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Advancing Diffusion Model for Diffusion in a Cube of Medium

  • C.-C. Lin (a1), C.-L. Tsai (a2), P.-K. Wu (a2) and H.-J. Lee (a2)

Abstract

A solution based on an advancing model for the content of diffusion material in a cube of medium is derived. The cube is assumed to be surrounded by diffusion material, and the diffusion material penetrates through all six surfaces and diffuses toward the center of the cube. The model accounts for the interaction between the diffusions in the three principle coordinates of the Cartesian coordinate system. For the first time, an exact solution of the content of the diffusion material based on the advancing model is derived in a clean form for a three-dimensional case.

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*Corresponding author (tsaicl@yuntech.edu.tw)

References

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1. Crank, J., The Mathematics of Diffusion, 2nd Ed., Oxford University Press, Oxford, NY (1975).
2. 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. 957974 (2008).
3. Wang, C.-H., Quantifying Diffusion Substance through Medium Under Varying Environmental Conditions, a Ph.D Thesis, Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology, Taiwan (2010).
4. Pierron, F., Poirette, Y. and Vautrin, A., “A Novel procedure for Indentification of 3D Moisture Diffusion Parameters on Thick Composites: Theory, Validation and Experimental Results,” Journal of Composite Materials, 36, pp. 22192243 (2002).
5. Carslaw, H. S. and Jarger, J. C., Conduction of Heat in Solids, 2nd Ed., Oxford University Press, Oxford, NY (1986).

Keywords

Advancing Diffusion Model for Diffusion in a Cube of Medium

  • C.-C. Lin (a1), C.-L. Tsai (a2), P.-K. Wu (a2) and H.-J. Lee (a2)

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