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Analysis of Mass Transfer by Jet Impingement and Heat Transfer by Convection

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Analysis of Mass Transfer by Jet Impingement and Heat Transfer by Convection Analysis of Mass Transfer by Jet Impingement and Study of Heat Transfer in a Trapezoidal Microchannel by Ejiro Stephen Ojada A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department 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 ©Copyright 2009, Ejiro Stephen Ojada i TABLE OF CONTENTS 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 (Heat Transfer in a Microchannel) 7 1.4 Literature Review (Heat Transfer in a Microchannel) 8 CHAPTER 2: ANALYSIS OF MASS TRANSFER 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 Results and Discussion 48 CHAPTER 4: CONCLUSION 65 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 86 i LIST OF FIGURES Figure 2.1a Confined liquid jet impingement between 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 (Rej=1000, Rer=2310, =1.0, and Sc=2315). 22 Figure 2.4 Local Sherwood number and dimensionless concentration for different jet Reynolds numbers (=1.0, Rer=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, Rej=800, and Sc=2315). 27 Figure 2.6 Local Sherwood number and dimensionless concentration for different dimensionless heights (Rej=1500, Rer=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 (Rer=2310, and Sc=2315). 32 Figure 2.9 Average Sherwood number with jet Reynolds number at different Schmidt number (=1.15, nickel disk, ferricyanide electrolyte, and Rer=5082). 33 ii Figure 2.10 Dimensionless concentration for different electrolytes - 3 NaOH, HCl, Fe(CN)6 (Rej=650, Rer=0, and =1.0). 34 Figure 2.11 Local Sherwood number and dimensionless concentration over dimensionless radial distance for different impingement plate geometries, nickel disk with ferricyanide electrolyte (Rej=1000, Rer=5082, =1.15, and Sc=2315). 35 Figure 2.12 Average Sherwood number comparison with the experimental results obtained by Arzutuğ et al. [13] under various jet Reynolds and Schmidt numbers (left: =1.0, Sc=2315, Rer=2310; right: (=1.0, Rej=1000, and Rer=5082). 37 Figure 2.13 Average Sherwood number comparison with other studies within the core region for various Schmidt numbers ( =1.0, Rej=800, Rer=2310). 38 Figure 2.14 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 temperature over the dimensionless axial coordinate for different grid sizes (magnetic field = 5T, Re =1600, D=150 μm, L=2.3 cm). 49 Figure 3.3 Variation of peripheral average Nusselt number along the channel dimensionless axial coordinate for different Reynolds number (Magnetic field = 5T, D=150 μm, L=2.3 cm). 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 μm, L=2.3 cm). 51 Figure 3.5 Variation of Nusselt number along the channel dimensionless axial coordinate for different heat generation rates (Re = 1600, 2400, 3000, D=150 μm, L=2.3 cm). 52 Figure 3.6 Variation of peripheral average dimensionless interface temperature along the channel dimensionless axial coordinate for different thickness of the magnetic slab (Re= 1600, Magnetic field = 5T, D=150 μm, L=2.3 cm). 54 iii Figure 3.7 Variation of Nusselt number along the channel dimensionless axial coordinate 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 Variation of Nusselt number over the dimensionless axial coordinate for different spacing between the channels (Re = 2400, magnetic field = 5T, D=150 μm, L=2.3 cm). 57 Figure 3.10 Comparison between simulation and standard convection relation (Dh=154μm, Magnetic field = 5T, D=150 μm, L=2.3 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 (Magnetic field = 5T, D=150 μm, L=2.3 cm). 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 experimental results obtained by Wu and Chen [38] under various jet (Magnetic field = 5T, 40 < Re < 200, D=150 μm, L=4.0 cm). 64 iv LIST OF SYMBOLS b Height of gadolinium slab, m B Substrate width, m Bc Channel width, m Bs Half of channel width (at bottom), m r C Average interface concentration, kg/m3, 2 d avg C r dr 2 rd 0 Cp Constant pressure specific heat, J/kg-K C Solute concentration, kg/m3 dn Diameter of nozzle, m dd Diameter of rotating disk, m D Diffusion coefficient, m2/s Dp Dimensionless pump power Dh Hydraulic diameter, m g Acceleration due to gravity, m/s2 go Heat generation rate within the solid, W/m3 G Mass flux, kg/m2.s 2 h Heat transfer coefficient, qint / (Tint−Tb), W/m 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, m2/s2 K Mass transfer coefficient, G/ (Cint–Cj), m/s L Channel length, m Nu Nusselt number P Pressure, N/m2 v Pd Dimensionless pressure Pp Pumping power Prt Turbulent Prandtl number q Heat flux, W/m2 Q Dimensionless Concentration, 2(Cint – Cj) / (Gdn) r Radial coordinate, m R Radius of rotating disk, m Re Reynolds number, (Vjdn)/ or ρf .u in .Dh /μ Sh Sherwood number, (kdn)/D S Spacing between channels, m T Temperature, ⁰C ΔT Temperature difference between inlet and outlet, °C Vj Jet velocity, m/s Vr, 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 Velocity component in z-direction, m/s z Axial coordinate, m Greek Symbols α Thermal diffusivity, m2/s Dimensionless nozzle to target spacing, H/dn ϵ Dissipation rate of turbulent kinetic energy, m2/s3 Dynamic viscosity, kg/m–s Kinematic viscosity, m2/s 2 νt Eddy diffusivity, m /s Angular coordinate, rad Dimensionless interface temperature Density, kg/m3 Angular velocity, rad/s vi Subscripts b Bulk avg. Average f Fluid g Gadolinium i Species i in Inlet int Interface j jet inlet max Maximums si Silicon s Solid vii Analysis of Mass Transfer by Jet Impingement and Study of Heat Transfer in a Trapezoidal Microchannel Ejiro S. Ojada 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)), -4 0.02moles per liter ferrocyanide (FeCN6 ), 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. viii The study of heat transfer involved a microchannel for a composite channel of trapezoidal cross-section fabricated by etching a silicon <100> 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.
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