallel to the target plate examined using numerical simulations. The flow was modeled using a k w turbulence model. The Reynolds number simulated ranged from 450 to 20000, Prandtl or Schmidt numbers from 0 to 2400 and the slot jets varied between 2 and 8 times the width of the slot jet. Chen et al. [10] conducted experiment on mass and heat transf er for high Schmidt numbers with a laminar jet impingement flow onto rotating and stationary disks. The experiment used naphthalene sublimation technique where three regimes where

PAGE 14

4 observed, namely the impingement dominated regime, the mixed regime and the rotation dominated regime. Using a conical shaped impingement plate, Miranda and Campos [11] investigated mass transfer in a laminar by impinging jet. The distance between the nozzle and the plate was less than one nozzle diameter, the laminar flow was l ess than 1600, and the Schmidt was up to 50000. Oduoza [12] worked on mass transfer on a heated electrode by simulating high speed wire plating with simultaneous heat transfer in the laminar region. The working fluid used for the study was ferricyanide. In the simulation, it showed a distinct effect of thermally driven natural convection at a lower Reynolds number and but as the Reynolds number increased, it merged with the Leveque solution. Arzutu et al. [13] compared the mass transfer distribution from a jet to a plate between a submerged conventional impinging jet (CIJ) and multichannel conventional impinging jet (MCIJ). Electrochemical limiting diffusion current technique (ELDCT) was used to me asure the local mass transfer coefficients. The values that were obtained for the mean mass transfer coefficients over the surface for CIJ and MCIJ were found to be relatively close to each other with MCIJ having slightly higher values. Quiroz et al. [14] also used the electrochemical limiting diffusion current technique (ELDCT) to measure the mass transfer between parallel disk cells with the help of the Levique relation. Sedahmed et al. [15] studied the rate of mass transfer between two immiscible liqui ds, an aqueous layer and a mercury pool upon which an axial jet was impinging under turbulent flow conditions and measured by electrochemical limiting diffusion limiting current technique (ELDCT).

PAGE 15

5 Sara et al. [16] measured the mass transfer coefficient usi ng the ELDCT method of an electrochemical system from an impinging liquid jet to a rotating disk in a fully confined environment. The study used a rotational Reynolds number of up to 120000, and a jet Reynolds number of up to 53000 with a non dimensional j et to disk spacing of 2 8. They found out that the jet impingement had a considerable effect on the enhancement of the mass transfer compared to the case of the rotating disk without jet. The effects on mass/heat transfer on rotation by impingement jet wer e also studied by Hong et al. [17]. Their research covered a wide range of rotational Reynolds numbers (400 to 10,000) including laminar, turbulent and transitional regimes. Hong et al. [18] investigated the mass transfer characteristics on a concave surf ace for rotating impinging jets. A jet with Reynolds number of 5,000 was applied to the concave surface and a flat surface. They found out that compared to flat surface, the heat/mass transfer on the concave surface is enhanced with increasing the span wis e direction due to the curvature effect, providing a higher averaged Sherwood value. Research has also been done involving heat transfer in jet impingement processes. Lallave et al [19] studied the characterization of conjugate heat transfer for a confi ned liquid jet impinging on a rotating and uniformly heated solid disk of finite thickness and radius. The study showed that the plate materials with higher thermal conductivity had a more uniform temperature distribution at the solid fluid interface, and the local heat transfer coefficient increased with an increasing in Reynolds number which reduced the wall to fluid temperature difference over the entire interface. Lallave and Rahman [20]

PAGE 16

6 worked on conjugate heat transfer characterization of a partiall y confined liquid jet impinging on a rotating and uniformly heated solid disk of finite thickness and radius. Even though a number of publications have considered the heat/mass transfer rate effect of numerous parameters, not enough research has been done on mass transfer during laminar jet impingement on a rotating disk in a fully confined environment using an electrolyte. The intent of this research is to investigate the mass transfer effect in a uniform laminar flow from the jet nozzle onto a rotating di sk in a fully confined space. The study parameter includes five jets Reynolds numbers, five rotational Reynolds numbers and stationary disk, five heights measured from the nozzle to the target disk, five Schmidt numbers, and different confinement plate sha pes such as conical, convex, and concave. Present results offer a better understanding of the fluid mechanics and mass transfer behavior of liquid jet impingement under confinement on top of a spinning target because of the incorporation of the varying pa rameters Even though no new numerical technique has been developed, results obtained in this investigation are entirely new. The numerical results showing the quantitative effects of different parameters as well as the correlation for average Sherwood num bers will be practical guides for enhancement of mass transfer during the electrolyte synthesis and etching processes.

PAGE 17

7 1.3 Introduction (Heat Transfer in a Microchannel) Microchannels of trapezoidal cross section are widely used in silicon based microsystems The study of fluid flow and heat transfer is critical to the development of these microsystems. This thesis presents a systematic analysis of fluid flow and heat transfer processes during the magnetic heating of a magnetocaloric material which is bonded to the substrate. The substrate has an array of trapezoidal channels through which heat is transferred to the working fluid. When a magnetic field is imposed on a magnetocaloric material, heat is generated. This results in increase in temperature of the ma terial. Similarly, the temperature drops during demagnetization when the field is removed. The purpose of this thesis is to study the effects of change in different geometrical and thermal parameters on fluid flow and heat transfer when a magnetic field is applied to the substrate material.

PAGE 18

8 1.4 Literature Review (Heat Transfer in a Microchannel) Wu and Little [ 3 1 ] measured the friction factors of laminar gas flow in the trapezoidal silicon/glass microchannels, and found that the surface roughness affected th e values of the friction factors even in the laminar flow, which is different from the conventional macrochannel flow. Harley et al. [ 3 2 ] presented experimental and theoretical results of low Reynolds number, high subsonic Mach number, compressible gas flo w in channels. Nitrogen, helium, and argon gases were used. D etailed data on velocity, density a nd temperature distributions were obtained. The effect of the Mach number on profiles of axial and transversa l velocities and temperature were revealed. Chen an d Wu [3 3 ] investigated the microchannel flow in miniature TCDs (thermal conductivity detectors). Effects of channel size and boundary conditions were examined in details. It was found that the change in heat transfer rate in the entrance region depends pri marily on the thermal conductivity change in the conduction dominant region. Qu et al. [ 3 4 ] investigated heat transfer characteristics of water flowing through trapezoidal silicon microchannels. A numerical analysis was carried out by solving a conjugate h eat transfer problem. Rahman [ 3 5 ] presented new experimental measurements for pressure drop and heat transfer coefficient in microchannel heat sinks. Tests were performed with devices fabricated using standard Silicon < 100 > wafers Channels of different d epths (or aspect ratios) were studied. Tests were carried out using water as the working fluid. The fluid flow rate as well as the pressure and temperature of the fluid at the inlet and outlet of the device, and temperature at several locations in the wafe r were measured. These

PAGE 19

9 measurements were used to calculate local and average Nusselt number and coefficient of friction in the device. Toh et al. [ 3 6 ] studied the fluid flow and heat transfer in a microchannel by number computation. The results of the num erical computations where compared to experimental data for validation. Their research revealed that heat in put lowers frictional losses at mostly lower Reynolds numbers since an increase in temperature leads to a decrease in viscosity thereby leading to smaller frictional losses. Qu and Mudawar [ 3 7 ] also investigated the heat transfer behavior in a rectangular microchannel. They observed that when the thermal conductivity of a substrate is increased in which the fluid flows through while keeping all par ameters constant, the temperature at the base surface of the heat sink reduces. They concluded that a higher laminar Reynolds number at 1400 will not be a fully developed flow in a microchannel and as a result will lead to enhanced heat transfer. Wu and Cheng [ 38 ] observed the same behavior of an approximate linear correlation between the Nusselt number and Reynolds number at Re < 100. They studied what effect the surface roughness of the microchannel y) has on the Nusselt number. The investigation showed that there is an increase in the laminar Nusselt number when the surface roughness or hydrophilic property is increased. The apparent friction constant also increased with an increase in the surface roughness. Wu and Cheng [ 39 ] measured the friction factor of laminar flow of deionized water in smooth silicon micro channels of trapezoidal cross section. The experimental data were found to be in agreement within 11% with an existing analytical solution for an incompressible, fully developed, laminar flow under the no slip boundary condition. It

PAGE 20

10 was confirmed that Navier Stokes equations are still valid for the laminar flow of deionized water in smooth micro channels having hydraulic diameter as small as 25.9 from laminar to turbulent flow occurred at Re = 1500 2000. Li et al. [ 40 ] conducted a numerical simulation on a silicon based microchannel heat sink. The finite d ifference numerical code developed to solve the governing equations was the Tri Diagonal Matrix Algorithm. The behavior flow and the heat transfer were investigated to observe how the geometric parameters of the channel and thermo physical properties affe ct them. The outcome of this study revealed that the thermo physical properties of the liquid used in the analysis can considerably affect both flow and heat transfer in the microchannel heat sink. Mo et al. [ 4 1 ] studied the flow of nitrogen gas in a rec tangular channel by forced convection. The different parameter varied during the study showed considerable effect on the heat transfer characteristic in the channel. The main parameters were temperature, hydraulic diameter, and aspect ratio. The researc h revealed that heat addition had the most influence on the system, followed by the channel aspect ratio, Reynolds number which is a function of the hydraulic diameter, and Prandtl number. Owhaib and Palm [ 4 2 ] experimentally investigated the heat transfe r characteristics of single phase forced convection flow through circular microchannels. The results were compared to correlations for heat transfer in macroscale channels. The results showed good agreement between classical correlations and experimentally measured data. Wu and Cheng [ 4 3 ] carried out a series of experiments to study different boiling instability modes of water flowing in microchannels at various heat flux and mass

PAGE 21

11 flux with the outlet of the channels at atmospheric pressure. Eight parallel silicon microchannels with an identical trapezoidal cross section were used in this experiment. Morini et al. [ 4 4 ] investigated the rarefaction effects on the pressure drop for an incompressible flow through silicon microchannels having a rectangular and trapezoidal cross section. The roles of Knudsen number and the cross section aspect ratio on the friction factor reduction due to the rarefaction were pointed out. Chen and Cheng [ 4 5 ] performed a visualization study on condensation of steam in microchannel s etched in a silicon <100> wafer that was bonded by a thin Pyrex glass plate from the top. Saturated steam flowed through these parallel microchannels, whose walls were cooled by natural convection of air at room temperature. Stable droplet condensation w as observed near the inlet of the microchannel. It was predicted that the droplet condensation heat flux increases as the diameter of the microchannel is decreased. The experimental investigation of heat transfer in a rectangular microchannel was also per formed by Lee et al. [ 4 6 ]. They explored the validity of classical correlations based on conventionalized channels for predicting the thermal behavior in a single flow. This study also showed that at a given flow rate within the laminar region, the heat t ransfer coefficient will increase with a decreasing channel size. In applying a uniform heat flux to a trapezoidal microchannel, Cao et al. [ 4 7 ] showed the effect of velocity slip on the Nusselt number and friction coefficient of the system. It was disco vered that values of Nusselt number for a slip flow was larger than that of a no slip flow and an increase in aspect ratio will result in an increase in fully Nusselt number. Hetsroni et al. [ 48 ] compared experimental result based on theoretical and numer ical results for heat transfer in a microchannel at

PAGE 22

12 small Knudsen numbers. The effect of the geometric and axial heat flux parameters on the system was analyzed. The thermal conduction through the working fluid, channel walls and energy dissipation was o bserved with regards to the parameters. Zhuo et al. [ 49 ] also studied the heat transfer behavior in both triangular and trapezoidal microchannel by numerical and experimental processes. The intersection angle between the temperature and velocity gradien t was observed and the synergy for Reynolds numbers below 100 was much better. The field synergy principle was confirmed with an almost linear relationship between the Reynolds number and their corresponding Nusselt number for Re < 100. Li et al. [ 5 0 ] sh owed through studies that Nusselt number and heat transfer coefficient will reduce along the flow of a microchannel with the least values at the outlet. Husain and Kim [ 5 1 ] used numerical methods in order to optimized microchannel heat sink using a surroga te analysis and evolutionary algorithm. In the optimization, the objective functions of thermal resistance and pumping power in the microchannel where formulated to evaluate the performance of the heat sink. Rahman et al. [ 5 2 ] investigated the convective heat transfer related to a magnetic field in a circular microchannel with rectangular substrate. The heat source was from gadolinium, a magnetocaloric material that generates heat within a magnetic field and different parameters where varied to see the in fluence on the heat transfer coefficient. Li and Kleinstreuer [ 5 3 ] compared the thermal conductivity model for nanofluids; one involved the application of a model based on the Brownian motion induced micro mixing and the other was based on Navier Stokes. The study was done on the flow of nanofluids pure water and CuO water through a trapezoidal microchannel. Their research revealed

PAGE 23

13 that nanofluids improved thermal performance of microchannel mixture flow but with a pressure drop. Hooman [ 5 4 ] presented investigation on the convective characteristics of a rectangular microchannel with a porous medium while factoring parameters such as temperature jump, velocity profile, duct geometry, friction factor and slip coefficient. Their influence on the Nusselt nu mber was analyzed. Hasan et al. [ 5 5 ] studied the effect of channel geometry on a microchannel heat exchanger. Numerical simulations were carried out to solve developing flow and conjugate heat transfer. The shapes investigated include square, rectangular trapezoidal and iso triangle. Their investigation showed that with the parameters used, when the volume of a channel is decreased or the number of channels are increase, heat transfer increases, pressure drops and pumping power increases. This study wi thin the parameters used showed the circular channel having the most effective thermal efficiency. Hsieh and Lin [ 5 6 ] performed experiment to determine the thermal characteristics of a fluid in rectangular microchannel. The fluids used in the experiments were deionized water, methanol and ethanol solutions. The parameters were aspect ratio, hydraulic diameter, Reynolds numbers, surface conditions, thermal properties and the different fluids. From within the extent of these parameters, it was observed th at the hydrophilic surfaces had higher local heat transfer coefficients than that of hydrophobic for all test fluids. Chen et al. [ 5 7 ] studied the thermal behavior of heat transfer in different shapes of microchannels. These shapes include trapezoidal, r ectangular and triangular shapes. In the study, the Nusselt number was seen to be highest at the inlet of the heat sink and least at the outlet. In comparison with the

PAGE 24

14 different shapes of microchannel that were studied, it was observe d that the triangul ar shaped model had the most thermal efficiency. DeGregoria et al. [ 58 ] tested an experimental magnetocaloric refrigerator designed to operate within a temperature range of about 4 to 80 K. Helium gas was used as the heat transfer fluid. A si ngle magnet was used to charge and discharge two in line beds of magnetocaloric material. Zimm et al. [ 59 ] investigated magnetic refrigeration for near room temperature cooling. Water was used as the heat transfer fluid. A porous bed of magnetocaloric mate rial was used in the experiment. It was found that using a 5T magnetic field, a refrigerator reliably produces cooling powers exceeding 500W at coefficient of performance 6 or more. Pecharsky and Gschneidner [ 6 0 ] discussed new magnetocaloric materials with respect to their magnetocaloric properties. Recent progress in magnetocaloric refrigerator design was reviewed. The objective of the present investigation is to take a step ahead in study of micro channels of trapezoidal cross section by investigating com posite trapezoidal channels. A composite trapezoidal microchannel structure is formed by bonding a slab of gadolinium with silicon wafer where microchannels of trapezoidal cross section have been etched out of the silicon substrate. The study presents diff erent parametric variations and its effect on the fluid flow and heat transfer characteristics of the channel.

