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The sudden melting of a thin vertical flat plate in a Darcian free convection flow

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In this paper a solution of the unsteady free convection boundary-layer equations in porous media is presented for the sudden melting of a thin semi-infinite vertical flat plate. It is assumed that fort<0 that the steady state temperature and velocity has been obtained and at timet=0 the plate starts to melt. Three distinct phases of the temporal development of the flow are considered. An analytical solution is presented which is valid fort≪1 and which shows the initial decay of the boundary-layer. At very large values oft the boundary-layer will disappear and an analytical solution showing this approach is obtained. A numerical solution which matches these two limiting solutions has been obtained by means of a step-by-step method and these results show good agreement with the theoretical results that are valid at small and large values of time.

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Authors and Affiliations

  1. Department of Applied Mathematical Studies, The University of Leeds, LS2 9JT, Leeds, England

    D. B. Ingham

  2. Faculty of Mathematics, University of Cluj, CP 253, R-3400, Cluj, Romania

    I. Pop

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  1. D. B. Ingham
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  2. I. Pop
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Ingham, D.B., Pop, I. The sudden melting of a thin vertical flat plate in a Darcian free convection flow. Acta Mechanica 71, 77–93 (1988). https://doi.org/10.1007/BF01173939

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  • DOI: https://doi.org/10.1007/BF01173939

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