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Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition

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Abstract

The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m, the exponent of the outer flow; λ, the mixed convection parameter and B, the Biot number, as well as the Prandtl number. \({m = \frac{1}{5}}\) is found to be a transitional case with different behaviour depending on whether \({m > \frac{1}{5}}\) or \({m < \frac{1}{5}}\). For \({m > \frac{1}{5}}\), there is a critical value λ c with solutions only for λ ≥ λ c, a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For \({0 < m < \frac{1}{5}}\), there is a value of B where there is a change in behaviour from that seen for \({m > \frac{1}{5}}\) to solutions terminating at a finite value of λ > 0 and continuing to large values of |λ|. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m < 0, though still in the range when there is a solution to the Falkner–Skan, λ = 0, problem, the behaviour is similar to that seen for \({m > \frac{1}{5}}\).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, P.C. 123 Al-Khod, Muscat, Sultanate of Oman

    M. M. Rahman

  2. Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    J. H. Merkin

  3. Department of Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    I. Pop

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  1. M. M. Rahman
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  2. J. H. Merkin
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  3. I. Pop
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Correspondence to J. H. Merkin.

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Rahman, M.M., Merkin, J.H. & Pop, I. Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition. Acta Mech 226, 2441–2460 (2015). https://doi.org/10.1007/s00707-015-1334-2

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  • DOI: https://doi.org/10.1007/s00707-015-1334-2

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