2.4 Steady Heat Conduction with Variable Heat Conductivity

In this chapter we address several possible variation of the thermal conductivity that can addressed in the BEM formulation. Variation of the thermal conductivity with temperature when are large temperature gradients leads to non-linear heat conduction as k = K(T). In certain applications, the heat conductivity is anisotropic or orthotropic, the conductivity is a second order symmetric tensor, and the BEM methodology developed so far can readily accommodate such cases. Finally, the medium of interest may have a non-homogenous conductivity and this may be accommodated by piece-wise constant modeling of the variation of k, leading to concepts of domain decomposition that are used later in the book in the context of large-scale problems, may be accommodated in restricted cases by a transformation, or may be addressed in a more general sense through a new approach to the fundamental solution. Each of these cases are now addressed in turn.