PAGE 25

15 CHAPTER 2 ANALYSIS OF MASS TRANSFER BY JET IMPINGEMENT 2.1 Mathematical Model The diagram of figure 2.1 is a schematic of the problem being ana lyzed. It involves an axi symmetric feature with the ejection of liquid jet from the nozzle which impin ges on a rotating disk. Figure 2 .1 a and 2 .1 b are the 2D and 3D schematic s respectively. The nozzle diameter, d n is 0.15cm which is kept as a constant fun ction of Re j used in simulation and calculations of local and average Sherwood number in equations (13 and 14). The rotating disk has a diameter, d d of 1.5cm where a 10 to 1 ratio with d n was intended. Dimensionless height, is calculated H/d n In analysi s, is made to vary to observe the effect it has on the mass transfer rate. The numerical model parameters include a Newtonian fluid with constant properties, an incompressible flow under laminar and steady state conditions. As part of this computational analysis, the system under study was under isothermal conditions neglecting the heat transfer effects of the energy equation. The equations describing the conservation of mass, momentum (r, and z directions respectively) can be written as [28]. (1) (2)

PAGE 26

16 (3) (4) The mass transport equation of momentum accommodates the chemical species in the following form: (5) In addition, the ion mass flux (moles/area time) which involves the transfer of ions between an electrolyte and the electrode is defined by: (6) Where N is ion mass flux, which is related to the mass transfer coefficient, K, c is the concentration of ions in the bulk fluid and c int is the concentration of ions on the interface. The following boundary conditions were used. (7) (8) (9) ( 10) (11) The boundary conditions applied to the flow is a no slip condition where the velocity parallel to the walls and on the wall is zero. The formula used to determine the

PAGE 27

17 average mass transfer coefficient has the same form that the average heat transfer coefficient equation used by Rahman and Lallave [20]. (12) Where C int is the average concentration at the solid liquid interface, C j and C int are the jet and interface concentrations, respe ctively. The local and average Sherwood numbers are calculated according to the following expressions : (13) (14)

PAGE 28

18 Figure 2.1a Confined liquid jet impingement between a rotating disk and an impingement plate, two dimensional schematic. Figure 2.1b Confined liquid jet impingement between a rotating disk and an im pingement plate three dimensional schematic

PAGE 29

19 2.2 Numerical Simulation In calculating the numerical computation, a few conditions have to be met which include the continuity equation (1), momentum, mass transport, and ion flux equations (2 6), and boundary conditions (7 11). The above equations were solved using the Newton Raphson method through a finite element program, FIDAP TM [26]. This num erical analysis method helped to accommodate the non linearity of the velocity and concentration computations. The finite element analysis was done using four node quadrilateral elements. Even though temperature did not play a big role in this simulation, an approximate value close to the room temperature and inlet velocity was assigned at the jet nozzle which corresponds to several Reynolds numbers. In addition, the velocity, pressure, and concentration were factored into the computations of each element; taking into account the boundary condition s for the electrolyte concentration at the jet nozzle. To enhance the accuracy of the numerical model the mesh elements of the electrolyte region close to the solid interface were smaller than those above in the bu lk region. Since, it is an ele ctrolyte used in the simulation; the electrochemical system is best used in a controlled system of etching. The one electron model as seen in equation (15) was used ibution at the spinning disk (cathode) as presented by Moreno et al. [6]. (15) An additional assumption made as part of this numerical study includes the absence of chemical reaction in the bulk fluid. The specie s of electrolyte in the system are assumed to be independent of one another in the fluid and therefore the system is uncoupled for the simulation. This uncoupling implies that the cathodic reaction of the

PAGE 30

20 rotating disk is independent of the flow or diffusi on of the fluid and because of this assumption, the etch rate or chemical reaction can be ignored in the analysis. The properties of the following electrolytes (NaOH), K 3 [Fe(CN) 6 ], and HCl, were obtained from Moreno et al.[6], Sara et al. [16], Quiroz et a l.[14], Guggenheim [21] and Fary [22] For this simulation, the Soret effect is negligible therefore, the flow was assumed to have only a mass transfer by convection and a mass transfer by diffusion which is as a result of a concentration gradient which c (16) During the iteration, the values begin to converge relative to their previous values and the residuals are summed up for each variable which is less that 10 6 To verify that the conservat io n of mass was met, the flow rate at the outlet was compared with the flowrate at the nozzle of the jet to make sure the ir sum is zero. The suitable number of element to be used in the simulation was determined by a n independent systematic pick A graph of the best of meshes can be seen in figure 2.3. The most accurate mesh of model shows a grid size of 20 x 500 divisions of elements in the axial (z) and radial (r) directions, respectively. Numerical results for this grid compared to the others gave almost i dentical results with an average margin error of 1.2%. The result of the electrolyte interface concentration distribution obtained from the finite element analysis is used to calculate the mass transfer coefficient, local and average Sherwood numbers.

PAGE 31

21 2.3 Re sults and Discussion The mesh used for simulation can be seen in figure 2.2 and figure 2.3 which shows the best of all meshes plotted together. Figure 2.3 facilitates the process of choosing an optimum mesh with the lowest number of percentage difference. The mesh used is the 20x500 mesh grid spacing having the smallest number of divergence when compared to the others at an average of 1.21%. The amount of grid spacing in the vertical direction was made denser under the jet nozzle to accommodate the mass tra nsport equation. The Schmidt number focused on in this study results in a thin boundary layer and for this reason, the closer the grid spacing was to the interface the smaller grids got in the horizontal direction to facilitate the transport equation of th e ions. Figure 2.2 Mesh plot for a grid spacing of 20 x 500 in the axial and radial directions.

PAGE 32

22 Figure 2.3 Dimensionless interface temperature distributions for different number of elements in r and z directions (Re j =1000, Re r =2310, =1.0, and Sc=23 15). 0 00 0 05 0 10 0 15 0 20 0 25 0 30 0 35 0 40 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Interface Concentration, C int (g/cm 3 ) Dimensionless Radial Distance, r/R NZ x NR = 10 x 280 NZ x NR = 20 x 500 NZ x NR = 30 x 290 NZ x NR = 35 x 320 NZ x NR = 40 x 340

PAGE 33

23 Figure 2. 4 plots the dimensionless radial distance, r/R versus local Sherwood number and dimensionless concentration. This figure involved analysis at jet Reynolds numbers limited to the laminar region ranging from 600 to 1500 with a spin rate of 12 5 rpm and = 1.0. Figure 2.4 shows that Sh is highest at the stagnation point and then it quickly decreases as r/R increases. The local Sherwood becomes almost a constant at r/R = 0.2 after the rapid drop but continues to decrease. This corresponds appro ximately to the boundary between the impingement dominated and mixed region. A similar behavior was reported by Arzutu et al. [13] for impinging jet on a rotating disk and by Metzger et al. [27]. The dynamics that affect the behavior of the local Sherwood number include the geometry of the system, flow factor such as the shape of the nozzle, Reynolds number, turbulence o r laminar level at the jet nozzle, jet to impinging surface gap and rotation of the disk. The plot in figure 2.4 shows the highest Reynolds number 1500 with the highest local Sherwood number at the stagnation point and continues like that to r/R = 1.0. The lower the Reynolds number, the lower the local Sherwood numbers from the stagnation point to the outer limit of r/R. This shows that an increase in velocity at the nozzle increases the mass transfer rate of the species. For the behavior of the interface c oncentration, one can see three regions which are the impingement dominated, mixed region where the jet impingement and rotational effect of the disk have equal influence on the flow and then rotational dominated region where the expansion of the fluid tak es place as r/R increases away from the center of the disk. The impingement dominated region has the slightly average positive slope until approximately r/R = 0.075, the mixed region starts with a sudden steep average positive slope up to approximately r/R = 0.18,

PAGE 34

24 and the rotational region also has a steep slope but not as much as the mixed region. The lowest Reynolds number 600 has the highest concentration at the center of the stagnation point and continues like that to r/R = 1.0 because the lower the vel ocity of the flow over the disk or lower the Reynolds number at the nozzle, the more species component interact with the rotating disk interface. Also, the velocity of the fl uid as it flows out reduces which lead s to an increase in concentration on the out er edge of the disk. Figure 2. 5 is a plot of the local Sherwood number and interface dimensionless concentration which reflect the behavior of the rotational Reynolds number, Re r as the disk rotates. The range of the rotational Reynolds is from 0 to 6007, zero being a stationary disk. It was plotted with Re j = 800, = 1.0 and Sc = 2315. This figure shows that the changes to the rotational Reynolds number do not have a significant effect on the mass transfer rate. It can be seen from the plot of the dimen sionless interface concentration, the different rotational condition depict s the existence of three regions as pointed out by Sara et al. [16]. It can further be deduced that the dimensionless concentration in figure 2.5 has an expansion region that begins when to that point, they all lie on the same curve and begin to expand thereafter; this is where the different plots of rotational Reynolds diverge from each other. As stated by Miranda and Campos [11], the velocity profile inside the mass bo undary layer explains this behavior where they are linear along the impingement and mixed regions but deviate from linearity at the expansion region. From the data collected, the lower the jet Reynolds number the more pronounced the deviation of the rotati onal Reynolds for the concentration would be. When the disk is stationary at Re r = 0, it has the highest

PAGE 35

25 concentration at the outer radius of the disk compared to when the disk is rotating. The velocity can once again be used to explain this action. An in crease in velocity as a result of the rotational speed leads to less concentration of the species on the disk. Therefore, the increment of spinning rate or rotational Reynolds number (Re r ) will decrease the dimensionless concentration, ( ) as seen in figur e 2.5. The distance between the nozzle and the rotating disk is simulated at different heights. Figure 2. 6 shows the result of this action on the local Sherwood number and dimensionless concentration over the dimensionless radial distance for = 0.5 to 2 0. The conditions applied to the simulation include Re j = 1500 and Re r = 2310. From the data, the highest dimensionless height = 2.0 has the higher mass transfer rate than when = 0.5 at the center of the disk, but towards the end of the disk, = 0.5 h as a higher mass transfer rate than when it is 2.0. This occurs because of the difference in the length of their potential core and the characteristics of the jet. The graph shows that an increment of the dimensionless height ( ) will cause the species co ncentration on the disk to increase along the dimensionless radial distance (r/R). The rotation dominated region on the concentration data begins at a point that corresponds with proportionality to the dimensionless height ( ) at the dimensionless radial distance of r/R 0.2. The local Sherwood number shows the same behavior at figure 2. 4 and 2. 5 but as the dimensionless height increases, the local Sherwood number increases for each radius in the expansion region. The axis of the disk has the highest local Sherwood value which decreases rapidly which is as a result of the increase in thickness of the mass boundary layer in the mixed

PAGE 36

26 region. As the flow begins to expand, a minimum value of local Sherwood number is reached. Figure 2 .4 Local Sherwood number and dimensionless concentration for different jet Reynolds numbers ( =1.0, Re r =2310, nickel disk, and Sc=2315) 0 50 100 150 200 250 300 350 400 0 500 1000 1500 2000 2500 3000 3500 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Dimensionless Concentration, Q (C int /C j ) Local Sherwood Number, Sh Dimensionless Radial Distance (r/R) Sh, Re = 650 Sh, Re = 800 Sh, Re = 1000 Sh, Re = 1250 Sh, Re = 1500 Q, Re = 750 Q, Re = 800 Q, Re = 1000 Q, Re = 1250 Q, Re = 1500 Sh, Re j = 650 Sh, Re j = 800 j Sh, Re j = 1000 j Sh, Re j = 1250 j Sh, Re j = 1500 Q, Re j = 650 Q, Re j = 800 j Q Re j = 1000 j Q Re j = 1250 j Q Re j = 1500

