A stable and convergent three-level finite difference scheme for solving a dual-phase-lagging heat transport equation in spherical coordinates

Heat transport at the microscale is of vital importance in microtechnology applications. The heat transport equation is different from the traditional heat diffusion equation since a second-order derivative of temperature with respect to time and a third-order mixed derivative of temperature with respect to space and time are introduced. In this study, we consider the heat transport equation in spherical coordinates and develop a three level finite difference scheme for solving the heat transport equation in a microsphere. It is shown that the scheme is unconditionally stable and convergent. The method is illustrated by two numerical examples.