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A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab

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  • Ryoichi Chiba

Abstract

A two-dimensional differential transform method is applied to solve one-dimensional phase change problems in a slab of finite thickness, which is subjected to convective thermal loading at one surface and a constant prescribed temperature at the other. In the problems, the initial temperature of the slab does not necessarily have to be the same as the fusion temperature. A series solution is derived for the temperature profile in the melting or solidifying slab with temperature-dependent thermal conductivity and volumetric heat capacity. The latent heat effect of the phase change is incorporated into the temperature-dependent heat capacity. Numerical results demonstrate the effects of the temperature-dependent parameters on the transient temperature profile of the slab.

Suggested Citation

  • Ryoichi Chiba, 2014. "A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, November.
    • Handle: RePEc:hin:jnlaaa:684293
    DOI: 10.1155/2014/684293
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    Cited by:

    1. P. V. Ananth Subray & B. N. Hanumagowda & S. V. K. Varma & A. M. Zidan & Mohammed Kbiri Alaoui & C. S. K. Raju & Nehad Ali Shah & Prem Junsawang, 2022. "Dynamics of Heat Transfer Analysis of Convective-Radiative Fins with Variable Thermal Conductivity and Heat Generation: Differential Transformation Method," Mathematics, MDPI, vol. 10(20), pages 1-15, October.

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