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

  • C.-L. Tsai (a1), C.-C. Lin (a2), H.-J. Lee (a1) and C.-H. Wang (a3)

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.

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2.Carslaw, H. S. and Jarger, J. C., Conduction of Heat in Solids, 2nd Edition, Oxford University Press, Oxford, NY (1986).
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6.Tsai, C.-L. and Lin, C.-C., “Diffusion in Quadri-Infinite Medium,” The 35th National Conference on Theoretical and Applied Mechanics, November 18–19, Tainan, Taiwan (2011).

Keywords

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

  • C.-L. Tsai (a1), C.-C. Lin (a2), H.-J. Lee (a1) and C.-H. Wang (a3)

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