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Mathematical Principles of Heat Transfer

ISBN: 1-56700-217-X

Mathematical Principles of Heat Transfer

K. N. Shukla
Karunya Institute of Technology and Sciences Coimbatore-641114, India


This book presents an investigative account of Mathematical Principles of Heat Transfer. It is concerned with three aspects of heat transfer analysis: theoretical development of conservation equations, analytical and numerical techniques of the solution, and the physical processes involved in the three basic modes of heat transfer, namely conduction, convection, and radiation. A concept of mathematical modeling is developed through the use of differential equations. In doing so, the well-posed boundary value problems are constructed and the solutions are attempted.

© 2005

Table of contents:

Chapter 1 Basic Concepts of Heat Transfer
1.1 Basic Modes of Heat Transfer
1.1.1 Temperature field
1.1.2 Temperature gradient
1.2 Conduction
1.3 Thermal Conductivity
1.3.1 Thermal conductivities of gases
1.3.2 Thermal conductivities of liquids
1.3.3 Thermal conductivities of solids
1.4 Convection
1.5 Radiation
1.6 Heat Transfer with Change of Phase
1.7 Units and Dimensions
Chapter 2 Conservation Equations
2.1 General Conservation Equation
2.2 Equation of Continuity
2.3 Equation of Motion
2.4 Equation of Energy
2.5 Equation of Entropy
Chapter 3 Similarity Theory and the Generalized Variables
3.1 Boundary Value Problem in Generalized Variables: A Mathematical Presentation
3.2 Method of Dimensionality
Chapter 4 Mathematical Methods for Boundary Value Problems
4.1 Separation of Variables
4.2 Integral Transform Method
4.3 Laplace Transform
4.3.1 Laplace transform-fundamental properties
4.3.2 Inversion theorem for Laplace transform
4.4 Fourier Kernals
4.5 The Hankel Transform
4.6 Finite Integral Fourier and Hankel Transforms
4.7 Limiting Cases of Laplace Transform
4.8 Green's Function for the Solution of Heat Conduction
4.9 Approximate Methods in the Solution of Heat Transfer Problems
4.9.1 Integral method
4.9.2 Variational method
4.9.3 Ritz method
4.9.4 Galerkin method
4.9.5 Least-squares method
Chapter 5 Numerical Methods in Heat Transfer
5.1 Finite Difference Method
5.2 Gauss Elimination Method
5.3 Gauss-Seidel Method of Iteration
5.4 Successive Overrelaxation Method
5.5 Derivative Type of Boundary Conditions
5.6 Stability: Analytical Treatment
5.7 Convergence: Analytical Treatment
5.8 Compatibility
5.9 Two-Dimensional Problem of Heat Conduction
5.9.1 Locally one-dimensional method
Chapter 6 Steady-State Heat Conduction
6.1 Heat Transfer in a Slab
6.1.1 Dirichlet boundary conditions
6.1.2 Temperature-dependent thermal conductivity
6.1.3 Composite slab
6.1.4 Newtonian boundary conditions
6.1.5 Mixed boundary conditions
6.2 Heat Transfer through a Cylindrical Wall
6.2.1 Dirichlet boundary conditions
6.2.2 Temperature-dependent thermal conductivity
6.2.3 Composite cylindrical wall
6.2.4 Newtonian boundary conditions
6.2.5 Mixed boundary conditions
6.3 Heat Transfer through a Spherical Wall
6.3.1 Dirichlet boundary conditions
6.3.2 Temperature-dependent thermal conductivity
6.4 Critical Thickness of Insulation
6.5 Heat Conduction through a Thin Rod
6.6 Extended Surface
6.6.1 Longitudinal fin
6.6.2 Rectangular profile
6.6.3 Optimum dimension
6.6.4 Rectangular fin of minimum weight
6.6.5 Efficiency of the fin
6.6.6 Longitudinal fin of triangular profile
6.6.7 Optimum dimension
6.6.8 Radial fin
6.7 Steady Heat Flow in a Rectangle
6.7.1 Conjugate functions
Chapter 7 Transient Heat Conduction
7.1 Infinite Plate
7.2 Infinite Cylinder
7.3 The Sphere
7.4 Composite Solids
7.4.1 For Γ= 0
7.4.2 For Γ= 1
7.4.3 For Γ= 2
7.5 Periodic Variation of Ambient Temperature
Chapter 8 Heat Conduction with Phase Change
8.1 Statement of Problem and Existence of Solution
8.2 State-of-the-Art Solution Technique
8.3 Solidification of a Semi-Infinite Liquid
8.4 Axisymmetric Melting
8.5 Spherical Melting
8.6 Dynamics of Melt Growth and Axisymmetric Melting
8.6.1 Energy equation
Chapter 9 Convection
9.1 Hydrodynamics and Thermal Boundary Layers
9.2 Similarity Solution for Boundary Layers
9.2.1 Skin friction and heat transfer
9.2.2 Laminar boundary layers by the integral method
9.3 Similarity Solution for Boundary Layers, u = cxm
9.4 Finite Difference Solution
9.4.1 Transient solution for a pipe flow
9.5 Natural Convection
9.5.1 Natural convection from an isothermal vertical plate
9.6 Turbulence
Chapter 10 Diffusive Processes
10.1 Conservation Equations
10.2 Isothermal Ternary System
10.3 Nonisothermal Binary System
10.4 Thermohaline Convection
10.4.1 Free boundaries with specified solute concentration and temperature
10.4.2 Diffusive convection
10.5 Chaos
10.6 Diffusion Processes in Material Processing and Microgravity Environments
Chapter 11 Radiation Heat Transfer
11.1 Radiation Intensity
11.2 Blackbody Radiation
11.3 Surface Radiation
11.4 Environmental Radiation
11.5 Radiant Interchange between Surfaces Separated by a Nonparticipating Medium
11.6 View Factor
11.6.1 Evaluation of integral
11.6.2 Contour integral representation
11.7 Electrical Network Analog for an Enclosure
11.8 Enclosures with Diffuse Gray Surfaces
11.9 Enclosure with Specularly Reflecting Surfaces
11.9.1 Solution for radiative transfer
11.10 Radiative Transfer in a Plane Layer
11.11 Radiative Flux
11.12 Radiation with Conduction
11.12.1 Limiting cases
11.12.2 Optically thin
11.12.3 Optically thick limit: The diffusion approximation
11.12.4 Pure scattering
Appendix A
Appendix B
B.1 Configuration factor for some common surfaces