Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-11T03:58:58.369Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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.

Keywords

Complementary methodDiffusionMulti-dimensional
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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Crank, J., The Mathematics of Diffusion, 2nd Edition, Oxford University Press, Oxford, NY (1975).Google Scholar
2.Carslaw, H. S. and Jarger, J. C., Conduction of Heat in Solids, 2nd Edition, Oxford University Press, Oxford, NY (1986).Google Scholar
3.Chang, T.-W., Wang, C.-H. and Tsai, C.-L., “Advancing Boundary Model for Moisture Expansion in a Composite Laminate,” Journal of Composite Materials, 42, pp. 957–974 (2008).Google Scholar
4.Wang, C.-H., “Quantifying Diffusion Substance through Medium under Varying Environmental Conditions,” Ph.D Thesis, Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology, Taiwan (2010).Google Scholar
5.Lin, C.-C., Tsai, C.-L., Wu, P.-K. and Lee, H.-J., “Advancing Diffusion Model for Diffusion in a Cube of Medium,” Journal of Mechanics, 28, pp. 345–354 (2011).Google Scholar
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).Google Scholar