• front-matter (1)
• Chapter 01 (14)
  • BASIC CONCEPTS (14)
    • Examples of Conduction Problems (14)
    • Focal Point in Conduction Heat Transfer (15)
    • Fourier's Law of Conduction (15)
    • Conservation of Energy: Differential Formulation of the Heat Conduction Equation in Rectangular Coordinates (18)
    • The Heat Conduction Equation in Cylindrical and Spherical Coordinates (22)
    • Boundary Conditions (23)
      • Surface Convection: Newton's Law of Cooling (23)
      • Surface Radiation: Stefan-Boltzmann Law (24)
      • Examples of Boundary Conditions (25)
    • Problem Solving Format (28)
    • Units (29)
    • REFERENCES (30)
• Chapter 02 (37)
  • ONE-DIMENSIONAL STEADY STATE CONDUCTION (37)
    • Examples of One-dimensional Conduction (37)
    • Extended Surfaces: Fins (47)
      • The Function of Fins (47)
      • Types of Fins (47)
      • Heat Transfer and Temperature Distribution in Fins (48)
      • The Fin Approximation (49)
      • The Fin Heat Equation: Convection at Surface (50)
      • Determination of $\frac{dA_{s}}{dx}$ (52)
      • Boundary Conditions (53)
      • Determination of Fin Heat Transfer Rate $q_{f}$ (53)
      • Steady State Applications: Constant Area Fins with Surface Convection (54)
      • Corrected Length $L_{c}$ (57)
      • Fin Efficiency $\eta_{f}$ (57)
      • Moving Fins (58)
      • Application of Moving Fins (60)
      • Variable Area Fins (62)
    • Bessel Differential Equations and Bessel Functions (65)
      • General Form of Bessel Equations (65)
      • Solutions: Bessel Functions (65)
      • Forms of Bessel Functions (67)
      • Special Closed-form Bessel Functions:$n = \frac{odd integer}{2}$ (67)
      • Special Relations for n = 1, 2, 3, …. (68)
      • Derivatives and Integrals of Bessel Functions [2,3] (69)
      • Tabulation and Graphical Representation of Selected Bessel Functions (69)
    • Equidimensional (Euler) Equation (71)
    • Graphically Presented Solutions to Fin Heat Transfer Rate [5] (72)
    • REFERENCES (73)
• Chapter 03 (85)
  • TWO-DIMENSIONAL STEADY STATE CONDUCTION (85)
    • The Heat Conduction Equation (85)
    • Method of Solution and Limitations (86)
    • Homogeneous Differential Equations and Boundary Conditions (86)
    • Sturm-Liouville Boundary-Value Problem: Orthogonality [1] (87)
    • Procedure for the Application of Separation of Variables Method (89)
    • Cartesian Coordinates: Examples (96)
    • Cylindrical Coordinates: Examples (110)
    • Integrals of Bessel Functions (115)
    • Non-homogeneous Differential Equations (116)
    • Non-homogeneous Boundary Conditions: The Method of Superposition (122)
    • REFERENCES (124)
• Chapter 04 (132)
  • TRANSIENT CONDUCTION (132)
    • Simplified Model: Lumped-Capacity Method (132)
      • Criterion for Neglecting Spatial Temperature Variation (132)
      • Lumped-Capacity Analysis (134)
    • Transient Conduction in Plates (137)
    • Non-homogeneous Equations and Boundary Conditions (141)
    • Transient Conduction in Cylinders (145)
    • Transient Conduction in Spheres (151)
    • Time Dependent Boundary Conditions: Duhamel’s Superposition Integral (154)
      • Formulation of Duhamel’s Integral [1] (155)
      • Extension to Discontinuous Boundary Conditions (157)
      • Applications (158)
    • Conduction in Semi-infinite Regions: The Similarity Method (163)
    • REFERENCES (167)
• Chapter 05 (176)
  • CONDUCTION IN POROUS MEDIA (176)
    • Examples of Conduction in Porous Media (176)
    • Simplified Heat Transfer Model (177)
      • Porosity (177)
      • Heat Conduction Equation: Cartesian Coordinates (178)
      • Boundary Conditions (180)
