Applications of Mathematical Heat Transfer and Fluid Flow Models in Engineering and Medicine

Abram S. Dorfman, Doctor of Science, Ph. D. was born in 1923 in Kiev. He was a leading scientist in fluid mechanic and heat transfer at the Institute of Thermophiysics of the Ukrainian Academy of Science and associate editor of Promyshlennaya Teploteknika translated by Wiley as Applied Thermal Science. He earned his Ph.D. with a thesis Investigation of Supersonic Flows in Nozzles and received a Doctor of Science degree with a thesis and a book Heat Transfer in Flows around the Nonisothermal bodies. He emigrated to the United States in 1990 and continues his research as a visiting professor at the University of Michigan. During that time, he published several articles in leading American journals and two books. Dr. Dorfman has been an adviser to Ph. D. students and has published more than 140 papers and four books. More than 50 of his papers published in Russian have been translated into English.

• Series Preface xiiiPreface xvAcknowledgments xxviiAbout the Author xxixNomenclature xxxiPart I APPLICATIONS IN CONJUGATE HEAT TRANSFERIntroduction 1When and why Conjugate Procedure is Essential 1A Core of Conjugation 31 Universal Functions for Nonisothermal and Conjugate Heat Transfer 51.1 Formulation of Conjugate Heat Transfer Problem 51.2 Methods of Conjugation 91.2.1 Numerical Methods 91.2.2 Using Universal Functions 101.3 Integral Universal Function (Duhamel’s Integral) 101.3.1 Duhamel’s Integral Derivation 101.3.2 Influence Function 121.4 Differential Universal Function (Series of Derivatives) 131.5 General Forms of Universal Function 15Exercises 1.1–1.32 161.6 Coefficients gk and Exponents C1 and C2 for Laminar Flow 191.6.1 Features of Coefficients gk of the Differential Universal Function 191.6.2 Estimation of Exponents C1 and C2 for Integral Universal Function 221.7 Universal Functions for Turbulent Flow 24Exercises 1.33–1.47 271.8 Universal Functions for Compressible Low 281.9 Universal Functions for Power-Law Non-Newtonian Fluids 291.10 Universal Functions for Moving Continuous Sheet 321.11 Universal Functions for a Plate with Arbitrary Unsteady Temperature Distribution 341.12 Universal Functions for an Axisymmetric Body 351.13 Inverse Universal Function 361.13.1 Differential Inverse Universal Function 361.13.2 Integral Inverse Universal Function 371.14 Universal Function for Recovery Factor 38Exercises 1.48–1.75 412 Application of Universal Functions 452.1 The Rate of Conjugate Heat Transfer Intensity 452.1.1 Effect of Temperature Head Distribution 452.1.2 Effect of Turbulence 502.1.3 Effect of Time-Variable Temperature Head 582.1.4 Effects of Conditions and Parameters in the Inverse Problems 602.1.5 Effect of Non-Newtonian Power-Law Rheology Fluid Behavior 662.1.6 Effect of Mechanical Energy Dissipation 672.1.7 Effect of Biot Number as a Measure of Problem Conjugation 68Exercises 2.1–2.33 702.2 The General Convective Boundary Conditions 732.2.1 Accuracy of Boundary Condition of the Third Kind 732.2.2 Conjugate Problem as an Equivalent Conduction Problem 762.3 The Gradient Analogy 782.4 Heat Flux Inversion 822.5 Zero Heat Transfer Surfaces 842.6 Optimization in Heat Transfer Problems 862.6.1 Problem Formulation 872.6.2 Problem Formulation 892.6.3 Problem Formulation 92Exercises 2.34–2.82 953 Application of Conjugate Heat Transfer Models in External and Internal Flows 1023.1 External Flows 1023.1.1 Conjugate Heat Transfer in Flows Past Thin Plates 102Exercises 3.1–3.38 1233.1.2 Conjugate Heat Transfer in Flows Past Bodies 1263.2 Internal Flows-Conjugate Heat Transfer in Pipes and Channels Flows 1414 Specific Applications of Conjugate Heat Transfer Models 1554.1 Heat Exchangers and Finned Surfaces 1554.1.1 Heat Exchange Between Two Fluids Separated by a Wall (Overall Heat Transfer Coefficient) 1554.1.2 Applicability of One-Dimensional Models and Two-Dimensional Effects 1664.1.3 Heat Exchanger Models 1704.1.4 Finned Surfaces 1754.2 Thermal Treatment and Cooling Systems 1804.2.1 Treatment of Continuous Materials 1804.2.2 Cooling Systems 