Abstract
Heat transport at the microscale is of vital importance in microtechnology applications. The heat transport equation is different from the traditional heat diffusion equation because 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 three-dimensional 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. The method is illustrated by numerical examples.
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