Boundary Value Problems of Heat Conduction

by Ozisik, M. Necati

• ISBN13: 9780486495156
• ISBN10: 0486495159
• Format: Hardcover
• Copyright: 2002-05-01
• Publisher: Dover Publications

Summary

Intended for first-year graduate courses in heat transfer, including topics relevant to aerospace engineering and chemical and nuclear engineering, this hardcover book deals systematically and comprehensively with modern mathematical methods of solving problems in heat conduction and diffusion. Includes illustrative examples and problems, plus helpful appendixes. 134 illustrations. 1968 edition.

Table of Contents

Basic Relations	1	(42)
The Heat Flux	1	(3)
Total Heat Flow	4	(1)
The Differential Equation of Heat Conduction	5	(2)
The Boundary Conditions	7	(2)
Use of Dimensionless Parameters in Heat-Conduction Problems	9	(3)
Homogeneous and Nonhomogeneous Boundary-Value Problems of Heat Conduction	12	(1)
On the Solution of Homogeneous Problem by Separation of Variables	13	(4)
The Integral-Transform Technique (General Considerations)	17	(3)
Use of Integral Transforms in the Solution of Boundary-Value Problems of Heat Conduction in Finite Regions	20	(9)
Splitting Up of Heat-Conduction Problem into Simpler Problems	29	(3)
Orthogonality of Eigenfunctions	32	(2)
Transformation of Coordinates	34	(3)
Thermal Properties	37	(6)
Heat Conduction In The Cartesian Coordinate System	43	(82)
Integral Transform (Fourier Transform) and Inversion Formula	43	(11)
One-Dimensional Homogeneous Boundary-Value Problems of Heat Conduction in Finite Regions (Solution With Separation of Variables)	54	(5)
One-Dimensional Nonhomogeneous Boundary-Value Problems of Heat Conduction in Finite Regions (Solution with Integral Transform)	59	(10)
One-Dimensional Homogeneous Boundary-Value Problems of Heat Conduction in a Semi-Infinite Region (Solution with Separation of Variables)	69	(3)
One-Dimensional Nonhomogeneous Boundary-Value Problems of Heat Conduction in a Semi-Infinite Region (Solution with Integral Transform)	72	(7)
One-Dimensional Homogeneous Boundary-Value Problem of Heat Conduction in an Infinite Region (Solution with Separation of Variables)	79	(1)
One-Dimensional Nonhomogeneous Boundary-Value Problem of Heat Conduction in an Infinite Region (Solution with Integral Transform)	80	(4)
Two- and Three-Dimensional Nonhomogeneous Boundary-Value Problems of Heat Conduction (Solution by Integral Transform)	84	(17)
Steady-State Problems	101	(9)
Steady-State Problems Involving Periodic Boundary Conditions	110	(4)
Transient Temperature Charts	114	(4)
Summary of Integral Transform of Laplacian in the Cartesian Coordinate System	118	(7)
Heat Conduction In The Cylindrical Coordinate System	125	(69)
Separation of Homogeneous Differential Equation of Heat Conduction	125	(6)
Bessel Functions	131
The Integral Transform (Hankel Transform) and the Inversion Formula	128	(9)
One-Dimensional Homogeneous Boundary-Value Problem of Heat Conduction (Solution with Separation of Variables)	137	(11)
One-Dimensional Nonhomogeneous Boundary-Value Problem of Heat Conduction (Solution with Integral Transform)	148	(15)
Homogeneous Boundary-Value Problems of Heat Conduction Involving More Than One Space Variable (Solution with Separation of Variables)	163	(5)
Nonhomogeneous Boundary-Value Problems of Heat Conduction Involving More Than One Space Variable (Solution with Integral Transform)	168	(13)
Steady-State Problems	181	(5)
Transient Temperature Charts	186	(1)
Summary of Hankel Transform of Part of the Laplacian in the Cylindrical Coordinate System	187	(7)
Heat Conduction In The Spherical Coordinate System	194	(49)
Separation of Homogeneous Differential Equation of Heat Conduction	194	(4)
Legendre Functions and Legendre's Associated Functions	198	(4)
The Integral Transform and the Inversion Formula	202	(3)
Removal of Partial Derivatives with Legendre Transform	205	(6)
One-Dimensional Nonhomogeneous Boundary-Value Problems of Heat Conduction	211	(12)
Homogeneous Boundary-Value Problems of Heat Conduction Involving More Than One Space Variable (Solution with Separation of Variables)	223	(2)
Nonhomogeneous Boundary-Value Problems of Heat Conduction Involving More Than One Space Variable (Solution with Integral Transform)	225	(7)
Steady-State Problems	232	(4)
Transient Temperature Charts	236	(1)
Summary of Legendre Transform of Part of the Laplacian in the Spherical Coordinate System	236	(7)
Duhamel's Method and Use of Green's Functions in the Solution of Heat-Conduction Problems	243	(19)
Duhamel's Method	243	(2)
A Comparison of Solutions Obtained with Duhamel's Method and with Integral Transform Technique	245	(2)
Application of Duhamel's Method	247	(3)
