Volume 21, Issue 5
An Unconditionally Stable Hybrid FE-FD Scheme for Solving a 3-D Heat Transport Equation in a Cylindrical Thin Film with Sub-Microscale Thickness

Wei-zhong Dai & Raja Nassar

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J. Comp. Math., 21 (2003), pp. 555-568

Published online: 2003-10

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  • 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 weth two levels in time for the three dimensional heat transport equation in a cylindrical thin film with submicroscale 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

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@Article{JCM-21-555, author = {}, title = {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 = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {5}, pages = {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 weth two levels in time for the three dimensional heat transport equation in a cylindrical thin film with submicroscale 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8887.html} }
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 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 KW - Finite difference KW - Stability KW - Heat transport equation KW - Thin film KW - Microscale AB - 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 weth two levels in time for the three dimensional heat transport equation in a cylindrical thin film with submicroscale 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.
Wei-zhong Dai & Raja Nassar . (1970). 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. 21 (5). 555-568. doi:
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