Heat Transfer Explained

XINYU ZHAO, PHD, is an Associate Professor in the Department of Mechanical Engineering at the University of Connecticut, where she has taught Heat Transfer and Computational Fluid Dynamics since 2015. Her research focuses on radiative heat transfer, reactive flows, and propulsion system design through multi-scale modeling. She has received major honors, including the AFOSR YIP Award and the NSF CAREER Award.

• About the Author xiPreface xiiiAcknowledgments xv1 Introduction 11.1 What Is Heat Transfer? 11.2 Three Basic Heat Transfer Modes 21.3 Relations to Thermodynamics 61.3.1 The First Law of Thermodynamics 61.3.2 Zeroth Law and Second Law 101.4 A Brief Review of the Prerequisite 111.4.1 Coordinate Systems 111.4.2 Units and Dimensions 111.4.3 Integration 121.4.4 Solving Second-order Ordinary Differential Equations 131.4.5 The Problem Solution Procedure 151.5 Summary 15Bibliography 162 Introduction to Conduction 172.1 Thermal Conductivity 172.2 General Description of Conduction 202.2.1 General Form of Fourier’s Law 202.2.2 Derivation of Heat Equation 222.2.3 Boundary Conditions and Initial Conditions 242.3 General Solution Procedure to 1D Steady-state Heat Equation 272.4 Steady-state Conduction with No Internal Source: The Thermal Resistance Network Method 282.5 Summary 33Bibliography 333 Multidimensional Conduction 353.1 Conduction Beyond Steady-state One-dimensional Problems 353.1.1 Zero-dimensional Transient Conduction: The Lumped Capacitance Method 363.1.2 Steady-state 2D Conduction 403.1.3 Transient 1D Conduction Without Source/Sink 413.1.4 Transient 3D Conduction with Moving Source 443.1.5 A Note on Analytical Solutions 453.2 Numerical Methods 453.2.1 Approximation to Derivatives 463.2.2 Finite Volume Method 483.2.3 Treatment of Time 533.2.4 Accuracy Versus Stability 563.2.5 Virtual Laboratory: 1D Transient Conduction in a Semi-infinite Wall 573.3 Summary 61Bibliography 614 Introduction to Convective Heat Transfer 634.1 Boundary Layers 634.2 Nusselt Number 684.3 Connecting Momentum Transport and Heat Transfer: Prandtl Number 694.4 Reynolds Analogy 714.5 Impact of Turbulence 724.6 Virtual Laboratory: Boundary Layer Measurement 734.7 Summary 77Bibliography 775 Forced Convection 795.1 External Convection 815.1.1 Flat Plate 815.1.2 Other Bluff Bodies 855.1.3 Virtual Laboratory: Determination of the Convective Heat Transfer Coefficient for a Rotating Disk 875.2 Internal Convection 915.2.1 Pipes 935.2.2 Ducts with Other Cross-sectional Shape 945.2.3 Total Heat Transfer Rate 955.2.4 Virtual Laboratory: Heat Transfer Characteristics for Detonation in Narrow Channel 975.3 Summary 101Bibliography 1026 Natural Convection and Phase Change 1056.1 The Physical Processes of Natural Convection and Phase Change 1056.1.1 Relevant Scales for Natural Convection 1056.1.2 Relevant Scales for Boiling and Condensation 1086.2 Correlations for Natural Convection 1116.2.1 External Natural Convection 1116.2.2 Internal Natural Convection 1136.2.3 Mixed Regime Convection 1146.2.4 Virtual Laboratory: Natural Convection in an Ethylene–Air Pool Fire 1146.3 Correlations for Phase Change Process 1186.4 Summary 119Bibliography 1197 Introduction to Radiative Heat Transfer 1217.1 The Physical Process of Thermal Radiation 1217.2 Basic Concepts in Radiation 1227.2.1 Solid Angle 1227.2.2 The Electromagnetic Spectrum 1237.2.3 Radiative Intensity 1247.3 The Idealized “Blackbody” 1257.3.1 Fraction of Blackbody Emissive Power 1267.3.2 Virtual Laboratory: Key Observations for Blackbody Radiation 1267.4 Surface Properties 1287.4.1 Spectral and Directional Dependence of Surface Properties 1297.4.2 Kirchhoff’s Law 1307.4.3 Virtual Laboratory: Measuring Emissivity of Semiconductor Wafer 1317.5 Summary 133Bibliography 1338 Radiative Exchange Between Surfaces 1358.1 View Factor 1358.1.1 Properties of View Factor 1378.1.2 Two-dimensional Geometries: The Crossed-string Method 1388.1.3 The Monte Carlo Method for Determination of View Factors 1408.2 Surface Exchange Between Gray Diffuse Surfaces 1448.2.1 Surface Exchange Between Black Surfaces 1448.2.2 Analytical Methods for Surface Exchange Between Gray Diffuse Surfaces 1458.2.3 The Monte Carlo Methods for Surface Exchange Between Gray Diffuse Surfaces 1478.3 Virtual Laboratory: Radiation Within a Backward-facing Step Combustor 1488.4 Summary 150Bibliography 1509 Radiation in Participating Media 1519.1 The Characteristics of Gaseous Radiation 1519.2 The Characteristics of Radiative Interactions with Particles 1539.3 The Characteristics of Radiation in Semitransparent Medium 1549.4 Radiative Absorption: The Beer’s Law 1549.5 Radiative Emission 1569.6 Virtual Laboratory: Measurement of Wall Temperature in a Combustor Using IR Camera 1579.7 Summary 159Bibliography 15910 Applications: Fin and Heat Exchanger 16110.1 Fins 16210.1.1 Heat Transfer Rate 16310.1.2 Efficiency and Effectiveness 16710.1.3 Virtual Laboratory: Determination of Efficiency and Effectiveness for Fins with Arbitrary Shape 16810.2 Heat Exchanger 17310.2.1 Classification 17310.2.2 Overall Heat Transfer Coefficient 17410.2.3 Log-mean Temperature Difference 17510.2.4 Effectiveness-NTU Method 17710.2.5 A Practical Example 18110.3 Summary 186Bibliography 18711 Contemporary Application of Heat Transfer 18911.1 A Simplified Energy Balance for Earth 19111.2 Conjugate Heat Transfer Within a Thermal Barrier Coating Layer 19611.3 Electronics Cooling 20111.4 Thermal Runaway of Lithium-ion Batteries 20811.5 Summary 213Bibliography 213Index 215