      • Heat Conduction Equation: Cylindrical Coordinates (181)
    • Applications (181)
    • REFEENCES (187)
• Chapter 06 (197)
  • CONDUCTION WITH PHASE CHANGE: MOVING BOUNDARY PROBLEMS (197)
    • Introduction (197)
    • The Heat Equations (198)
    • Moving Interface Boundary Conditions (198)
    • Non-linearity of the Interface Energy Equation (201)
    • Non-dimensional Form of the Governing Equations: Governing Parameters (202)
    • Simplified Model: Quasi-Steady Approximation (203)
    • Exact Solutions (210)
      • Stefan’s Solution (210)
      • Neumann’s Solution: Solidification of Semi-Infinite Region (213)
      • Neumann’s Solution: Melting of Semi-infinite Region (216)
    • Effect of Density Change on the Liquid Phase (217)
    • Radial Conduction with Phase Change (218)
    • Phase Change in Finite Regions (222)
    • REFERENCES (223)
• Chapter 07 (228)
  • NON-LINEAR CONDUCTION PROBLEMS (228)
    • Introduction (228)
    • Sources of Non-linearity (228)
      • Non-linear Differential Equations (228)
      • Non-linear Boundary Conditions (229)
    • Taylor Series Method (229)
    • Kirchhoff Transformation (233)
      • Transformation of Differential Equations (233)
      • Transformation of Boundary Conditions (234)
    • Boltzmann Transformation (237)
    • Combining Boltzmann and Kirchhoff Transformations (239)
    • Exact Solutions (240)
    • REFERENCES (243)
• Chapter 08 (249)
  • APPROXIMATE SOLUTIONS: THE INTEGRAL METHOD (249)
    • Integral Method Approximation: Mathematical Simplification (249)
    • Procedure (249)
    • Accuracy of the Integral Method (250)
    • Application to Cartesian Coordinates (251)
    • Application to Cylindrical Coordinates (259)
    • Non-linear Problems [5] (264)
    • Energy Generation (273)
    • REFERENCES (277)
• Chapter 09 (282)
  • PERTURBATION SOLUTIONS (282)
    • Introduction (282)
    • Solution Procedure (283)
    • Examples of Perturbation Problems in Conduction (284)
    • Perturbation Solutions: Examples (286)
    • Useful Expansions (309)
    • REFERENCES (309)
• Chapter 10 (315)
  • Heat Transfer in Living Tissue (315)
    • Introduction (315)
    • Vascular Architecture and Blood Flow (315)
    • Blood Temperature Variation (317)
    • Mathematical Modeling of Vessels-Tissue Heat Transfer (318)
      • Pennes Bioheat Equation [1] (318)
      • Chen-Holmes Equation [5] (325)
      • Three-Temperature Model for Peripheral Tissue [7] (326)
      • Weinbaum-Jiji Simplified Bioheat Equation for Peripheral Tissue [8] (328)
      • The $s$-Vessel Tissue Cylinder Model [16] (336)
    • REFERENCES (345)
• Chapter 11 (360)
  • MICROSCALE CONDUCTION (360)
    • Introduction (360)
      • Categories of Microscale Phenomena (361)
      • Purpose and Scope of this Chapter (363)
    • Understanding the Essential Physics of Thermal Conductivity Using the Kinetic Theory of Gases (364)
      • Derivation of Fourier’s Law and an Expression for the Thermal Conductivity (364)
    • Energy Carriers (368)
      • Ideal Gases: Heat is Conducted by Gas Molecules (368)
      • Metals: Heat is Conducted by Electrons (372)
      • Electrical Insulators and Semiconductors: Heat is Conducted by Phonons (Sound Waves) (374)
      • Radiation: Heat is Carried by Photons (Light Waves) (385)
    • Thermal Conductivity Reduction by Boundary Scattering: The Classical Size Effect (390)
      • Accounting for Multiple Scattering Mechanisms: Matthiessen’s rule (390)
      • Boundary Scattering for Heat Flow Parallel to Boundaries (392)
      • Boundary Scattering for Heat Flow Perpendicular to Boundaries (400)
    • Closing Thoughts (406)
    • REFERENCES (409)
• back-matter (416)