Computational and Analytical Heat Conduction

In this rigorous and thorough analysis three concepts of heat conduction are studied: improved lumped-differential formulations, the generalized integral transform technique, and symbolic computation. Addressing problem formulation, solution methodology and computational implementation, the authors develop an improved lumped-differential formulation for heat conduction problems, present a unified hybrid numerical-analytical solution methodology for linear and nonlinear problems, and provide an introduction to mixed symbolic-numerical computation. Special topics and applications illustrate the theory, including extended surfaces, drying, ablation, conjugated problems and anisotropic media. Sample computer programs, using mixed symbolic-numerical computation, are presented in notebook format, developed within the Mathematica system.