An exact Analysis of Melting Phenomena Based on Non-Classical Heat Equation with Moving Boundary Problem: Application of Melting-Freezing

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Abstract Purpose: The purpose of this study is to introduce a melting phenomena based non-classical heat equation with latent heat as a function of the moving interface and its velocity, which has not often been taken into consideration previously in the literature available due to the non-linearity of the interface condition. In view of these problems, three mathematical models are proposed for non-classical moving boundary problems including both conduction and convection effects. The applied heat flux on the surface is subjected to a control function at x = 0. In a certain situation, latent heat varies with moving interface and its velocity, and in another, latent heat may be treated as constant. Design/methodology: In the context of non-linear variable latent heat, we provided an analytical analysis for single-phase and double-phase moving boundary problems. The similarity transformation approach has been used to obtain analytical results. The impact of associated problem parameters are discussed in detail. Findings: From this study, it is observed that in the case of variable latent heat, moving interface get accelerated more in comparison to constant latent heat. Furthermore, when the Peclet number and the value of the coefficient of control function increase then the melting process become enhanced. In the present study, convection plays a key role during the melting process. This study may improve the theoretical and mathematical understanding of a shoreline problem and is applicable in geology and thermal management systems.

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