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Explicit Solutions for the Solomon‐Wilson‐Alexiades’s Mushy Zone Model with Convective or Heat Flux Boundary Conditions

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  • Domingo A. Tarzia

Abstract

We complete the Solomon‐Wilson‐Alexiades’s mushy zone model (Solomon, 1982) for the one‐phase Lamé‐Clapeyron‐Stefan problem by obtaining explicit solutions when a convective or heat flux boundary condition is imposed on the fixed face for a semi‐infinite material. We also obtain the necessary and sufficient condition on data in order to get the explicit solutions for both cases which is new with respect to the original model. Moreover, when these conditions are satisfied, the two phase‐change problems are equivalent to the same problem with a temperature boundary condition on the fixed face and therefore an inequality for the coefficient which characterized one of the two free interfaces of the model is also obtained.

Suggested Citation

  • Domingo A. Tarzia, 2015. "Explicit Solutions for the Solomon‐Wilson‐Alexiades’s Mushy Zone Model with Convective or Heat Flux Boundary Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnljam:v:2015:y:2015:i:1:n:375930
    DOI: 10.1155/2015/375930
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    References listed on IDEAS

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    1. Yong Huang & Yadong Shang, 2012. "The Bäcklund Transformations and Abundant Exact Explicit Solutions for a General Nonintegrable Nonlinear Convection‐Diffusion Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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