AN UNCONDITIONALLY STABLE HYBRID FE-FD SCHEME FOR SOLVING A 3-D HEAT TRANSPORT EQUATION IN A CYLINDRICAL THIN FILM WITH SUB-MICROSCALE THICKNESS

• 来源期刊: 计算数学（英文版）
• 关键词: Finite element Finite difference Stability Heat transport equation Thin film Microscale
• 年，卷（期）: 2003,（5）
• 页码范围: 555-568
• 页数: 14页
• 语种: 英文

摘要

Heat transport at the microscale is of vital importance in microtechnology applications.The heat transport equation is different from the traditional heat transport equation sincea second order derivative of temperature with respect to time and a third-order mixedderivative 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 intime 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 isthen employed to obtain the temperature rise in a sub-microscale cylindrical gold film. Themethod can be applied to obtain the temperature rise in any thin films with sub-microscalethickness, where the geometry in the planar direction is arbitrary.