A. Introduction

The widespread use of numerical techniques for the solution of heat conduction problems is very well documented in the technical literature. A number of factors have contributed to the popularity of numerical techniques. They are capable of handling complex geometrical configurations, composite media, both nonlinear and linear boundary conditions, and variable termophysical properties. Transient as well as steady-state conduction problems can be analyzed. Perhaps the most important factor, however, has been the rapid increase in the availability of digital computers to practicing engineers, enabling them easily to apply numerical techniques for the solution of everyday engineering problems.

Numerical techniques, as applied to conduction heat transfer, can be classified as either finite-difference or finite-element methods. This section will deal only with finite-difference methods; Section 166 concentrates on finite-element methods.

A general discussion of finite-difference methods and their use for flow predictions has been presented in Section 1.4. This section will concentrate on the application of these methods to conduction problems, in which the geoemtrical configuration of the region is of considerable importance. Although a number of generalized conduction programs are commercially available, the practicing engineer can easily employ the techniques to be described to obtain satisfactory accuracy with computational power as small as that provided by a desktop personal computer (PC).

The steps used to obtain a finite-difference solution can be categorized as follows: