Two exact solutions of a Stefan problem with varying diffusivity

V. R. Voller; F. Falcini

doi:10.1016/j.ijheatmasstransfer.2012.11.003

Two exact solutions of a Stefan problem with varying diffusivity

V. R. Voller, F. Falcini

Civil, Environmental, and Geo- Engineering

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

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	https://doi.org/10.1016/j.ijheatmasstransfer.2012.11.003
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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10.1016/j.ijheatmasstransfer.2012.11.003

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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.",

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AU - Voller, V. R.

AU - Falcini, F.

N1 - 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.

PY - 2013

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N2 - 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.

AB - 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.

KW - Analytical solution

KW - Stefan problem

KW - Variable diffusivity

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JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

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ER -

Two exact solutions of a Stefan problem with varying diffusivity

Abstract

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Keywords

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