A hyperbolic microscopic model and its numerical scheme for thermal analysis in an N-carrier system

We extend the concept of the well-known hyperbolic two-step model for micro heat transfer to the case of energy exchanges in a generalized N-carrier system. The model satisfies an energy estimate and hence is well-posed. Based on this result, a finite difference scheme is developed for solving the hyperbolic microscopic model. The scheme is shown to satisfy a discrete analogue of the energy estimate, implying that it is unconditionally stable. Finally, the scheme is tested by an example. The difference between the hyperbolic model and the corresponding parabolic model for a multi-carrier system is also compared.