PAGE 37

27 F ig ure 2 .5 Local Sherwood number and dimensionless concentration for different rotational Reynolds numbers ( =1.0, nickel disk, Re j =800, and Sc=2315) 0 50 100 150 200 250 300 0 130 260 390 520 650 780 910 1040 1170 1300 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Dimensionless Concentration, Q (C int /C j ) Local Sherwood Number, Sh Dimensionless Radial Distance, (r/R) 0 231 0 415 8 508 2 600 6 c 0 c 231 0 c 415 8 c 508 2 c 600 6 Q, Re r = 0 Q, Re r = 2310 j Q Re r = 4159 j Q Re r = 5083 Q, Re r = 6007 Sh Re r = 0 Sh Re r = 2310 Sh Re r = 4159 Sh Re r = 5083 Sh Re r = 6007

PAGE 38

28 Fig ure 2 .6 Local Sherwood number and dimensionless concentration for different dimensionless heights (Re j =1500, Re r =2310, and Sc=2315). 0 50 100 150 200 250 300 350 0 500 1000 1500 2000 2500 3000 3500 4000 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Dimensionless Concentration, Q (C int /C j ) Local Sherwood Number, Sh Dimensionless Radial Distance (r/R) Sh, = 0 5 Sh, = 0 75 Sh, = 1 0 Sh, = 1 5 Sh, = 2 0 H/d = 0 5 c H/d = 0 75 c H/d = 1 0 c H/d = 1 5 c H/d = 2 0 c Sh = 0 5 Sh = 0 75 Sh = 1 0 Sh = 1 5 Sh = 2 0 Q = 0 5 Q = 0 75 Q = 1 0 Q = 1 5 Q = 2 0 `

PAGE 39

29 Figure 2 .7 Average Sherwood numbers with jet Reynolds numbers at various rotational Reynolds numbers ( =1.0, nickel disk, and ferricyanide electrolyte and Sc=2315). 30 32 34 36 38 40 42 44 46 48 50 0 2000 4000 6000 Average Sherwood Number, Sh avg Rotational Reynolds, Re r 650 J 800 J 1000 J 1250 1500 Re j = 650 Re j = 800 Re j = 1000 Re j = 1250 Re j = 1500

PAGE 40

30 In figure 2. 7, the average Sherwood number was plot ted for different values of jet Reynolds at increases with a relatively small difference when the rotational speed is increased which points out the fact that it has little effect on the outcome of the average Sherwood number. The result of the average Sherwood number shows that the effect of the mass transfer influenced by the rotational Reynolds is relatively trivial compared to the influence by the jet Reynolds. This shows that the impingement on the disk dominates the flow of the fluid with the spin rates that were used for the simulations and that the critical velocity of the rotational speed was not attained. Figure 2. 7 also shows that the jet Reynolds greatly affects the results of the Sh avg The results obtained in figu re 2. 7 are similar to those of previous works. It is quite obvious that the three regions of flow previously mentioned can no longer be observed because the curves are smoother since average Sherwood number is now cumulative, and the rapid changes are att enuated by the sum of the previous values. Figure 2. 8 shows the investigation of how affects Sh avg for where The length of the potential core has an effect on the local Sherwood and as a result it has an inf luence on the average Sherwood number because as increases, Sh avg decreases. Another factor causing the decrease in Sh avg is the increased decay in average velocity as height of the nozzle from the rotating disk increases. As the nozzle to target spacin g increases, there are more instances where there is mixing of induced turbulence occurs and the fluid does not expand as much as when the spacing is smaller. W ith the increasing distance with the nozzle of the jet, a large portion of the

PAGE 41

31 disk will stay i nside the low velocity region of the jet. Therefore, the mass transfer rate will decrease with an increasing distance from the nozzle of the jet. Figure 2. 9 shows the investigation of how for Schmidt numbers af fects Sh avg over at It depicts Sh avg increasing with Sc. The Schmidt number can be used to optimize the kinematic viscosity or diffusion coefficient needed for a system. It can also be interpreted as the average Sherwood number increasing with an increase in kinematic viscosity or decrease in diffusion coefficient which is suitable in simulating fluids at specific properties. The lower the Schmidt number the less the local Sherwood number over the radial direction will be and therefore lead to a decline in the average ma ss transfer rate over the disk. Figure 2. 10 is a comparison between electrolytes. These electrolytes are potassium ferricyanide (K 3 [Fe(CN) 6 ] ) being replaced with Sodium Hydroxide (NaOH) and the o ther is Hydrochloric acid (HCl). Their properties from Fary [ 22 ] and Guggenheim [ 21 ] give us Sc = 791 and 655 at 25deg C for HCl and NaOH respectively because of their much larger diffusion coefficient. The difference in Sc between K 3 [Fe(CN) 6 at 2315 an d the other two electrolytes being compared to it is very different from the ferricyanide having the highest concentration distribution followed by Hydrochloric acid and then Sodium Hydroxide. The trend seen from this figure shows that the lower the Schmi dt number, the lower the distribution of concentration.

PAGE 42

32 Figure 2.8 Average Sherwood number with jet Reynolds number at different dimensionless nozzle to target spacing (Re r =2310, and Sc=2315). 20 25 30 35 40 45 50 55 60 65 70 0 50 0 75 1 00 1 25 1 50 1 75 2 00 Average Sherwood Number, Sh avg Dimensionless Nozzle to Target Spacing, J 650 J 800 J 1000 J 1250 J 1500 Re = 650 Re = 800 Re = 1000 Re = 1250 Re = 1500

PAGE 43

33 Figure 2.9 Average Sherwood number with jet Reynolds number at different Schmidt number ( =1.15, nickel disk, ferricyanide electrolyte, and Re r =5082). 25 27 29 31 33 35 37 39 41 43 45 1700 1900 2100 2300 2500 Average Sherwood Number, Sh avg Schimdt Number, Sc J 650 J 800 J 1000 J 1250 J 1500 Re j = 650 Re j = 800 Re j = 1000 Re j = 1250

PAGE 44

34 Figure 2.10 Dimensionless concentration for different electrolytes NaOH, HCl, (Re j =650, Re r =0, and =1.0). 0 50 100 150 200 250 300 0 0 2 0 4 0 6 0 8 1 Local Sherwood Number, Sh Dimensionless Radial Distance (r/R) Conc, Ferricyanide Conc, Hydrochloric Acid Conc, Sodium Hydroxide Q Ferricyanide Q Hydrochloric Acid Q Sodium Hydroxide

PAGE 45

35 Figure 2.11 Local Sherwood number and d imensionless c oncentration over d imensionless r adial d istance for different impingement plate geometries, nickel disk with ferricyanide electrolyte (Re j =1000, Re r =5082, =1.15, and Sc=2315). 0 50 100 150 200 250 0 500 1000 1500 2000 2500 3000 0 0 2 0 4 0 6 0 8 1 Dimensionless Concenctration, Q ( C int /C j ) Local Sherwood Number, Sh Dimensionless Radial Distance, r/R Sh, Parallel Sh, Conical Sh, Concave Sh, Convex Q, Parallel Q, Conical Q, Concave Q, Convex

PAGE 46

36 The graph in fig. 2. 11 shows the distribu tion of mass transfer of local Sherwood numbers and dimensionless concentration ( ) over r/R for different confinements plates at Re j = 1000 and Sc = 2315. The change in geometries is only with the confinement plate which are conical, convex and concave sh aped relative to the rotating disk. Figure 2. 11 plot shows the three geometries being compared to the parallel confinement plate used in this study. For the range of parameters used, the values of the Sh coincide for most part of the disk except for the ra nge where the conical shaped impingement plate starts with highest local Sherwood number and the parallel begins with the lowest. The dimensionless radial distance of r/R = 0.025 is equivalent to a radius 0.035cm. When comparing a pa rallel confinement plate to a conical plate, Miranda and Campos [ 11 ] study showed that lower Reynolds and Schmidt numbers create a clear distinction of local Sherwood number results at the expansion region. At the outer edge of the disk, the mass transfer rates are still almost the same with the parallel disk still having the lowest Sherwood numbers and the convex confinement plate having the highest. The conical shape had the highest Sh avg followed by the concave with the parallel impingement plate having the lowest. For the dimensionless concentration part of the graph, the behavior is very much different. Starting with the impingement region, they all start out alike and this can be explained by the fact that they approximately have the same impingement p late shape within this region. At the region that is dominated by rotation, the interface concentration begin to behave differently and at this region the shape on the confinement plate begins to play a big role on the concentration distribution on the dis k. From the various confinement plate geometries

PAGE 47

37 that were examine d the conical shaped showed the best mass transfer rate which agrees with a previous study done by Miranda and Campos [ 11 ]. Figure 2.12 Average Sherwood number comparison with the exper imental results obtained by Arzutu et al. [1 3 ] under various jet Reynolds and Schmidt numbers (left: =1.0, Sc=2315, Re r =2310; right: ( =1.0, Re j =1000, and Re r =5082). 32 33 34 35 36 37 38 39 40 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 20 25 30 35 40 45 50 700 900 1100 1300 1500 1700 1900 2100 Schmidt Number, Sc Average Sherwood Number, Sh avg Jet Reynolds Number, Re Present results Arzutug et al. [ 8 ] Sc Present results Sc Arzutug et al. [ 8 ] rrrbrbrbrbrg rrrbrbrbr Present results 13 ] [13] [13]

PAGE 48

38 Figure 2.13 Average Sherwood number comparison with other studies within the core region for various Schmidt numbers ( =1.0, Re j =800, Re r =2310). 0 40 80 120 160 200 240 280 320 360 1700 1900 2100 2300 2500 Average Sherwood Number, Sh avg Schmidt Numbers, Sc Present Study Chin & Tsang[ 1 ] Sara[ 12 ] Wang[ 27 ]

PAGE 49

39 Figure 2.14 Comparison of predicted average Sherwood number using Equation 17 with present numerical data. 0 20 40 60 80 0 20 40 60 80 Actual Average Sherwood Number, Sh avg Predicted Average Sherwood Number, Sh avg

PAGE 50

40 Figure 2. 12 shows two different average Sherwood number comparison for a range of jet Reynolds and Schmidt numbers. The right plot shows a varying jet Reynolds number and the left shows a range of Schmidt number. This is an attempt to show how close the present result obtained comes close to the correlation gotten by Arzutu et al. [ 13 ]. The results of the plot on the left side were obtained for with Sc = 2315 at The average difference with the results from this plot was an absolute 4.9% with a maximum of 10.3%. On the right graph the comparison was done at Re j = 1000 and Re r = 5082. The average difference here was 0.6% with the highest deviation of 1% from Arzutu et al. [ 13 ]. The illustrations shown in fig. 2. 13 are used to discuss the behavior of the average Sherwood number wit hin the impingement dominated zone. Figure 2. 13 shows the average Sherwood data in the impingement zone of present study, correlations obtained by Chin and Tsang [ 3 ], Sara et al. [1 6 ], and Wang et al. [2 5 ] on a flat surface. The Sherwood number is used to show the mass transfer in a dimensionless parameter versus the Schmidt number of the electrolyte. The thicker line shows the finite element analysis results of present study. The computations involved had a jet Reynolds number (Re j =800) with a range of In this impingement zone with the parameters used, the Sherwood number were close to being proportional the square root of Re j while being proportional to the cubic root of the Sc. The average Sherwood number in the core region compared to Chin and Tsang [ 3 ], Sara et al. [ 16 ], and Wang et al. [ 25 ] shows an absolute difference that range from 1 to 17% and had an average absolute difference of 7.73%.

PAGE 51

41 A correlation for the average Sherwood number developed used the following parameters Re j Re r , and Sc as variables. In this correlation, various parameters were used and the data point employed corresponded with the electrolyte having a Sc = 2315(where =0.01275 cm 2 /s). equation [ 23 ] for a si ngle confined liquid jet impingement was kept constant as part of present numerical correlation. The least square curve fitting technique was adopted to develop the correlation and the least square fit of the corresponding logarithmic equation. The behavio r of the average Sherwood number with the various parameters determined the signs for the exponents. The correlation obtained for the present study can be seen in equation (17) and illustrated in figure 2. 14. Sh avg = 0.404 Re j 0.286 Re r 0.0074 0.714 Sc 0.33 (17) The highest absolute percentage difference between the actual Sh avg and the predicted results was 10.20% with an average absolute percentage difference of 3.89%. The data of dimensionless parameters used for the correlation of this study take in to account jet Reynolds number rotational Reynolds number, dimensionless height, Schmidt number, and geometrical confinement plates: conical, convex, and conca ve layout. The present study correlation of a liquid jet impingement on a rotating disk in a fully confined space can help in predicting the mass transfer rates during the electrolyte synthesis as a process, especially for etching processes.

