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A freezing problem with varying thermal coefficients and convective boundary condition

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Abstract

This study investigates a one-dimensional Stefan problem by taking variable specific heat and thermal conductivity which depends on temperature. Time dependent heat flux is also assumed at the boundary x = 0 in the problem. The similarity solution for the problem is constructed when \( \alpha = \beta \) and \( p = q = 1 \). The uniqueness and existence of the similarity solution to the problem have been also established. The problem is solved approximately for all \( \alpha \) and \( \beta \) with the aid of the shifted Chebyshev tau method. To check the precision of the proposed approximate solution, we have made its comparisons with the obtained exact solution. The comparisons done are shown by tables which sufficiently agree with the exact solution. The effects of the parameters on the movement of interface and temperature profiles are also carried out.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    Ajay Kumar, Abhishek Kumar Singh &  Rajeev

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  1. Ajay Kumar
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  2. Abhishek Kumar Singh
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  3. Rajeev
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Correspondence to Rajeev.

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Kumar, A., Singh, A.K. & Rajeev A freezing problem with varying thermal coefficients and convective boundary condition. Int. J. Appl. Comput. Math 6, 148 (2020). https://doi.org/10.1007/s40819-020-00894-3

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  • DOI: https://doi.org/10.1007/s40819-020-00894-3

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