Table of Content

Open Access iconOpen Access

ARTICLE

Analytic Closed Solution for the Heat Conduction with Time Dependent Heat Convection Coefficient at One Boundary

Han Taw Chen1, Shao Lun Sun1, Hui Chen Huang1, Sen Yung Lee1,2

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China
Corresponding author. Tel: +886-6-2757575 ext. 62150; E-mail: sylee@mail.ncku.edu.tw.

Computer Modeling in Engineering & Sciences 2010, 59(2), 107-126. https://doi.org/10.3970/cmes.2010.059.107

Abstract

A new solution method is proposed to develop the analytic closed form solution for the one dimensional heat conduction with one mixed type boundary condition and general time dependent heat convection coefficient for the first time. The solution method is the combination of an extension of the shifting function method developed by Lee and his colleagues and a series expansion. It is shown that the solution is simple and accurate. The convergence of the present analysis is very fast. One can find that when the dimensionless Fourier number is greater than 0.2, the error for the one term approximation solution of the infinite serious solution can be less than 2%. Examples are given to reveal the solution method. Numerical results are compared with those in the existing literature.

Keywords


Cite This Article

Chen, H. T., Sun, S. L., Huang, H. C., Lee, S. Y. (2010). Analytic Closed Solution for the Heat Conduction with Time Dependent Heat Convection Coefficient at One Boundary. CMES-Computer Modeling in Engineering & Sciences, 59(2), 107–126.



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 1169

    View

  • 1009

    Download

  • 0

    Like

Share Link