TY - JOUR
T1 - An Unconditionally Stable Hybrid FE-FD Scheme for Solving a 3-D Heat Transport Equation in a Cylindrical Thin Film with Sub-Microscale Thickness
AU - Dai , Wei-Zhong
AU - Nassar , Raja
JO - Journal of Computational Mathematics
VL - 5
SP - 555
EP - 568
PY - 2003
DA - 2003/10
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8887.html
KW - Finite element, Finite difference, Stability, Heat transport equation, Thin film, Microscale.
AB - <p style="text-align: justify;">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.</p>