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1 v TABLE OF CONTENTS CHAPTER TITLE PAGE TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS LIST OF APPENDICES v viii ix xii xiv CHAPTER 1 INTRODUCTION 1.1 Introduction Literature Review Objectives Scopes of Study 10
2 vi CHAPTER 2 GOVERNING EQUATIONS 2.1 Continuity and Momentum Equations Energy Equations Related Equations Assumptions 16 CHAPTER 3 METHODOLOGY 3.1 Computational Fluid Dynamics Pre-processing: GAMBIT Solver: FLUENT Post-processing: FLUENT Pre-processing: Domain of Computational Solver: Parameters Solver: Method of Solution Expected Outcome 29 CHAPTER 4 MODEL VALIDATION 4.1 Model Validation Methodology Grid Dependency Test Model Validation with Numerical Results Comparison 34
3 vii CHAPTER 5 RESULTS AND DISCUSSIONS 5.1 Simulation of the Normal Blood Flow in an Artery (Straight Tube) Simulations of Abnormal Blood Flow in an Artery under Heating Conditions (Straight Tube) Simulations of Blood Flow in an Artery (Tapered and Stenois Tubes) Simulations of Blood Flow in an Artery (Tapered Tube) Simulations of Blood Flow in an Artery (Stenois Tube) 56 CHAPTER 6 CONCLUSION 6.1 Conclusion 68 REFERENCES 70 APPENDICES A-M 73
4 viii LIST OF TABLES TABLE NO TITLE PAGE Blood and water properties Variation for normal blood flow in an artery Variation for abnormal blood flow in an artery under heating condition Variation for abnormal blood flow under tapered and stenois channel Summary of meshing size for grid dependency test 31
5 ix LIST OF FIGURES FIGURE NO TITLE PAGE Blood flow categories History of blood flow studies in arteries History of blood flow studies in veins and capillaries Segregation solution method Coupled solution method Normal blood flow in an artery Abnormal blood flow in an artery under heating condition Normal blood flow in a tapered artery Abnormal blood flow in a tapered artery under heating condition Normal blood flow in a stenois artery Abnormal blood flow in a stenois artery under heating condition Percentage difference changing from one mesh size to another Number of iteration versus number of cells Local Nusselt number for simultaneously developing region in a circular duct Comparison of local Nusselt number with correlation results 36
6 x Axial velocity of blood flow (q = 0W/m 2, U m = 0.05m/s) at various radii Skin friction coefficient of blood flow (q = 0w/m 2, U m = 0.05m/s) at various radii Axial velocity of blood flow (q = 4W/m 2, U m = 0.0 m/s) at various radii Skin friction coefficient of blood flow (q = 4W/m 2, U m = 0.05m/s) at various radii Local Nusselt number of blood flow (q = 4W/m 2, U m = 0.05m/s) at various radii Axial velocity of blood flow (r = 5mm, U m = 0.05m/s) under various heating conditions Skin friction coefficient of blood flow (r = 5mm, U m = 0.05m/s) under various heating conditions Local Nusselt number of blood flow (r = 5mm, U m = 0.05m/s) under various heating conditions Plot of correlation of local Nusselt number for blood and water flow Plot of simulation and correlation of local Nusselt number for blood flow Zoom- in of Figure Axial velocity of blood flow (q = 0W/m 2, U m = 0.05m/s) under various taper angles Skin friction coefficient of blood flow (q = 0W/m 2, U m = 0.05m/s) under various taper angles Axial velocity of blood flows (q = 4W/m 2, U m = 0.05m/s) under various taper angles Skin friction coefficient of blood flow (q = 4W/m 2, U m = 0.05m/s) under various taper angles Local Nusselt numbers of blood flow (q = 4W/m 2, U m = 0.05m/s) under various taper angles 51
7 xi Axial velocity of blood flow (U m = 0.05m/s, θ = ) under various heating conditions Skin friction coefficient of blood flow (U m = 0.05m/s, θ = ) under various heating conditions Local Nusselt number of blood flow (U m = 0.05m/s, θ = ) under various heating conditions Axial velocity of blood flow (q = 0W/m 2, U m = 0.0 m/s) with various stenois heights Center axial velocity of blood flow (q = 0W/m 2, U m = 0.05m/s) with various stenois heights Skin friction coefficient of blood flow (q = 0W/m 2, U m = 0.05m/s) with various stenois heights Axial velocity of blood flow (q = 4W/m 2, U m = 0.05m/s) with various stenois heights Center axial velocity of blood flow (q = 4W/m 2, U m = 0.05m/s) with various stenois heights Skin friction coefficient of blood flow (q = 4W/m 2, U m = 0.05m/s) with various stenois heights Local Nusselt number of blood flow (q = 4W/m 2, U m = 0.05m/s) with various stenois heights Axial velocity of blood flow (a / r = 0.2, U m = 0.05m/s) under various heating conditions Center axial velocity of blood flow (a / r = 0.2, U m = 0.05m/s) under various heating conditions Skin friction coefficient of blood flow (a / r = 0.2, U m = 0.05m/s) under various heating conditions Local Nusselt number of blood flow (a / r = 0.8, U m = 0.05m/s) under various heating conditions 66
8 xii LIST OF SYMBOLS c p d F h h I J j Specific heat Diameter External body forces or any user-defined sources Enthalpy (ideal gases / incompressible flows) Heat transfer coefficient Unit tensor Diffusion flux of species j k eff Effective conductivity p q r S h S m t T m T w U c U m x ρ Static pressure Constant heat flux Radial coordinate / radius Heat of chemical reaction and any other user-defined heat sources Mass added to the continuous phase from the dispersed second phase or any user-defined sources Time Fluid bulk temperature Wall temperature Axial velocity at center of tube Fluid average inlet velocity Axial coordinate Fluid density
9 xiii ρ g Gravitational body force τ Tensor stress µ Molecular viscosity / fluid dynamics viscosity ν ν r ν x Fluid velocity Radial velocity Axial velocity T ν Effect of volume dilation Non-dimensional parameter Nu Nusselt number Pr Prandlt number Re Reynolds number
10 xiv LIST OF APPENDICES APPENDIX TITLE PAGE A Blood properties set up in Fluent 73 B Axial velocity profile for tapered tube (q = 4W/m 2, U m = 0.05m/s) 74 C Axial velocity profile for tapered tube (q = 4W/m 2, U m = 0.05m/s) 74 D Axial velocity profile for tapered tube (q = 4W/m 2, U m = 0.05m/s) 75 E Temperature contour for tapered tube (q = 4W/m 2, U m = 0.05m/s) 75 F Temperature contour for tapered tube (q = 5W/m 2, U m = 0.05m/s) 76 G Temperature contour for tapered tube (q = 6W/m 2, U m = 0.05m/s) 76 H Axial velocity profile for stenois height of 1mm (q = 0W/m 2, U m = 0.05m/s) 77 I Axial velocity profile for stenois height of 1.5mm (q = 0W/m 2, U m = 0.05m/s) 77 J Axial velocity profile for stenois height of 2mm (q = 0W/m 2, U m = 0.05m/s) 78
11 xv K L M Temperature contour for stenois height of 1mm (q = 4W/m 2, U m = 0.05m/s) 78 Temperature contour for stenois height of 1mm (q = 5W/m 2, U m = 0.05m/s) 79 Temperature contour for stenois height of 1mm (q = 6W/m 2, U m = 0.05m/s) 79
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