Summary

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.