PAGE 52

42 CHAPTER 3 ANALYSIS OF HEAT TRANSFER IN A TRAPEZOIDAL MICROCHANNEL 3.1 Modeling and Simulation The physical configuration of the system used in the present investigation is schematically shown in figure 3. 1. A slab of gadolinium is placed on the top of the channel and bonded with the silicon wafer in such a way that a part of heat generated in gadolinium is directly dissipated to the working fluid whereas part is conducted through the silicon structure. Neglecting the effects of inlet and outlet plenums, it was assumed that the fluid enters the channel with a uniform velocity and temperature. The applicable differential equations for the conservation of mass and momentum in the Cartesian coo rdinate system are [ 6 1 ], (1 8 ) (19 ) (20 ) (21 )

PAGE 53

43 The k governing the conservation of turbulent kinetic energy and its rate of dissipation were solved. These equations can be expressed as, (22 ) (23 ) (24 ) The empirical con stants appearing in equati ons (22) (24 ) are given by the following values, C =0.09, C 1 =1.44, C 2 k =1.3. These values hold good for high Reynolds numbers. For low Reynolds number the v alues of constants are [6 2 ], (24 a) Where, (24 b) (24 c) (24 d)

PAGE 54

44 The energy equation in the fluid region is (25 ) The equation for steady state heat conduction for gadoli nium is [ 6 3 ], (26 a) The equation for steady state he at conduction for silicon is [ 6 3 ], (26 b) To complete the physical model equations (18) (26 ) are subjected to following boundary conditions, At z=0, at fluid in let, u=0, v=0, w=w in T= T in (27 ) At z=0 on solid surfaces of silicon and gadolinium (28 ) At z=L, at fluid outlet, p=0 (29 ) At z=L, on solid surfaces of silicon and gadolinium, (30 ) At x=0, (H D)
PAGE 55

45 At x=0, 0
PAGE 56

46 Figure 3. 1 Schematic of the trapezoidal microchannel.

PAGE 57

47 The governing equations along with the boundary conditions were solved by usi ng the Galerkin finite element method. Four node quadrilateral elements were used. In each element, the velocity, pressure, and temperature fields were approximated which led to a set of equations that defined the continuum. The successive substitution alg orithm was used to solve the nonlinear system of discretized equations. An iterative procedure was used to arrive at the solution for the velocity and temperature fields. The solution was considered converged when the field values did not change from one iteration to the next by 0.05%. Figure 3. 2 shows a grid independence study carried out to determine the optimum grid size. In order to ensure that an accurate solution was obtained, the number of elements that were used to mesh the geometry had to be deem ed adequate. This was done by performing computations for several combinations of elements in all directions. The interface temperature plot was obtained. It was noted that the numerical simulation became grid independent at 18*18*90 elements. Computation with 18*18*90 elements produced results that were very close to the resu lts produced by 24*24*110 and 8*8*42 elements. The difference between the values obtained with 24*24*110 and 18*18*90 elements was 0.36 %. Therefore, 18*18*90 elements were chosen for the simulation.

PAGE 58

48 3.2 Results and Discussion For all the configurations studied the length of the microchannel (L) was kept constant at 23 mm. Magnetic field was varied from 2.5T to 10T. Rey nolds number used was between 10 00 3000. Height of the gadolinium s lab was varied between 1.5 mm to 5 mm and the depth of the channel was varied between 100 m to 300 m. The roughness of microchannel surfaces was neglected in the turbulent analysis. Figure 3.3 shows the variation of peripheral Nusselt number with dimensionless axial coordinate for different Reynolds number for magnetic field of 5T. Nusselt n umber is seen to be increasing with increase in Reynolds number. The temperature difference between fluid and solid is more at higher Reynolds number. Thus higher heat transfer coefficient is obtained at higher Reynolds number. Fluid gets heated as it pass es through the channel. The temperature difference between fluid and solid decreases as one moves along the length of the channel. Thermal boundary layer grows until fully developed flow is established. Therefore, the Nusselt number is higher at the entran ce and decreases downstream. The variation is larger at the entrance because of the rapid development of thermal boundary layer near the leading edge. Figure 3. 4 shows variation of peripheral dimensionless interface temperature for different Reynolds numbe r and different magnetic fields. The solid fluid interface temperature increases as the fluid moves downstream due to the development of thermal boundary layer starting with the entrance section as the leading edge. Interface temperature values increase wi th increase in magnetic field. It can be seen that, as Reynolds number increases, the interface temperature decreases. For low Reynolds

PAGE 59

49 number fluid remains in contact with the solid for longer time. Thus, high dimensionless interface temperature values ar e obtained at lower Reynolds number. Figure 3.2 Average dimensionless interface temperature over the dimensionless axial cm) 0 2 4 6 8 10 12 14 16 18 20 0 0 0 2 0 4 0 6 0 8 1 0 1 2 Nusselt Number, Nu Dimensionless Axial Coordinate, z/L x y z = 8 8 42 x y z = 12 12 72 x y z = 18 18 90 x y z = 24 24 110

PAGE 60

50 Figure 3.3 Variation of peripheral average Nusselt number along the channel dimensionless axial coordinate for differen t Reynolds number (Magnetic field = 5T, 0 2 4 6 8 10 12 14 16 18 0 0 0 2 0 4 0 6 0 8 1 0 1 2 Nusselt Number, Nu Dimensionless Axial Coordinate, z/L Re = 1000 Re = 1600 Re = 2400 Re = 3000

PAGE 61

51 Figure 3.4 Variation of peripheral average dimensionless interface temperature along the channel dimensionless axial coordinate for different Reynolds number and different magnetic fields (D 0 1 2 3 4 5 6 0 0 0 2 0 4 0 6 0 8 1 0 Dimensionless Interface Temperature, Dimensionless Axial Coordiate, z/L 2 5 T, Re = 1600 2 5 T, Re = 2400 2 5 T, Re = 3000 5 0 T, Re = 1600 5 0 T, Re = 2400 5 0 T, Re = 3000 10 .T, Re = 1600 10 .T, Re = 2400 10 .T, Re = 3000

PAGE 62

52 Figure 3.5 Variation of Nusselt number along the channel dimensionless axial cm) 0 2 4 6 8 10 12 14 16 18 20 0 0 0 2 0 4 0 6 0 8 1 0 1 2 Nusselt Number, Nu Dimensionless Axial Coordinate, z/L 5 T, Re = 1600 5 T, Re = 2400 5 T, Re = 3000 10 T, Re = 1600 10 T, Re = 2400 10 T, Re = 3000

PAGE 63

53 Figure 3. 5 shows variation of Nusselt number for different magnetic fields for Reynolds number of 1600, 2400 and 3000. Nusselt number at a particular cross section in the channel remains almost the same for different magnetic fields. Figure 3. 6 shows variation of dimensionless interface temperature along the lengt h of the channel for different thickness of magnetic slab. Reynolds number of fluid is 1600 and magnetic field is 5T. As shown in figure 1, the slab of magnetic material is placed on top of the microchannel. As thickness of the slab increases, more heat is generated in the magnetic material for the same magnetic field. The part of generated heat is directly dissipated to the working fluid from gadolinium whereas; part is conducted through the silicon structure and reaches the working fluid. It can be seen t hat interface temperature values increase with increase in slab thickness. It was found that Nusselt number at a particular cross section in the channel remains almost the same for different thickness of magnetic material slab. Figure 3. 7 shows the dimensi onless axial coordinate distribution of the Nusselt number for different channel depth and constant inlet velocity whose combined effect changes the Reynolds number. In all these plots, the local Nusselt number is large near the entrance and decreases down stream due to the development of thermal boundary channel depth over the entire

PAGE 64

54 Figure 3.6 Variation of peripheral average dimensionless interface temperature along the channel dimensionless a xial coordinate for different thickness of the magnetic slab 0 0 0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 0 0 0 2 0 4 0 6 0 8 1 0 Dimensionless Interface Temperature, Dimensionless Axial Coordinate, z/L Re = 1600 b = 0 05 mm Re = 1600 b = 1 5 mm Re = 1600 b = 2 5 mm Re = 1600 b = 5 mm

PAGE 65

55 Figure 3.7 Variation of Nusselt number along the channel dimensionless axial coordinate for different depths of the channel (Magnetic fi eld =5T, Constant velocity ) 0 2 4 6 8 10 12 14 16 18 20 0 0 0 2 0 4 0 6 0 8 1 0 Nusselt Number, Nu Dimensionless Axial Coordinate, z/L D = 100 m D = 150 m D = 200 m D = 250 m D = 300 m

PAGE 66

56 Figure 3.8 shows the variation of the total average dimensionless interface temperature of the system for different Reynolds number and different channel depths for a magnetic field of 5T. It can be seen that as the Reynolds number increases, the average temperature decreases. A faster moving fluid carries heat at the faster rate, presenting lower values of average dimensionless interface temperature. For the same Reynolds number, as the depth of the channel increases, average temperature decreases. Figure 3.8 Average dimensionless interface temperature numbers with Reynolds numbers at various channel depths (Magnetic field =5T, 1000 < Re < 3000) 0 0 0 5 1 0 1 5 2 0 2 5 3 0 750 1250 1750 2250 2750 3250 Average Dimensionless Interface Temperature, avg Reynolds Number, Re D = 161 m D = 400 m D = 1820 m

PAGE 67

57 Figure 3.9 Variation of Nusselt number over the dimensionless axial coord inate for L=2.3 cm) 0 2 4 6 8 10 12 14 0 0 0 2 0 4 0 6 0 8 1 0 Nusselt Number, Nu Dimensioless Axial Coordinate, z/L S = 2 7 mm S = 2 8 mm S = 2 9 mm S = 3 0 mm

PAGE 68

58 Figure 3.9 shows variation of Nusselt number along the length of the channel for different spacing between the channels. The results show that increasin g the solid path decreases the local Nusselt number along the channel degrading the thermal performance of the heat sink. The temperature gradient in the solid increases and the average solid temperature is slightly increased. Figure 3. 10 shows the compa rison between the standard convection correlation and the present simulation model. Nusselt number for laminar flow in a smooth pipe is calculated by [ 6 4 ], (42 ) Nusselt number for turbulent flow in a pipe i s calculated by [ 6 4 ], (43 ) The values of average Nusselt number for a circular channel with D h =154 were compared to that of the standard convection correlation for a trapezoidal channel with D h =154 compared to those for the trapezoidal channel, there was a difference of 2 .23 % to 6 .52 % between the simulation results and the correlation results. Figu re 3.11 shows variation of dimensionless pressure difference between inlet and outlet of the channel for different Reynolds numbers. It can be seen that the value of dimensionless pressure difference between the inlet and outlet of the channel increases as Reynolds number increases. This is expected because the velocity of the flow increases with Reynolds number. High velocity fluid creates higher pressure difference between inlet and outlet. For the same Reynolds number, as the depth of the channel increas es,

PAGE 69

59 velocity of the flow decreases. This results in lower values of dimensionless pressure difference between inlet and outlet of the channel. Figure 3.10 Comparison between simulation and standard convection relation 0 1 2 3 4 5 6 500 1000 1500 2000 2500 3000 3500 Average Nusselt Number, Nu avg Reynolds Number, Re Simulation Standard Convection Correlation [ 66 ]

PAGE 70

60 Figure 3.11 Variation of dimensionless pressure difference between inlet and outlet of the channel with Reynolds number (Magnetic field = 5T, L=2.3 cm) 0 2 4 6 8 10 12 14 800 1300 1800 2300 2800 3300 d Reynolds Number, Re D = 100 m D = 150 m D = 200 m D = 250 m

PAGE 71

61 Figure 3.12 Variation of the Nusselt numbers for different working fluids ( Magnetic 0 2 4 6 8 10 12 14 0 00 0 20 0 40 0 60 0 80 1 00 1 20 Nusselt Number, Nu Dimensionless Axial Coordinate, z/L Water Helium FC 72

PAGE 72

62 Figure 3. 12 shows variation of average Nusselt number along the dimensionless axial coordinate of the channel for different working fluids. Thermal conductivity of water (~ 0.6 W/m K) is higher than that of heliu m (~ 0.15 W/m K) and FC 72 (~ 0.057 W/m K). This results in better Nusselt number values for water as compared to helium and FC 72. Figure 3.13 shows variation of dimensionless pumping power required to pass the fluid through the channel for different Rey nolds numbers. Pumping power is calculated from volumetric flow rate and pressure difference between inlet and outlet of the channel. As Reynolds number of fluid increases, the volumetric flow rate and dimensionless pressure difference increases. For the s ame Reynolds number, as the depth of the channel increases, velocity of the flow decreases. Thus, fluid flowing at a higher velocity requires more pumping power than fluid flowing at a lower velocity. Figure 3.14 shows two different data of average Nusselt number comparison for a range of jet Reynolds. This is an attempt to show how close results of simulation from the present study come close to the experimental data gotten by Wu and Cheng [ 38 ]. The results of the plot were obtained for The average difference between the results from this plot was 7.17% with a maximum of 13.32%.

PAGE 73

63 Figure 3.13 Variation of dimensionless pumping power for different Reynolds numbers (Magnetic field = 5T, L=2.3 cm) 0 0 E+ 00 5 0 E+ 05 1 0 E+ 06 1 5 E+ 06 2 0 E+ 06 2 5 E+ 06 3 0 E+ 06 750 1250 1750 2250 2750 3250 Dimensionless Pumping Power, D p Reynolds Number, Re D = 100 m D = 150 m D = 200 m D = 250 m

PAGE 74

64 F igure 3.14 Average Nusselt number comparison with the experimental results obtained by Wu and Chen [ 3 8] under various jet (Magnetic field = 5T, 40 < Re < 200, 0 0 3 0 6 0 9 1 2 1 5 1 8 2 1 0 50 100 150 200 250 Average Nusselt Number, Nu avg Reynolds Number, Re Simulation Wu & Chen [ 8 ]

PAGE 75

65 CHAPTER 4 CONCLUSION Analysis of impinging jet on a rotating disk wa s performed. The parameters utilized include Reynolds number, nozzle height to diameter ratio, rotational speed, geometry, and fluid property by various Schmidt numbers. The CFD simulation presented here could be a great tool in understanding the character of a flow in engineering applications involving jet impingement especially for in etching processes. The behavior of local and average mass transfer through the dimensionless parameter Sherwood was investigated using finite element analysis. The conclusi on of this investigation is that the local Sherwood number decreases with an increasing radius of a rotating or stationary disk which is also the rate of mass transfer decreasing towards the edge of the disk. An increase in rotational speed of the disk or Reynolds number at the jet nozzle will lead to an increase in mass transfer rate but the jet Reynolds has more of an impact. Therefore the results from the investigation for a low rotational speed of a rotating disk can be approximately equivalent to that of a stationary disk. Also, with the Reynolds numbers been dealt with, an increase in the nozzle to target spacing will reduce the mass transfer rate of the species. One of the most important engineering applications that this study can lend itself is to w et process equipments and the analysis from this study can be used in design when trying to determine etching rates.

