An Unconditionally Stable Hybrid FE-FD Scheme for Solving a 3-D Heat Transport Equation in a Cylindrical Thin Film with Sub-Microscale Thickness (Journal of Computational Mathematics, 2021)
Heat transport at the microscale is of vital importace in microtechnology applications. The heat transport equation is different from the traditional heat transport 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 develop a hybrid finite element-finite difference (FE-FD) scheme with two levels in time for the three dimensional heat transport equation in a cylindrical thin film with sub-microscale thickness. It is shown that the scheme is unconditionally stable. The scheme is then employed to obtain the temperature rise in a sub-microscale cylindrical gold film. The method can be applied to obtain the temperature rise in any thin films with sub-microscale thickness, where the geometry in the planar direction is arbitrary.
Keywords: Finite element; Finite difference; Stability; Heat transport equation; Thin film; Microscale.