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Complementary Method for Deriving Concentration of Diffusing Substance in a Medium for Multi-Dimensional Diffusion

Published online by Cambridge University Press:  14 November 2013

C.-L. Tsai ,
C.-C. Lin ,
H.-J. Lee  and
C.-H. Wang
C.-L. Tsai
Affiliation:
Department of Construction Engineering, National Yunlin University of Science & Technology, Yunlin, Taiwan 64002, R.O.C.
C.-C. Lin*
Affiliation:
Department of Civil Engineering, Feng Chia University, Taichung, Taiwan 40724, R.O.C.
H.-J. Lee
Affiliation:
Department of Construction Engineering, National Yunlin University of Science & Technology, Yunlin, Taiwan 64002, R.O.C.
C.-H. Wang
Affiliation:
Center for General Education, TransWorld University, Yunlin, Taiwan 64063, R.O.C.
*
cclin@fcu.edu.tw

Abstract

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Concentration of a diffusing substance in a medium was derived in various cases of uni-dimensional diffusion, including in a semi-infinite medium and a plate-shaped medium. Multi-dimensional diffusion involves boundary conditions in each coordinate direction. The algorithm dealing with uni-dimensional case becomes very complicated in multi-dimensional cases. This study proposes an algorithm, which is called the complementary method, that combines complementary functions of the normalized solution in uni-dimensional diffusion case by multiplication to solve those in various multi-dimensional diffusion cases with dramatically simplified mathematics. Besides, the complementary method is used to solve various kinds of boundary conditions for multi-dimensional diffusion.

Keywords

Complementary methodDiffusionMulti-dimensional

Information

Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 1 , February 2014 , pp. 29 - 38
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

References

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