Heat Conduction Using Green's Function

Introduction to Green's Functions Heat Flux and Temperature Differential Energy Equation Boundary and Initial Conditions Integral Energy Equation Dirac Delta Function Steady Heat Conduction in One Dimension GF in the Infinite One-Dimensional Body Temperature in an Infinite One-Dimensional Body Two Interpretations of Green's Functions Temperature in Semi-Infinite Bodies Flat Plates Properties Common to Transient Green's Functions Heterogeneous Bodies Anisotropic Bodies Transformations Non-Fourier Heat Conduction Numbering System in Heat Conduction Geometry and Boundary Condition Numbering System Boundary Condition Modifiers Initial Temperature Distribution Interface Descriptors Numbering System for g(x, t) Examples of Numbering System Advantages of Numbering System Derivation of the Green's Function Solution Equation Derivation of the One-Dimensional Green's Function Solution Equation General Form of the Green's Function Solution Equation Alternative Green's Function Solution Equation Fin Term m2T Steady Heat Conduction Moving Solids Methods for Obtaining Green's Functions Method of Images Laplace Transform Method Method Of Separation of Variables Product Solution for Transient GF Method of Eigenfunction Expansions Steady Green's Functions Improvement of Convergence and Intrinsic Verification Identifying Convergence Problems Strategies to Improve Series Convergence Intrinsic Verification Rectangular Coordinates One-Dimensional Green's Functions Solution Equation Semi-Infinite One-Dimensional Bodies Flat Plates: Small-Cotime Green's Functions Flat Plates: Large-Cotime Green's Functions Flat Plates: The Nonhomogeneous Boundary Two-Dimensional Rectangular Bodies Two-Dimensional Semi-Infinite Bodies Steady State Cylindrical Coordinates Relations for Radial Heat Flow Infinite Body Separation of Variables for Radial Heat Flow Long Solid Cylinder Hollow Cylinder Infinite Body with a Circular Hole Thin Shells, T = T (phi, t) Limiting Cases for 2D and 3D Geometries Cylinders with T = T (r, z, t ) Disk Heat Source on a Semi-Infinite Body Bodies with T = T (r, phi, t ) Steady State Radial Heat Flow in Spherical Coordinates Green's Function Equation for Radial Spherical Heat Flow Infinite Body Separation of Variables for Radial Heat Flow in Spheres Temperature in Solid Spheres Temperature in Hollow Spheres Temperature in an Infinite Region Outside a Spherical Cavity Steady State Steady-Periodic Heat Conduction Steady-Periodic Relations One-Dimensional GF One-Dimensional Temperature Layered Bodies Two- and Three-Dimensional Cartesian Bodies Two-Dimensional Bodies in Cylindrical Coordinates Cylinder with T = T (r, phi, z,omega) Galerkin-Based Green's Functions and Solutions Green's Functions and Green's Function Solution Method Alternative form of the Green's Function Solution Basis Functions and Simple Matrix Operations Fins and Fin Effect Conclusions Applications of the Galerkin-Based Green's Functions Basis Functions in some Complex Geometries Heterogeneous Solids Steady-State Conduction Fluid Flow in Ducts Conclusion Unsteady Surface Element Method Duhamel's Theorem and Green's Function Method Unsteady Surface Element Formulations Approximate Analytical Solution (Single Element) Examples Problems References Appendices Index