ABSTRACT
This chapter begins with the task of constructing a numerical method for solving the general differential equation, which governs the physical processes of interest here. Omission of the convection term reduces the situation to a conduction-type problem. Heat conduction provides a convenient starting point for formulation, because the physical processes are easy to understand and the mathematical complication is minimal. The objectives of the chapter, however, go far beyond presenting a numerical method for heat conduction alone. Other physical processes are governed by very similar mathematical equations. Among these are potential flow, mass diffusion, flow through porous media, and some fully developed duct flows. Three kinds of boundary conditions are encountered in heat conduction. These are: given boundary temperature, given boundary heat flux, boundary heat flux specified via a heat transfer coefficient and the temperature of the surrounding fluid.
