Complementary Method for Deriving Concentration of Diffusing Substance in a Medium for Multi-Dimensional Diffusion. (14th November 2013)

• Record Type: Journal Article
• Authors: Tsai, C.-L.; Lin, C.-C.; Lee, H.-J.; Wang, C.-H.
• Is Part Of: Journal of mechanics. Volume 30:Number 1(2014)
• Page Start: 29
• Page End: 38
• Publication Date: 2013-11-14
• Subjects: Complementary method -- Diffusion -- Multi-dimensional; Mechanics, Analytic -- Periodicals; Mechanics -- Periodicals; 620.1005
• DOI: 10.1017/jmech.2013.63
• Languages: English
• ISSNs: 1727-7191

Abstract

Abstract : 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.