An Unconditionally Stable Hybrid FE-FD Scheme for Solving a 3-D Heat Transport Equation in a Cylindrical Thin Film with Sub-Microscale Thickness
Year: 2003
Author: Wei-Zhong Dai, Raja Nassar
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 5 : pp. 555–568
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2003-JCM-8887
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 5 : pp. 555–568
Published online: 2003-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Finite element Finite difference Stability Heat transport equation Thin film Microscale.