A compact finite difference scheme for solving a three-dimensional heat transport equation in a thin film

Abstract

Heat transport at the microscale is of vital importance in microtechnology applications. The heat transport equation differs from the traditional heat diffusion equation in having a second-order derivative of temperature with respect to time and a third-order mixed derivative of temperature with respect to space and time. In this study, we develop a high-order compact finite difference scheme for the heat transport equation at the microscale. It is shown by the discrete Fourier analysis method that the scheme is unconditionally stable. Numerical results show that the solution is accurate. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 441–458, 2000