Abstract
A one-phase Stefan problem with a variable diffusivity is investigated. For two particular choices of diffusivity - one varying as a power law of position the other as a power function of the potential slope - exact similarity solutions are obtained. Unlike other similarity solutions that involve a time exponent n=12, the derived solutions can exhibit exponents in the range 0 < n < 1. Application of these solutions in the verification of a numerical scheme highlights the importance of a correct numerical treatment for handling variations in diffusivity.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 80-85 |
| Number of pages | 6 |
| Journal | International Journal of Heat and Mass Transfer |
| Volume | 58 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - 2013 |
Bibliographical note
Funding Information:This work was supported by the STC program of the National Science Foundation via the National Center for Earth-surface Dynamics under the agreement no. EAR-0120914 . The authors are also grateful to the reviewers useful suggestions.
Keywords
- Analytical solution
- Stefan problem
- Variable diffusivity
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