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The effect of uniform internal heat generation on the onset of steady Marangoni convection in a horizontal layer of fluid

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In this paper we use a combination of analytical and numerical techniques to analyse the effect of uniform internal heat generation on the onset of steady Marangoni convection in a horizontal layer of quiescent fluid heated from below. We obtain for the first time the closed form analytical solution for the onset of steady Marangoni convection and give a comprehensive description of the stability characteristics of the layer both when the lower boundary is conducting and when it is insulating to temperature perturbations. We also present asymptotically- and numerically-calculated results for the linear growth rates of the steady modes. In particular, we show that the effect of increasing the internal heat generation is always to destabilise the layer and give asymptotic expressions for the critical Marangoni number and critical wavenumber in the limit of large internal heat generation.

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  1. Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, G1 1XH, Glasgow, UK

    S. K. Wilson

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  1. S. K. Wilson
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Wilson, S.K. The effect of uniform internal heat generation on the onset of steady Marangoni convection in a horizontal layer of fluid. Acta Mechanica 124, 63–78 (1997). https://doi.org/10.1007/BF01213018

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  • DOI: https://doi.org/10.1007/BF01213018

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