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)|
|Number of pages||6|
|Journal||International Journal of Heat and Mass Transfer|
|State||Published - 2013|
Bibliographical noteFunding 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.
- Analytical solution
- Stefan problem
- Variable diffusivity