A stable finite difference scheme for thermal analysis in an N-carrier system

In this study, we extend the concept of the well-known parabolic two-step model for micro heat transfer to model the energy exchanges in a generalized N-carrier system with heat sources. We show that the multi-carrier system satisfies an energy estimate. Based on this result, a finite difference scheme is then developed for thermal analysis in the multi-carrier system. The developed numerical scheme is shown to satisfy a discrete analogue of the energy estimate, implying that it is unconditionally stable. The method is illustrated by several numerical examples.