1854.3 Simulation of Industrial Processes 1964.4 Technology Processes 2024.4.1 Heat and Mass Transfer in Multiphase Processes 2024.4.2 Drying and Food Processing 208Summary of Part I 219Effect of Conjugation 219Part II APPLICATIONS IN FLUID FLOW5 Two Advanced Methods 2255.1 Conjugate Models of Peristaltic Flow 2255.1.1 Model Formulation 2255.1.2 The First Investigations 2285.1.3 Semi-Conjugate Solutions 230Exercises 5.1–5.19 2365.1.4 Conjugate Solutions 237Exercises 5.20–5.31 2435.2 Methods of Turbulence Simulation 2445.2.1 Introduction 2445.2.2 Direct Numerical Simulation 2445.2.3 Large Eddy Simulation 2455.2.4 Detached Eddy Simulation 2475.2.5 Chaos Theory 249Exercises 5.32–5.44 2496 Applications of Fluid Flow Modern Models 2516.1 Applications of Fluid Flow Models in Biology and Medicine 2516.1.1 Blood Flow in Normal and Pathologic Vessels 2516.1.2 Abnormal Flows in Disordered Human Organs 2616.1.3 Simulation of Biological Transport Processes 2676.2 Application of Fluid Flow Models in Engineering 2736.2.1 Application of Peristaltic Flow Models 2736.2.2 Applications of Direct Simulation of Turbulence 278Part III FOUNDATIONS OF FLUID FLOW AND HEAT TRANSFER7 Laminar Fluid Flow and Heat Transfer 2957.1 Navier-Stokes, Energy, and Mass Transfer Equations 2957.1.1 Two Types of Transport Mechanism: Analogy Between Transfer Processes 2957.1.2 Different Forms of Navier-Stokes, Energy, and Diffusion Equations 2977.2 Initial and Boundary Counditions 3027.3 Exact Solutions of Navier-Stokes and Energy Equations 3037.3.1 Two Stokes Problems 3037.3.2 Steady Flow in Channels and in a Circular Tube 3047.3.3 Stagnation Point Flow (Hiemenz Flow) 3047.3.4 Couette Flow in a Channel with Heated Walls 3067.3.5 Adiabatic Wall Temperature 3067.3.6 Temperature Distributions in Channels and in a Tube 3067.4 Cases of Small and Large Reynolds and Peclet Numbers 3077.4.1 Creeping Approximation (Small Reynolds and Peclet Numbers) 3077.4.2 Stokes Flow Past Sphere 3087.4.3 Oseen’s Approximation 3087.4.4 Boundary Layer Approximation (Large Reynolds and Peclet Numbers) 3097.5 Exact Solutions of Boundary Layer Equations 3157.5.1 Flow and Heat Transfer on Isothermal Semi-infinite Flat Plate 3157.5.2 Self-Similar Flows of Dynamic and Thermal Boundary Layers 3197.6 Approximate Karman-Pohlhausen Integral Method 3207.6.1 Approximate Friction and Heat Transfer on a Flat Plate 3207.6.2 Flows with Pressure Gradients 3227.7 Limiting Cases of Prandtl Number 3237.8 Natural Convection 3248 Turbulent Fluid Flow and Heat Transfer 3278.1 Transition from Laminar to Turbulent Flow 3278.2 Reynolds Averaged Navier-Stokes Equation (RANS) 3288.2.1 Some Physical Aspects 3288.2.2 Reynolds Averaging 3298.2.3 Reynolds Equations and Reynolds Stresses 3308.3 Algebraic Models 3318.3.1 Prandtl’s Mixing-Length Hypothesis 3318.3.2 Modern Structure of Velocity Profile in Turbulent Boundary Layer 3328.3.3 Mellor-Gibson Model 3348.3.4 Cebeci-Smith Model 3358.3.5 Baldwin-Lomax Model 3368.3.6 Application of the Algebraic Models 3378.3.7 The 1/2 Equation Model 3388.3.8 Applicability of the Algebraic Models 3398.4 One-Equation and Two-Equations Models 3398.4.1 Turbulence Kinetic Energy Equation 3408.4.2 One-Equation Models 3408.4.3 Two-Equation Models 3418.4.4 Applicability of the One-Equation and Two-Equation Models 3439 Analytical and Numerical Methods in Fluid Flow and Heat Transfer 344Analytical Methods 3449.1 Solutions Using Error Functions 3449.2 Method of Separation Variables 3459.2.1 General Approach, Homogeneous, and Inhomogeneous Problems 3469.2.2 One-Dimensional Unsteady Problems 3479.2.3 Orthogonal Eigenfunctions 3489.2.4 Two-Dimensional Steady Problems 3519.3 Integral Transforms 3539.3.1 Fourier Transform 3539.3.2 Laplace Transform 3569.4 Green’s Function Method 358Numerical Methods 3619.5 What Method is Proper? 3619.6 Approximate Methods for Solving Differential Equations 3639.7 Computing Flow and Heat Transfer Characteristics 3689.7.1 Control-Volume Finite-Difference Method 3689.7.2 Control-Volume Finite-Element Method 37110 Conclusion 373References 376Author Index 397Subject Index 409