PAGE 76

66 For the microchannel, the simulation was performed by varying the channel aspect ratio, Reynolds number, heat generation rate and spacing between channels. At a smaller flow rate outlet temperature increased as the low velocity fluid remained in contact with the solid for longer time. Heat transfer coefficient and Nusselt number at a particular cross section in the channel remains almost t he same for different heat generation rates. The peripheral average heat transfer coefficient and Nusselt number decreases along the length of the channel due to the development of thermal boundary layer. Large variation in the Nusselt number near the entr ance can be attributed to large growth rate of thermal boundary layer near the leading edge. It is seen that the temperature in the channel drops down as the hydraulic diameter decreases. For the same channel, the maximum temperature decreases as the Reyno lds number increases. The pressure drop in the channel increases as the Reynolds number increases. It is also seen that, as the Reynolds number increases, the power required for pumping the fluid through the channel increases. Nusselt number increases as t he depth of the channel is increased. For the same channel, Nusselt number increases with Reynolds number.

PAGE 77

67 REFERENCES [1] 104. [2] V Transfer 21 (1978) 1175 1184. [3] Journa l of the Electrochemical Soc. Electrochemical Science and Technology 125 (9) (1978) 1461 1470. [4] Journal of the Electrochemical Society 134 (2) (1987) 294 299. [5] Journal of the Electrochemical Society 138 (1991) 2643 2650.

PAGE 78

68 [6] O.A. Moreno, Impinging Jet Confined between IBM J. Res. Develop. 37 ( 2) ( 1993) 143 154. [7] 201. [8] otating Circular Cylinders 41 (1998) 3441 3450. [9] International Journal of Heat and Mass Transfer 42 (199 9) 762 776. [10] M. Chen, R. Chalupa, A. C. West, V. Modi, Schmidt Mass Transfer in a Transfer 43 (2000) 3907 3915. [11] Conical Wall 1284.

PAGE 79

69 [12] C.F. Oduoza Electrochemical Mass Transfer at a Heated Electrode in a Vertical 928. [13] M. E. Arzutu International Communications in Heat and Mass Transfer 32 (2005) 842 854. [14] M.A. Quiroz, U.A. Martinez Huitle and C.A. Martinez Journal Mex. Chem. Soc 49 (3) (2005) 279 283. [15] mass transfer cont rolled processes at the interface between two immiscible liquids (2007) 10 16. [16] International Communications in Heat and Mass Transfer 35 (2008) 289 298.

PAGE 80

70 [17] S. K. Hong, D. H. Lee and H. H. Cho concave surface in rotating jet impingement Journal of Mechanical Science and Technology 22 (2008) 1952 1958 [18] Transfer of Rotating Impingement Jet Applied Thermal Engineering 29 (2009) 2914 2920. [19] Journal of Heat and Fluid Flow 28 (2007) 7 20 734 [20] Heat Transfer from a Spinning Disk during Semi Confined Axial Impingement from a Rotating Nozzle International Journal of Heat and Mass Transfer 51 (2008) 4400 4414. [21] E.A. Guggenheim The Diffusion Coefficient of Sodium Chloride Dept. of Chemistry, The University, Reading 1 (1954) 1048 1049. [22] of Paper Chemistry, Appleton, Wisconsin Doctor's Dissertation, January (1966) 73 74

PAGE 81

71 [23] Academic Press, New York, Advances in Heat Transfer 13 (1977) 1 60. [24] an Impinging Round Jet Journ al of Heat Transfer 108 (1986) 357 364. [25] X.S. Wang, Z. Dagan, and L. Impinging Jet and a Solid Surface with Non uniform Wall Temperature or Wall Heat Flux 2. Solution for the Boundary Layer Region Int ernatio nal Journal Heat Mass Transfer 32 (1989) 1361. [26] FIDAP Theoretical Manual Fluid Dynamics International, Inc., Evanston, IL, (1991). [27] Measurement of Local Heat Transfer on a Rotating Disk wi th Jet impingement Turbomachinery 113 (1991) 52 59. [28] pp. 1 17, pp. 595 600.

PAGE 82

72 [29] Leveque Problem for Mass T ransfer in Swirling Flows in the Entrance Region of a Cylindrical Section Doklady Physics 47(9) (2002) 685 689. Translated from Doklady Akademii Nauk 386 (1) (2002) 51 55. [30] Ad iabatic Wall International Journal of Heat and Mass Transfer 46 (2003) 2947 2955. [31] P.Y. Wu and W.A. Little in very fine channels used for microminiature Joule Tho Cryogenics 24 ( 1983) 273 277. [32] J.C. Harley Y. Hu ang, H.H. Bau and J.N. Zewel Journal of Fluid Mechanic s 284 (1995) 257 274. [33] K. Chen and Y. Wu in miniature thermal conductivity de t 79 (2000) 211 218. [34] W. Qu, G. M. Mala and D. Lee Heat transfer for flow in trapezoidal silicon microchannels Jo urnal of Heat and Mass Transfer 21 (2000) 3925 36.

PAGE 83

73 [35] M.M. Rahman International Communications in Heat and Mass Transfe r 27 (1) (2000) 495 506. [36] 4 5 (2002) 5133 5141 [37] dimensional heat transfer in micro 3973 3985 [38] sfer in Heat and Mass Transfer 46 (2003) 2547 2556 [39] H.Y. Wu and P. Cheng, rnational Jo urnal of Heat and Mass Transfer 46 (2003) 2519 2525. [40] dimensional analysis of heat transfer in a micro Transfer 47 (2004) 4215 4231

PAGE 84

74 [41] Cryogenics 44 (2004) 301 307 [42] W. Owhaib and B. Palm phase convecti ve ntal Thermal and Fluid Sciences 28 (2004) 105 110. [43] H.Y. Wu and P. Cheng urnal of Heat and Mass Transfer 4 7 (2004) 3631 3641. [44] G.L. Morini M. Spiga and P. Tartarinic perlattices and Microstructures 35 (2004) 587 599. [45] Y. Chen and P. International Communica tions in Heat and Mass Transfer 32 (2005) 175 183 [46] 1704

PAGE 85

75 [47] B. Heat and Mass Transfer 32 (2005) 1211 1220 [48] sfer in micro International Journal of Heat and Mass Transfer 48 (2005) 5580 5601 [49] L. Zhuo, T. Wen Quan and H. Ya convective heat transfer in micro channel with non circular cross International Journal of Thermal Sciences 45 (2006) 1140 1148 [50] Thermal Engineering 27 (2007) 2803 2814 [51] 1101 1107

PAGE 86

76 [52] er in circular Transfer 44 (2008) 463 472 [53] nanofluids flow in 1221 1232 [54] 5804 5810 [55] geomet International Journal of Thermal Sciences 48 (2009) 1607 1618 [56] tional Journal of Heat and Mass Transfer 52 (2009) 260 270

PAGE 87

77 [57] dimensional numerical simulation Communications in Heat and Mass Transfer 36 (2009) 917 920 [58] A.J. DeGregoria, L.J. Feuling, J.F. Laatsch, J.R. Rowe J.R. Trueblood and A.A. Wang Cryogeni c Engineering 37 (1992) 875 882. [59] C. Zimm, A. Jastrab, A. Sternbe rg, V. Pecharsky, K. Gschneidner, M. Osborne and I. room temperature 43 (1998) 1759 1766. [60] V.K. Pecharsky and K.A. t and magnetic gnetism and Magnetic Materials 200 (1999) 44 56. [61] K.K. Ambatipudi and M.M. Numerical Heat Transfer 37 (A) (2000) 711 731. [62] Hwang C.B. and Li n C.A. urnal of Heat and Mass Transfer 42 (2000) 3217 3230.

PAGE 88

78 [63] M.N. Ozisik Heat Conduction 2 nd edition Wiley (1993) 403 420. [64] A. Bejan Convection Heat Transfer 2 nd edition Interscience (1994) 797 857

PAGE 89

79 APPENDICES

PAGE 90

80 A ppendix A: FIDAP Code for Analysis of Mass Transfer by Jet Im p ingement TITLE( ) JET IMPINGMENT ON ROTATING DISK R1550/W13.09/FLUX FI GEN( ELEM = 1, POIN = 1, CURV = 1, SURF = 1 NODE = 0, MEDG = 1, MLOO = 1, MFAC = 1, BEDG = 1, SPAV = 1, MSHE = 1, MSOL = 1, COOR = 1, TOLE = 0.0001 ) WINDOW(CHANGE= 1, MATRIX ) 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.00000 0 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 10.00000 10.00000 7.50000 7.50000 7.50000 7.50000 //ADD POINTS //POINTS 1,2,3,4,5,6 POINT( ADD, COOR ) 0, 0 0.01, 0 0.16, 0 0.16, 0.075 0. 16, 1.5 0.16, 1.85 0.01, 1.85 0, 1.85 0, 1.5 0, 0.075 0.01, 0.075 0.01, 1.5 0.01, 1.5 //CONNECT POINTS WITH LINES //LINES 1,2,3,4,5,6 POINT( SELE, ID ) 1 2 3 4 5 6 7 8 9 10 1 CURVE( ADD LINE ) POINT( SELE, ID ) 2 11 12 7 CURVE( ADD, LINE ) POINT( SELE, ID ) 12

PAGE 91

81 Appendix A : (Continued) 9 CURVE( ADD, LINE ) //USE CORNER POINTS TO MAKE SURFACE // POINT( SELE, ID = 1 ) POINT( SELE, ID = 3 ) POINT( SELE, ID = 8 ) POINT( SELE, ID = 6 ) SURFACE( ADD, POIN, ROWW = 2, NOAD ) //CREATE MESH EDGES //CREATE MESH EDGES //MEDGE 1,2,3,4,5,6,7,8 CURVE( SELE, ID = 1 ) MEDGE( ADD, SUCC, INTE = 10, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 2 ) MEDGE( ADD, LSTF, INTE = 20, RATI = 4, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 3 ) MEDGE( ADD, SUCC, INTE = 30, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 4 ) MEDGE( ADD, SUCC, INTE = 460, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 5 ) MEDGE( ADD, SUCC, INTE = 10, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 6 ) MEDGE( ADD, FRST, INTE = 20, RATI = 4, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 7 ) MEDGE( ADD, SUCC, INTE = 10, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 8 ) MEDGE( ADD, SUCC, INTE = 10, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 9 ) MEDGE( ADD, SUCC, INTE = 460, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 10 ) MEDGE( ADD, SUCC, INTE = 30, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 11 ) MEDGE( ADD, SUCC, INTE = 30, RATI = 0, 2RAT = 0, PCEN = 0 ) CU RVE( SELE, ID = 12 ) MEDGE( ADD, SUCC, INTE = 460, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 13 ) MEDGE( ADD, SUCC, INTE = 10, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 14 ) MEDGE( ADD, SUCC, INTE = 10, RATI = 0, 2RAT = 0, PCEN = 0 ) //MAKE A LOOP OUT THE LINES //LOOP 1 CURVE( SELE, ID ) 1 11 12 14 9 10 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2 ) //LOOP 2 CURVE( SELE, ID )

PAGE 92

82 Appendix A: (Continued) 14 13 7 8 MLOOP( ADD, MAP, VISI, NOSH EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) //LOOP 3 CURVE( SELE, ID ) 2 3 4 5 6 13 12 11 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 3, EDG3 = 1, EDG4 = 3 ) //ADD A FACE //FACE 1 SURFACE( SELE, ID = 1 ) MLOOP( SELE, ID = 1 ) MFACE( ADD ) //FACE 2 SURFACE( SELE, ID = 1 ) MLOOP( SELE, ID = 2 ) MFACE( ADD ) //FACE 3 SURFACE( SELE, ID = 1 ) MLOOP( SELE, ID = 3 ) MFACE( ADD ) //ADD MESH //MESH 1 MFACE( SELE, ID = 1 ) ELEMENT( SETD, QUAD, NODE = 4 ) MFACE( MESH, MAP, NOSM, ENTI = "n ickel" ) //MESH 2 MFACE( SELE, ID = 2 ) ELEMENT( SETD, QUAD, NODE = 4 ) MFACE( MESH, MAP, NOSM, ENTI = "water" ) //MESH 3 MFACE( SELE, ID = 3 ) ELEMENT( SETD, QUAD, NODE = 4 ) MFACE( MESH, MAP, NOSM, ENTI = "water" ) //MESH MAP ELEMENT ID // ELEMENT( SETD, EDGE, NODE = 2 ) MEDGE( SELE, ID = 1 ) MEDGE( MESH, MAP, ENTI = "outside" ) MEDGE( SELE, ID = 2 ) MEDGE( MESH, MAP, ENTI = "axis" ) MEDGE( SELE, ID = 3 ) MEDGE( MESH, MAP, ENTI = "inflow" ) MEDGE( SELE, ID = 4 )