Green's Functions in the Solution of Three-Dimensional Boundary-Value Problems of Heat Conduction for Finite Regions	250	(4)
A Comparison of Solutions Obtained with Green's Function and the Integral-Transform Technique	254	(1)
Green's Function in the Solution of One- and Two-Dimensional Boundary Value Problems of Heat Conduction for Finite Regions	255	(2)
Application of Green's Functions	257	(5)
Composite Regions	262	(39)
The Adjoint Solution Technique---Basic Concepts	263	(2)
Adjoint Solution for a Multilayer Slab with Prescribed Temperature at Outer Surfaces	265	(4)
Adjoint Solution for a Multilayer Slab for other Boundary Condition at the Outer Surfaces	269	(2)
Adjoint Solution for a Multilayer Slab at Steady State	271	(2)
Orthogonal Expansion Technique over a Multilayer Region	273	(3)
Homogeneous Heat-Conduction Problem for a Multilayer Region with Perfect Thermal Contact at the Interfaces	276	(3)
Two-Region Concentric Cylinder with Perfect Thermal Contact at the Interface	279	(3)
Two-Layer Slab with Contact Resistance at the Interface	282	(5)
Nonhomogeneous Heat-Conduction Problem for a Multilayer Region with Perfect Thermal Contact at the Interfaces	287	(7)
Two-Region Concentric Cylinder with Heat Generation	294	(7)
Approximate Methods in the Solution of Heat-Conduction Problems	301	(47)
The Integral Method-General Considerations	301	(7)
Problems in One-Dimensional Finite Region	308	(3)
Problems with Cylindrical and Spherical Symmetry	311	(5)
Problems Involving Heat Generation	316	(2)
Problems Involving Nonlinear Boundary Conditions	318	(5)
Problems Involving Temperature-Dependent Thermal Properties	323	(3)
Problems Involving Melting and Solidification	326	(6)
Problems Involving Ablation	332	(6)
Method of Galerkin in the Solution of Steady, Two-Dimensional Heat-Conduction Problems	338	(5)
Application of Galerkin's Method	343	(5)
Nonlinear Boundary-Value Problems of Heat Conduction	348	(40)
Semi-Infinite Region with Nonlinear Boundary Condition	348	(5)
Problems Involving Temperature Dependent Thermal Properties--Use of Kirchhoff Transformation	353	(3)
Transformation of Independent Variable---Use of Boltzmann Transformation	356	(2)
Semi-Infinite Region with Variable Thermal Conductivity	358	(3)
Transformation of Independent Variable Using Similarity via One-Parameter Group-Theory Method	361	(2)
Similarity Solution of One-Dimensional, Time-Dependent Heat Conduction Equation with Variable Thermal Conductivity and Specific Heat	363	(5)
Similarity Transformation of Two-Dimensional, Time-Dependent Heat Conduction Equation with Variable Thermal Conductivity and Specific Heat	368	(3)
Similarity Solution of Melting of a Slab Initially at Fusion Temperature	371	(3)
Charts for Nonlinear, Transient Heat-Conduction Problems	374	(14)
Numerical Solution of Heat-Conduction Problems	388	(67)
Finite-Difference Approximation of Derivatives	389	(3)
Errors Involved in the Finite Differences	392	(5)
An Explicit Method of Finite-Difference for One-Dimensional Heat Conduction Problems	397	(5)
An Implicit Method of Finite-Difference (Crank-Nicolson Method)	402	(3)
A Direct Method of Solution of Simultaneous Algebraic Equations	405	(2)
An Iterative Method of Solution of Simultaneous Algebraic Equations	407	(2)
Alternating-Direction Implicit Method	409	(3)
Finite Differences in the Cylindrical and Spherical Coordinate Systems	412	(8)
An Implicit Finite Difference for Three-Dimensional, Time-Dependent Heat-Conduction Equation	420	(3)
Curved Boundaries	423	(3)
Various Forms of Approximations for Derivatives	426	(1)
Finite Differences for Problems Involving Change of Phase	427	(8)
Monte Carlo Methods in the Solution of Heat-Conduction Problems	435	(2)
The Fixed-Random-Walk Monte Carlo in the Solution of Steady-State Problems	437	(3)
The Floating-Random-Walk Monte Carlo in the Solution of Steady-State Problems	440	(15)
Heat Conduction In Anisotropic Solids	455	(26)
Thermal Conductivity Tensor	457	(1)
Thermal Resistivity Tensor	458	(2)
Transformation of Axes	460	(1)
Symmetry Considerations in Crystals	461	(1)
A Geometrical Interpretation of Conductivity Tensor	462	(5)
Determination of Principle Conductivities	467	(2)
Differential Equation of Heat Conduction	469	(2)
Example---Heat Flow Across an Anisotropic Slab	471	(1)
Example---Heat Flow Along an Anisotropic Rod	472	(1)
Example---Rectangular Solid with Orthotropic Thermal Properties	473	(8)
APPENDICES	481	(17)
Appendix I Roots of Transcendental Equations	481	(2)
Appendix II Numerical Values of Error Function	483	(2)
Appendix III Numerical Values of Bessel Functions	485	(8)
Appendix IV Some Properties of Bessel Functions	493	(2)
Appendix V Numerical Values of Legendre Polynomials of the First Kind	495	(3)
Index	498