ABSTRACT
This chapter considers the solution of ordinary differential equations that govern one-dimensional steady-state conduction. The computational aspects are considered in terms of the basic mechanisms involved and physical interpretation of the numerical results. The basic governing equation for conductive heat transfer processes is obtained by applying the principle of conservation of energy to a differential element located at a given position in the conduction region. In many cases of practical interest, complex boundary conditions, arbitrary geometry of the conduction region, and material property variation with temperature complicate the problem. Numerical methods then become necessary to obtain the information needed for analysis and design. A nite element formulation is often appropriate for multidimensional steady-state conduction, especially when the geometric boundaries of the conducting region are irregular and are not aligned with a natural coordinate system. In several problems the variation of temperature in the conduction region is large enough to cause a signi cant variation in thermal conductivity of the material.