PAGE 93

83 Appendix A: (Continued) MEDGE( SELE, ID = 5 ) MEDGE( MESH, MAP, ENTI = "stationary disk" ) MEDGE( SELE, ID = 6 ) MEDGE( SELE, ID = 7 ) MEDGE( MESH, MAP, ENTI = "wall" ) MEDGE( SELE, ID = 8 ) MEDGE( MESH, MAP, ENTI = "outflow" ) MEDGE( SELE, ID = 9 ) MEDGE( SELE, ID = 10 ) MEDGE( MESH, MAP, ENTI = "bottom" ) MEDGE( SELE, ID = 11 ) MEDGE( SELE, ID = 12 ) MEDGE( MESH, MAP, ENTI = "interface" ) END( ) FIPREP( ) //FLUID AND SOLID PROPERTIES //PROPERTIES OF FLUID @ 25 deg Celcius DENSITY( ADD, SET = "water", CONS = 1.085 ) CONDUCTIVITY( ADD, SET = "wat er", CONS = 0.001434034 ) VISCOSITY( ADD, SET = "water", CONS = 0.013832 ) SPECIFICHEAT( ADD, SET = "water", CONS = 0.999521 ) SURFACETENSION( ADD, SET = "water", CONS = 72 ) //PROPERTIES OF SOLID DENSITY( ADD, SET = "nickel", CONS = 8.88 ) CONDUCTIVITY( A DD, SET = "nickel", CONS = 0.144979459 ) SPECIFICHEAT( ADD, SET = "nickel", CONS = 0.109869112 ) //DEFININING ENTITIES ENTITY( ADD, NAME = "outside", PLOT ) ENTITY( ADD, NAME = "axis", PLOT ) ENTITY( ADD, NAME = "inflow", PLOT ) ENTITY( ADD, NAME = "statio nary disk", PLOT ) ENTITY( ADD, NAME = "wall", PLOT ) ENTITY( ADD, NAME = "outflow", PLOT ) ENTITY( ADD, NAME = "bottom", PLOT ) ENTITY( ADD, NAME = "interface", ESPE = 1, ATTA = "water", NATT = "nickel" ) ENTITY( ADD, NAME = "water", FLUI ) ENTITY( ADD, N AME = "nickel", SOLI ) //VELOCITY BOUNDARY CONDITIONS BCNODE( ADD, URC, ENTI = "axis", ZERO ) BCNODE( ADD, URC, ENTI = "inflow", ZERO ) BCNODE( ADD, UZC, ENTI = "inflow", CONS = 127.48 ) BCNODE( ADD, VELO, ZERO, ENTI = "stationary disk" ) BCNODE( ADD, VELO ZERO, ENTI = "wall" ) BCNODE( ADD, VELO, ZERO, ENTI = "bottom" ) BCNODE( ADD, VELO, ZERO, ENTI = "interface" ) BCNODE( ADD, VELO, ZERO, ENTI = "outside" ) /DETERMINES THE CONCENTRATION OF THE ELECTROLYTE AT THE INFLOW BCNODE( SPEC = 1, CONS = 0.07734, EN TI = "inflow" ) //THERMAL BOUNDARY CONDITIONS BCNODE( ADD, TEMP, CONS = 20, ENTI = "inflow" ) /BCFLUX( ADD, HEAT, CONS = 2.9855, ENTI = "bottom" )

PAGE 94

84 Appendix A: (Continued) //MASS FLUX BCFLUX( ADD, SPEC = 1, ENTI = "interface", CONS = 0.0001624 ) //THIS BOU NDARY CONDITION IS EQUIVALENT TO 1436 RPM BCNODE( UTHE, POLY = 1, ENTI = "nickel" ) 0, 13.09, 0, 1, 0 BODYFORCE( ADD, CONS, FX = 981, FY = 0, FZ = 0 ) PRESSURE( ADD, MIXE = 1e 11, DISC ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRINTOU T( ADD, NONE, BOUN ) OPTIONS( ADD, UPWI ) UPWINDING( ADD, STRE ) PROBLEM( ADD, CYLI, INCO, TRAN, LAMI, NONL, NEWT, MOME, ISOT, FIXE, SING, SPEC = 1 ) /PROBLEM( ADD, CYLI, INCO, TRAN, LAMI, NONL, NEWT, MOME, ENERGY, FIXE, SING, SPECIES = 1 ) SOLUTION( ADD, N.R. = 50, KINE = 20, VELC = 0.0001, RESC = 0.0001 ) TIMEINTEGRATION( ADD, BACK, NSTE = 301, TSTA = 0, DT = 1e 05, VARI, WIND = 1, NOFI = 10 ) POSTPROCESS( NBLO = 2 ) 1, 95, 47 95, 301, 1 CLIPPING( ADD, MINI ) 0, 0, 0, 0, 20, 0, 0, 0, 0.07734 ICNODE( ADD, URC, ENTI = "water", CONS = 10 ) ICNODE( ADD, UTHE, ENTI = "water", CONS = 5 ) //ADDED FOR MASS TRANSFER AND DIFFUSION COEFFICIENTS RESPECTIVELY //SPTRANSFER( ADD, SET = 1, CONSTANT = 0.0000002029, POWER=1. 0, TEMPERATURE ) DIFFUSIVITY( SET = 1, CONS = 5.508e 06, ISOT, TEMP ) CAPACITY( CONS = 1 ) END( ) CREATE( FISO ) RUN( FISOLV, BACK, AT = "", TIME = "NOW", COMP ) / File closed at Fri Aug 7 18:01:35 2009. / File opened for append Fri Aug 7 18:48:23 2009. FIPOST( ) TIMESTEP( STEP = 1 ) TIMESTEP( STEP = 95 ) LINE( SPEC = 1, ENTI = "interface" ) END( ) END( ) FIPOST( ) DEVICE( POST, FILE = "MESHPLOT" ) MESH( ) END( ) END( ) FIPOST( ) DEVICE( POST, FILE = "VECTPLOT" ) VECTOR( VELO, FACT = 50 )

PAGE 95

85 Append ix A: (Continued) END( ) END( ) / File closed at Sun Aug 23 19:15:27 2009. / File opened for append Mon Aug 24 01:39:20 2009. FIPOST( ) DEVICE( POST, FILE = "VECT3PLOT" ) VECTOR( VELO, FACT = 50 ) END( ) FIPOST( ) DEVICE( POST, FILE = "STRM3PLOT" ) C ONTOUR( STRE, AUTO = 40 ) END( )

PAGE 96

86 A ppendix B : FIDAP Code for Fluid Flow and Heat Transfer in a Composite Trapezoidal Microchannel TITLE( ) MICROCHANNEL FI GEN( ELEM = 1, POIN = 1, CURV = 1, SURF = 1, NODE = 0, MEDG = 1, MLOO = 1, MFAC = 1, BEDG = 1, SPA V = 1, MSHE = 1, MSOL = 1, COOR = 1, TOLE = 0.0001 ) WINDOW(CHANGE= 1, MATRIX ) 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0 .000000 1.000000 10.00000 10.00000 7.50000 7.50000 7.50000 7.50000 /^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ / COORDINATES FOR POINTS /^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^ POINT( ADD, COOR ) 0, 0, 0 0.305, 0, 0 0.305, 0.01, 0 0.305, 0.025, 0 0.305, 0.525, 0 0, 0.525, 0 0, 0.025, 0 0, 0.01, 0 0.3006, 0.01, 0 0.29, 0.025, 0 0, 0.01, 2.3 0.305, 0.025, 2.3 0, 0, 0.5 0.305, 0, 0.5 0.305, 0.01, 0.5 0.305, 0.025, 0.5 0.305, 0.525, 0.5 0, 0.525, 0.5 0, 0.025, 0.5 0, 0.01, 0.5 0.3006, 0.01, 0.5 0.29, 0.025, 0.5 0, 0, 1 0.305, 0, 1 0.305, 0.01, 1 0.305, 0.025, 1 0.305, 0.525, 1 0, 0.525, 1 0, 0.025, 1 0, 0.01, 1 0.3006, 0.01, 1 0.29, 0.025, 1 0, 0, 1.5 0.305, 0, 1.5

PAGE 97

87 Appendix B : (Continued) 0.305, 0.01, 1.5 0 .305, 0.025, 1.5 0.305, 0.525, 1.5 0, 0.525, 1. 5 0, 0.025, 1.5 0, 0.01, 1.5 0.3006, 0.01, 1.5 0.29, 0.025, 1.5 0, 0, 2 0.305, 0, 2 0.305, 0.01, 2 0.305, 0.025, 2 0.305, 0.525, 2 0, 0.525, 2 0, 0.025, 2 0, 0.01, 2 0.3006, 0.01, 2 0.29, 0.025, 2 0, 0, 2.3 0.305, 0, 2.3 0.305, 0.01, 2.3 0.305, 0.025, 2.3 0.305, 0.525, 2.3 0, 0.525, 2.3 0, 0.025, 2.3 0, 0.01, 2.3 0.3006, 0.0 1, 2.3 0.29, 0.025, 2.3 /^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ / CONNECTING POINTS WITH LINES /^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ //PART ONE /LINES 1 8 POINT( SELE, ID ) 1 2 3 4 5 6 7 8 1 CURVE( ADD, LINE ) /LINES 9 POINT( SELE, ID ) 9 3 CURVE( ADD, LINE ) /LINES 10 11 POINT( SELE, ID ) 7

PAGE 98

88 Appendix B: (Continued) 10 4 CURVE( ADD, LINE ) /LINES 12 POINT( SELE, ID ) 9 10 CURVE( ADD, LINE ) /LINES 13 POINT( SELE, ID ) 8 9 CURVE( ADD, LINE ) /LINES 14 POINT( SELE, ID ) 8 11 CURVE( ADD, LINE ) /LINES 15 POINT( SELE, ID ) 4 12 CURVE( ADD, LINE ) //PART TWO /LINES 16 23 POINT( SELE, ID ) 13 14 15 16 17 18 19 20 13 CURVE( ADD, LINE ) /LINES 24 POINT( SELE, ID ) 21 15 CURVE( ADD, LINE ) /LINES 25 26 POINT( SELE, ID ) 19 22 16 CURVE( ADD, LINE ) /LINES 27 POINT( SELE, ID ) 21 22 CURVE( ADD, LINE )

PAGE 99

89 Append ix B: (Continued) /LINES 28 POINT( SELE, ID ) 20 21 CURVE( ADD, LINE ) //PART THREE /LINES 29 36 POINT( SELE, ID ) 23 24 25 26 27 28 29 30 23 CURVE( ADD, LINE ) /LINES 37 POINT( SELE, ID ) 31 25 CURVE( ADD, LINE ) /LINES 38 39 POINT( SELE, ID ) 29 32 26 CURVE( ADD, LINE ) /LINES 40 POINT( SELE, ID ) 31 32 CURVE( ADD, LINE ) /LINES 41 POINT( SELE, ID ) 30 31 CURVE( ADD, LINE ) //PART FOUR /LINES 42 49 POINT( SELE, ID ) 33 34 35 36 37 38 39 40 33 CURVE( ADD, LINE )

PAGE 100

90 Appendix B: (Continued) /LINES 50 POINT( SELE, ID ) 41 35 CURVE( ADD, LINE ) /LINES 51 POINT( SELE, ID ) 39 42 36 CURVE( ADD, LINE ) /LINES 53 POINT( SELE, ID ) 41 42 CURVE( ADD, LI NE ) /LINES 54 POINT( SELE, ID ) 40 41 CURVE( ADD, LINE ) //PART FIVE /LINES 55 62 POINT( SELE, ID ) 43 44 45 46 47 48 49 50 43 CURVE( ADD, LINE ) /LINES 63 POINT( SELE, ID ) 51 45 CURVE( ADD, LINE ) /LINES 64 POIN T( SELE, ID ) 49 52 46 CURVE( ADD, LINE ) /LINES 66 POINT( SELE, ID ) 51 52 CURVE( ADD, LINE ) /LINES 67 POINT( SELE, ID )

PAGE 101

91 Appendix B: (Continued) 50 51 CURVE( ADD, LINE ) //PART SIX /LINES 68 75 POINT( SELE, ID ) 53 54 55 56 57 58 59 60 53 CURVE( ADD, LINE ) /LINES 76 POINT( SELE, ID ) 61 55 CURVE( ADD, LINE ) /LINES 77 POINT( SELE, ID ) 59 62 56 CURVE( ADD, LINE ) /LINES 79 POINT( SELE, ID ) 61 62 CURVE( ADD, LINE ) /LINES 80 POINT( SELE, ID ) 60 61 CURVE( ADD, LINE ) /////////////////////////////////////////////////////////////////////// / //CREATING SURFACES CURVE( SELE, ID ) 1 2 3 4 5 6 7 8 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 3, EDG3 = 1, EDG4 = 3 ) CURVE( SELE, ID ) 16

PAGE 102

92 Appendix B: (Continued) 17 18 19 20 21 22 23 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 3, EDG3 = 1, EDG4 = 3 ) CURVE( SELE, ID ) 29 30 31 32 33 34 35 36 SURFACE( ADD, WIRE, EDG1 = 1, ED G2 = 3, EDG3 = 1, EDG4 = 3 ) CURVE( SELE, ID ) 42 43 44 45 46 47 48 49 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 3, EDG3 = 1, EDG4 = 3 ) CURVE( SELE, ID ) 55 56 57 58 59 60 61 62 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 3, EDG3 = 1, EDG4 = 3 ) CURVE( SELE, ID ) 68 69 70 71 72 73 74 75 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 3, EDG3 = 1, EDG4 = 3 ) /////////////////////////////////////////////////////////////////////// /// //CREATING MESH EDGES CURVE ( SELE, ID = 1 )

