ABSTRACT
This chapter applies the law of energy conservation to find the differential and integral equations of thermal transport. It reviews the conversion of the differential diffusion equation to a set of difference equations using finite-difference methods on a rectangular mesh. There are several options, some of which lead to severe constraints on the time step for numerical stability. The chapter derives thermal transport difference equations from the finite-element viewpoint on a conformal mesh. It is relatively easy to extend solutions to complex materials where the thermal conductivity and specific heat vary with temperature. The chapter discusses special problems of numerical stability on triangular meshes. Instabilities can be avoided by setting constraints on triangle geometry in the mesh generation process. The chapter shows that pulsed magnetic field penetration into conductive materials is governed by diffusion equations. It covers two-dimensional finite-element solutions with a single component of vector potential.