PAGE 103

93 Appendix B: (Continued) MEDGE( ADD, SUCC, INTE = 18, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 2 ) MEDGE( ADD, SUCC, INTE = 6, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 3 ) MEDGE( ADD, SUCC, INTE = 8, RATI = 0, 2RAT = 0, PCE N = 0 ) CURVE( SELE, ID = 4 ) MEDGE( ADD, SUCC, INTE = 4, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 5 ) MEDGE( ADD, SUCC, INTE = 18, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 6 ) MEDGE( ADD, SUCC, INTE = 4, RATI = 0, 2RAT = 0, PCEN = 0 ) CURV E( SELE, ID = 7 ) MEDGE( ADD, SUCC, INTE = 8, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 8 ) MEDGE( ADD, SUCC, INTE = 6, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 9 ) MEDGE( ADD, SUCC, INTE = 9, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 10 ) MEDGE( ADD, SUCC, INTE = 9, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 11 ) MEDGE( ADD, SUCC, INTE = 9, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 12 ) MEDGE( ADD, SUCC, INTE = 8, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 13 ) MEDG E( ADD, SUCC, INTE = 9, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 14 ) MEDGE( ADD, SUCC, INTE = 90, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, ID = 15 ) MEDGE( ADD, SUCC, INTE = 90, RATI = 0, 2RAT = 0, PCEN = 0 ) /////////////////////////////////// //////////////////////////////////// //// //CREATING LOOPS /LOOP 1 CURVE( SELE, ID ) 1 2 9 13 8 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) /LOOP 2 CURVE( SELE, ID ) 12 13 7 10 MLOOP( ADD, MAP ) /LOOP 3 CURVE( S ELE, ID ) 12 11 3

PAGE 104

94 Appendix B: (Continued) 9 MLOOP( ADD, MAP ) /LOOP 4 CURVE( SELE, ID ) 4 5 6 10 11 MLOOP( ADD, MAP, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 2 ) ///////////////////////////////////////////////////////////////// ////// ////// //CREATING FACE FOR MESH SURFACE( SELE, ID = 1 ) MLOOP( SELE, ID = 1 ) MFACE( ADD ) //CREATING FACE FOR MESH SURFACE( SELE, ID = 1 ) MLOOP( SELE, ID = 2 ) MFACE( ADD ) //CREATING FACE FOR MESH SURFACE( SELE, ID = 1 ) MLOOP( SELE, ID = 3 ) MFAC E( ADD ) //CREATING FACE FOR MESH SURFACE( SELE, ID = 1 ) MLOOP( SELE, ID = 4 ) MFACE( ADD ) /////////////////////////////////////////////////////////////////////// ///// //CREATING SOLID FOR THE MESH MFACE( SELE, ID = 1 ) CURVE( SELE, ID = 14 ) MSOLID( PRO J ) MFACE( SELE, ID = 2 ) CURVE( SELE, ID = 14 ) MSOLID( PROJ ) MFACE( SELE, ID = 3 ) CURVE( SELE, ID = 15 ) MSOLID( PROJ ) MFACE( SELE, ID = 4 ) CURVE( SELE, ID = 15 ) MSOLID( PROJ ) /////////////////////////////////////////////////////////////////////// ///// //CREATION OF THE MESH AND ASSIGNING CONTINUOUS ENTITIES MSOLID( SELE, ID = 1 ) ELEMENT( SETD, BRIC, NODE = 8 ) MSOLID( MESH, MAP, ENTI = "SILICON" ) MSOLID( SELE, ID = 2 ) ELEMEN T( SETD, BRIC, NODE = 8 ) MSOLID( MESH, MAP, ENTI = "SILICON" )

PAGE 105

95 A ppendix B : (Continued) MSOLID( SELE, ID = 3 ) ELEMENT( SETD, BRIC, NODE = 8 ) MSOLID( MESH, MAP, ENTI = "FLUID" ) MSOLID( SELE, ID = 4 ) ELEMENT( SETD, BRIC, NODE = 8 ) MSOLID( MESH, MAP, EN TI = "GADOLINIUM" ) /////////////////////////////////////////////////////////////////////// //// //ASSIGNING ENTITIES TO VARIOUS BOUNDARIES MFACE( SELE, ID = 3 ) MFACE( MESH, MAP, ENTI = "Fin" ) MFACE( SELE, ID = 15 ) MFACE( MESH, MAP, ENTI = "Fout" ) /MFAC E( SELE, ID = 12 ) /MFACE( SELE, ID = 17 ) /MFACE( MESH, MAP, ENTI = "HF" ) MFACE( SELE, ID = 8 ) MFACE( MESH, MAP, ENTI = "Fbot" ) MFACE( SELE, ID = 17 ) MFACE( MESH, MAP, ENTI = "Ftop" ) MFACE( SELE, ID = 16 ) MFACE( MESH, MAP, ENTI = "Faxis" ) MFACE( SE LE, ID = 14 ) MFACE( MESH, MAP, ENTI = "Fleft" ) MFACE( SELE, ID = 6 ) MFACE( MESH, MAP, ENTI = "Sbot" ) MFACE( SELE, ID = 7 ) MFACE( MESH, MAP, ENTI = "Saxis" ) MFACE( SELE, ID = 19 ) MFACE( MESH, MAP, ENTI = "Gaxis" ) MFACE( SELE, ID = 20 ) MFACE( MESH, MAP, ENTI = "Gtop" ) MFACE( SELE, ID = 21 ) MFACE( MESH, MAP, ENTI = "Gleft" ) MFACE( SELE, ID = 13 ) MFACE( MESH, MAP, ENTI = "Sleft1" ) MFACE( SELE, ID = 10 ) MFACE( MESH, MAP, ENTI = "Sleft2" ) MEDGE( SELE, ID = 23 ) MEDGE( MESH, MAP, ENTI = "RTedge" ) MEDGE( SELE, ID = 22 ) MEDGE( MESH, MAP, ENTI = "RBedge" ) MEDGE( SELE, ID = 24 ) MEDGE( MESH, MAP, ENTI = "LTedge" ) MEDGE( SELE, ID = 21 ) MEDGE( MESH, MAP, ENTI = "LBedge" ) END( ) FIPREP( ) //////////////////////////////////////////////////////////// /////////// //// //PROPERTY OF SILICON CONDUCTIVITY( ADD, SET = "SILICON", CONS = 0.29637, ISOT )

PAGE 106

96 A ppendix B : (Continued) DENSITY( ADD, SET = "SILICON", CONS = 2.329 ) SPECIFICHEAT( ADD, SET = "SILICON", CONS = 0.16778 ) //PROPERTY OF FLUID CONDUCTIVITY( A DD, SET = "FLUID", CONS = 0.0014435, ISOT ) DENSITY( ADD, SET = "FLUID", CONS = 0.9974 ) SPECIFICHEAT( ADD, SET = "FLUID", CONS = 0.9988 ) VISCOSITY( ADD, SET = "FLUID", CONS = 0.0098 ) //PROPERTY OF GADOLINIUM CONDUCTIVITY( ADD, SET = "GADOLINIUM", CONS = 0.0250956, ISOT ) DENSITY( ADD, SET = "GADOLINIUM", CONS = 7.895 ) SPECIFICHEAT( ADD, SET = "GADOLINIUM", CONS = 0.054971 ) /////////////////////////////////////////////////////////////////////// ///// //DEFINING ENTITIES ENTITY( ADD, NAME = "SILICON", SOL I ) ENTITY( ADD, NAME = "GADOLINIUM", SOLI ) ENTITY( ADD, NAME = "FLUID", FLUI ) ENTITY( ADD, NAME = "Fin", PLOT ) ENTITY( ADD, NAME = "Fout", PLOT ) /ENTITY( ADD, NAME = "HF", PLOT, ATTA = "FLUID", NATTA = "GADOLINIUM" ) ENTITY( ADD, NAME = "Fbot", PLOT, ATTA = "FLUID", NATT = "SILICON" ) ENTITY( ADD, NAME = "Ftop", PLOT, ATTA = "FLUID", NATT = "GADOLINIUM" ) ENTITY( ADD, NAME = "Faxis", PLOT ) ENTITY( ADD, NAME = "Fleft", PLOT, ATTA = "FLUID", NATT = "SILICON" ) ENTITY( ADD, NAME = "Sbot", PLOT ) ENTITY( ADD, NAME = "Saxis", PLOT ) ENTITY( ADD, NAME = "Gaxis", PLOT ) ENTITY( ADD, NAME = "Gtop", PLOT ) ENTITY( ADD, NAME = "Gleft", PLOT ) ENTITY( ADD, NAME = "Sleft1", PLOT ) ENTITY( ADD, NAME = "Sleft2", PLOT ) ENTITY( ADD, NAME = "RTedge", PLOT ) ENTITY( AD D, NAME = "RBedge", PLOT ) ENTITY( ADD, NAME = "LTedge", PLOT ) ENTITY( ADD, NAME = "LBedge", PLOT ) /////////////////////////////////////////////////////////////////////// ///// //INITIAL AND BOUNDARY CONDITION BCNODE( ADD, UX, ENTI = "Fin", ZERO ) BCNODE( ADD, UY, ENTI = "Fin", ZERO ) BCNODE( ADD, UZ, ENTI = "Fin", CONS = 1425.34 ) BCNODE( ADD, TEMP, ENTI = "Fin", CONS = 20 ) BCNODE( ADD, VELO, ENTI = "Fbot", ZERO ) BCNODE( ADD, VELO, ENTI = "Ftop", ZERO ) BCNODE( ADD, VELO, ENTI = "Fleft", ZERO ) BCNODE( ADD, UX, ENTI = "Faxis", ZERO ) /BCFLUX( ADD, HEAT, ENTI = "HF", CONS = 14.49 ) BCFLUX( ADD, HEAT, ENTI = "Sbot", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "Saxis", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "Gaxis", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "Gtop", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "Gleft", CONS = 0 )

PAGE 107

97 A ppendix B : (Continued) BCFLUX( ADD, HEAT, ENTI = "Sleft1", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "Sleft2", CONS = 0 ) SOURCE( ADD, HEAT, CONS = 6.080715996, ENTI = "GADOLINIUM" ) ICNODE( ADD, TEMP, CONS = 20, ENTI = "SILICON" ) ICNODE( ADD, TEMP, CONS = 20, ENTI = "GADOLINIUM" ) ICNODE( ADD, TEMP, CONS = 20, ENTI = "FLUID" ) /////////////////////////////////////////////////////////////////////// // //IF THE FLOW IT TURBULENT AND K E MODEL IS USED, ADD THE FOLLOWING //LINES OF CODES /VISCOSITY( ADD, SET = "FLUID", TWO CONS = 0.0098 ) /ICNODE( KINE, CONS = 0.003, ALL ) /ICNODE( DISS, CONS = 0.00045, ALL ) /BCNODE( KINE, CONS = 0.001, ENTI = "Fin" ) /BCNODE( DISS, CONS = 0.00045, ENTI = "Fin" ) ///////////// ////////////////////////////////////////////////////////// //// //EXECUTION COMMANDS DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, 3 D, INCO, STEA, LAMI, NONL, NEWT, MOME, ENER, FIXE, SING ) SOLUTION( ADD, SEGR = 10 PREC = 21, ACCF = 0, PPRO ) END( ) CREATE( FISO ) RUN( FISOLV, BACK, AT = "", TIME = "NOW", COMP ) END( ) FIPOST( ) PRINT( PRES, POIN, FILE = "comb.txt", SCRE ) 324 0.3006, 0.01, 0 0.301088889, 0.01, 0 0.301577778, 0.01, 0 0.30206666 7, 0.01, 0 0.302555556, 0.01, 0 0.303044444, 0.01, 0 0.303533333, 0.01, 0 0.304022222, 0.01, 0 0.304511111, 0.01, 0 0.305, 0.01, 0 0.305, 0.025, 0 0.303333333, 0.025, 0 0.301666667, 0.025, 0 0.3, 0.025, 0 0.298333333, 0.025, 0 0.296666667, 0.025, 0 0.295, 0.025, 0 0.293333333, 0.025, 0 0.291666667, 0.025, 0 0.29, 0.025, 0

PAGE 108

98 A ppendix B : (Continued) 0.291326715, 0.023126213, 0 0.29265343, 0.021252426, 0 0.293980145, 0.0193786 39, 0 0.29530686, 0.017504853, 0 0.296633575, 0.015631066, 0 0.29796029, 0.013757279, 0 0.299287005, 0.011883492, 0 0.3006, 0.01, 0.5 0.301088889, 0.01, 0.5 0.301577778, 0.01, 0.5 0.302066667, 0.01, 0.5 0.302555556, 0.01, 0.5 0.303044444, 0.01, 0.5 0.303533333, 0.01, 0.5 0.304022222, 0.01, 0.5 0.304511111, 0.01, 0.5 0.305, 0.01, 0.5 0.305, 0.025, 0.5 0.303333333, 0.025, 0.5 0.301666667, 0.025, 0.5 0.3, 0.025, 0.5 0.298333333, 0.025, 0.5 0.2966666 67, 0.025, 0.5 0.295, 0.025, 0.5 0.293333333, 0.025, 0.5 0.291666667, 0.025, 0.5 0.29, 0.025, 0.5 0.291326715, 0.023126213, 0.5 0.29265343, 0.021252426, 0.5 0.293980145, 0.019378639, 0.5 0.29530686, 0.017504853, 0.5 0.296633575, 0.015631 066, 0.5 0.29796029, 0.013757279, 0.5 0.299287005, 0.011883492, 0.5 0.3006, 0.01, 1 0.301088889, 0.01, 1 0.301577778, 0.01, 1 0.302066667, 0.01, 1 0.302555556, 0.01, 1 0.303044444, 0.01, 1 0.303533333, 0.01, 1 0.304 022222, 0.01, 1 0.304511111, 0.01, 1 0.305, 0.01, 1 0.305, 0.025, 1 0.303333333, 0.025, 1 0.301666667, 0.025, 1 0.3, 0.025, 1 0.298333333, 0.025, 1 0.296666667, 0.025, 1 0.295, 0.025, 1 0.293333333, 0.025, 1

PAGE 109

99 A ppendix B : (Continued) 0.291666667, 0.025, 1 0.29, 0.025, 1 0.291326715, 0.023126213, 1 0.29265343, 0.021252426, 1 0.293980145, 0.019378639, 1 0.29530686, 0.017504853, 1 0.296633575, 0.015631066, 1 0.29796029, 0.013757279, 1 0.299287005, 0.011883492, 1 0.3006, 0.01, 1.5 0.301088889, 0.01, 1.5 0.301577778, 0.01, 1.5 0.302066667, 0.01, 1.5 0.302555556, 0.01, 1.5 0.303044444, 0.01, 1.5 0.303533333, 0.01, 1.5 0.304022222, 0.01, 1.5 0.304511111, 0. 01, 1.5 0.305, 0.01, 1.5 0.305, 0.025, 1.5 0.303333333, 0.025, 1.5 0.301666667, 0.025, 1.5 0.3, 0.025, 1.5 0.298333333, 0.025, 1.5 0.296666667, 0.025, 1.5 0.295, 0.025, 1.5 0.293333333, 0.025, 1.5 0.291666667, 0.025, 1.5 0.29, 0.0 25, 1.5 0.291326715, 0.023126213, 1.5 0.29265343, 0.021252426, 1.5 0.293980145, 0.019378639, 1.5 0.29530686, 0.017504853, 1.5 0.296633575, 0.015631066, 1.5 0.29796029, 0.013757279, 1.5 0.299287005, 0.011883492, 1.5 0.3006, 0.01, 2 0.30 1088889, 0.01, 2 0.301577778, 0.01, 2 0.302066667, 0.01, 2 0.302555556, 0.01, 2 0.303044444, 0.01, 2 0.303533333, 0.01, 2 0.304022222, 0.01, 2 0.304511111, 0.01, 2 0.305, 0.01, 2 0.305, 0.025, 2 0.303333333, 0.025, 2 0.301666667, 0.025, 2 0.3, 0.025, 2 0.298333333, 0.025, 2 0.296666667, 0.025, 2

PAGE 110

100 A ppendix B : (Continued) 0.295, 0.025, 2 0.293333333, 0.025, 2 0.291666667, 0.025, 2 0.29, 0.025, 2 0.291326715, 0.023126213, 2 0.29265343, 0.021252426, 2 0.293980145, 0.019378639, 2 0.29530686, 0.017504853, 2 0.296633575, 0.015631066, 2 0.29796029, 0.013757279, 2 0.299287005, 0.011883492, 2 0.3006, 0.01, 2.3 0.301088889, 0.01, 2.3 0.301577778, 0 .01, 2.3 0.302066667, 0.01, 2.3 0.302555556, 0.01, 2.3 0.303044444, 0.01, 2.3 0.303533333, 0.01, 2.3 0.304022222, 0.01, 2.3 0.304511111, 0.01, 2.3 0.305, 0.01, 2.3 0.305, 0.025, 2.3 0.303333333, 0.025, 2.3 0.301666667, 0.025, 2 .3 0.3, 0.025, 2.3 0.298333333, 0.025, 2.3 0.296666667, 0.025, 2.3 0.295, 0.025, 2.3 0.293333333, 0.025, 2.3 0.291666667, 0.025, 2.3 0.29, 0.025, 2.3 0.291326715, 0.023126213, 2.3 0.29265343, 0.021252426, 2.3 0.293980145, 0.019378639, 2.3 0.29530686, 0.017504853, 2.3 0.296633575, 0.015631066, 2.3 0.29796029, 0.013757279, 2.3 0.299287005, 0.011883492, 2.3 0.3006, 0.008333333, 0 0.301088889, 0.008333333, 0 0.301577778, 0.008333333, 0 0.302066667, 0.008333333, 0 0 .302555556, 0.008333333, 0 0.303044444, 0.008333333, 0 0.303533333, 0.008333333, 0 0.304022222, 0.008333333, 0 0.304511111, 0.008333333, 0 0.305, 0.008333333, 0 0.305, 0.15, 0 0.303333333, 0.15, 0 0.301666667, 0.15, 0 0.3, 0.15, 0

PAGE 111

101 A ppendix B : (Continued) 0.298333333, 0.15, 0 0.296666667, 0.15, 0 0.295, 0.15, 0 0.293333333, 0.15, 0 0.291666667, 0.15, 0 0.257777778, 0.025, 0 0.259104493, 0.023126213, 0 0.260431208, 0.021252426, 0 0.261757923, 0.019378639, 0 0.263084638, 0.017504853, 0 0.264411353, 0.015631066, 0 0.265738068, 0.013757279, 0 0.267064783, 0.011883492, 0 0.3006, 0.008333333, 0.5 0.301088889, 0.008333333, 0.5 0.301577778, 0.008333333, 0.5 0 .302066667, 0.008333333, 0.5 0.302555556, 0.008333333, 0.5 0.303044444, 0.008333333, 0.5 0.303533333, 0.008333333, 0.5 0.304022222, 0.008333333, 0.5 0.304511111, 0.008333333, 0.5 0.305, 0.008333333, 0.5 0.305, 0.15, 0.5 0.303333333, 0.15, 0.5 0.301666667, 0.15, 0.5 0.3, 0.15, 0.5 0.298333333, 0.15, 0.5 0.296666667, 0.15, 0.5 0.295, 0.15, 0.5 0.293333333, 0.15, 0.5 0.291666667, 0.15, 0.5 0.257777778, 0.025, 0.5 0.259104493, 0.023126213, 0.5 0.260431208, 0.021252 426, 0.5 0.261757923, 0.019378639, 0.5 0.263084638, 0.017504853, 0.5 0.264411353, 0.015631066, 0.5 0.265738068, 0.013757279, 0.5 0.267064783, 0.011883492, 0.5 0.3006, 0.008333333, 1 0.301088889, 0.008333333, 1 0.301577778, 0.008333333, 1 0.302066667, 0.008333333, 1 0.302555556, 0.008333333, 1 0.303044444, 0.008333333, 1 0.303533333, 0.008333333, 1 0.304022222, 0.008333333, 1 0.304511111, 0.008333333, 1 0.305, 0.008333333, 1 0.305, 0.15, 1 0.303333333, 0.15, 1

PAGE 112

102 A ppendix B : (Continued) 0.301666667, 0.15, 1 0.3, 0.15, 1 0.298333333, 0.15, 1 0.296666667, 0.15, 1 0.295, 0.15, 1 0.293333333, 0.15, 1 0.291666667, 0.15, 1 0.257777778, 0.025, 1 0.259104493, 0.023126 213, 1 0.260431208, 0.021252426, 1 0.261757923, 0.019378639, 1 0.263084638, 0.017504853, 1 0.264411353, 0.015631066, 1 0.265738068, 0.013757279, 1 0.267064783, 0.011883492, 1 0.3006, 0.008333333, 1.5 0.301088889, 0.008333333, 1.5 0.301577778, 0.008333333, 1.5 0.302066667, 0.008333333, 1.5 0.302555556, 0.008333333, 1.5 0.303044444, 0.008333333, 1.5 0.303533333, 0.008333333, 1.5 0.304022222, 0.008333333, 1.5 0.304511111, 0.008333333, 1.5 0.305, 0.008333333, 1.5 0.305, 0.15, 1.5 0.303333333, 0.15, 1.5 0.301666667, 0.15, 1.5 0.3, 0.15, 1.5 0.298333333, 0.15, 1.5 0.296666667, 0.15, 1.5 0.295, 0.15, 1.5 0.293333333, 0.15, 1.5 0.291666667, 0.15, 1.5 0.257777778, 0.025, 1.5 0.259104493, 0 .023126213, 1.5 0.260431208, 0.021252426, 1.5 0.261757923, 0.019378639, 1.5 0.263084638, 0.017504853, 1.5 0.264411353, 0.015631066, 1.5 0.265738068, 0.013757279, 1.5 0.267064783, 0.011883492, 1.5 0.3006, 0.008333333, 2 0.301088889, 0.0083 33333, 2 0.301577778, 0.008333333, 2 0.302066667, 0.008333333, 2 0.302555556, 0.008333333, 2 0.303044444, 0.008333333, 2 0.303533333, 0.008333333, 2 0.304022222, 0.008333333, 2 0.304511111, 0.008333333, 2 0.305, 0.008333333, 2

PAGE 113

103 A ppendix B : (Continued) 0.305, 0.15, 2 0.303333333, 0.15, 2 0.301666667, 0.15, 2 0.3, 0.15, 2 0.298333333, 0.15, 2 0.296666667, 0.15, 2 0.295, 0.15, 2 0.293333333, 0.15, 2 0.291666667, 0.15, 2 0.257777 778, 0.025, 2 0.259104493, 0.023126213, 2 0.260431208, 0.021252426, 2 0.261757923, 0.019378639, 2 0.263084638, 0.017504853, 2 0.264411353, 0.015631066, 2 0.265738068, 0.013757279, 2 0.267064783, 0.011883492, 2 0.3006, 0.0083 33333, 2.3 0.301088889, 0.008333333, 2.3 0.301577778, 0.008333333, 2.3 0.302066667, 0.008333333, 2.3 0.302555556, 0.008333333, 2.3 0.303044444, 0.008333333, 2.3 0.303533333, 0.008333333, 2.3 0.304022222, 0.008333333, 2.3 0.304511111, 0.0083 33333, 2.3 0.305, 0.008333333, 2.3 0.305, 0.15, 2.3 0.303333333, 0.15, 2.3 0.301666667, 0.15, 2.3 0.3, 0.15, 2.3 0.298333333, 0.15, 2.3 0.296666667, 0.15, 2.3 0.295, 0.15, 2.3 0.293333333, 0.15, 2.3 0.291666667, 0.15, 2.3 0 .257777778, 0.025, 2.3 0.259104493, 0.023126213, 2.3 0.260431208, 0.021252426, 2.3 0.261757923, 0.019378639, 2.3 0.263084638, 0.017504853, 2.3 0.264411353, 0.015631066, 2.3 0.265738068, 0.013757279, 2.3 0.267064783, 0.011883492, 2.3 END( ) FIPOST( ) WINDOW( CHAN = 0, FRON ) CONTOUR( UX, AUTO = 50 ) CONTOUR( TEMP, AUTO = 50 ) CONTOUR( TEMP, AUTO = 25 ) CONTOUR( TEMP, AUTO = 10 ) CONTOUR( TEMP, AUTO = 15 )

PAGE 114

104 A ppendix B : (Continued) CONTOUR( TEMP, AUTO = 20 ) DEVICE( POST, FILE = "TEMPPLOT" ) CONTOUR( TEMP, AUTO = 20 ) END( )


xml version 1.0 encoding UTF-8 standalone no
record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd
leader nam 2200385Ka 4500
controlfield tag 001 002069519
005 20100422154634.0
007 cr bnu|||uuuuu
008 100422s2009 flu s 000 0 eng d
datafield ind1 8 ind2 024
subfield code a E14-SFE0003297
035
(OCoLC)608550466
040
FHM
c FHM
049
FHMM
090
TJ145 (Online)
1 100
Ojada, Ejiro Stephen.
0 245
Analysis of mass transfer by jet impingement and study of heat transfer in a trapezoidal microchannel
h [electronic resource] /
by Ejiro Stephen Ojada.
260
[Tampa, Fla] :
b University of South Florida,
2009.
500
Title from PDF of title page.
Document formatted into pages; contains 104 pages.
502
Thesis (M.S.M.E.)--University of South Florida, 2009.
504
Includes bibliographical references.
516
Text (Electronic thesis) in PDF format.
520
ABSTRACT: This thesis numerically studied mass transfer during fully confined liquid jet impingement on a rotating target disk of finite thickness and radius. The study involved laminar flow with jet Reynolds numbers from 650 to 1500. The nozzle to plate distance ratio was in the range of 0.5 to 2.0, the Schmidt number ranged from 1720 to 2513, and rotational speed was up to 325 rpm. In addition, the jet impingement to a stationary disk was also simulated for the purpose of comparison. The electrochemical fluid used was an electrolyte containing 0.005moles per liter potassium ferricyanide (K(Fe(CN)), 0.02moles per liter ferrocyanide (FeCN), and 0.5moles per liter potassium carbonate (KCO). The rate of mass transfer of this electrolyte was compared to Sodium Hydroxide (NaOH) and Hydrochloric acid (HCl) electrochemical solutions. The material of the rotating disk was made of 99.98% nickel and 0.02% of chromium, cobalt and aluminum.The rate of mass transfer was also examined for different geometrical shapes of conical, convex, and concave confinement plates over a spinning disk. The results obtained are found to be in agreement with previous experimental and numerical studies. The study of heat transfer involved a microchannel for a composite channel of trapezoidal cross-section fabricated by etching a silicon wafer and bonding it with a slab of gadolinium. Gadolinium is a magnetic material that exhibits high temperature rise during adiabatic magnetization around its transition temperature of 295K. Heat was generated in the substrate by the application of magnetic field. Water, ammonia, and FC-77 were studied as the possible working fluids. Thorough investigation for velocity and temperature distribution was performed by varying channel aspect ratio, Reynolds number, and the magnetic field. The thickness of gadolinium slab, spacing between channels in the heat exchanger, and fluid flow rate were varied.To check the validity of simulation, the results were compared with existing results for single material channels. Results showed that Nusselt number is larger near the inlet and decreases downstream. Also, an increase in Reynolds number increases the total Nusselt number of the system.
538
Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
590
Advisor: Muhammad M. Rahman, Ph.D.
653
Fully-confined fluid
Sherwood number
Rotating disk
Gadolinium
Heat sink
690
Dissertations, Academic
z USF
x Mechanical Engineering
Masters.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.3297