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MHD oblique stagnation-point flow towards a stretching/shrinking surface

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Abstract

The steady MHD oblique stagnation-point flow towards a stretching/shrinking surface in a viscous and electrically conducting fluid and in the presence of a uniform magnetic field is studied. The external magnetic field is parallel to the dividing streamline of the oblique stagnation-pint flow. The governing Navier–Stokes equations are reduced to a system of two ordinary differential equations. Solutions of these equations are evaluated numerically for various values of the governing parameters, namely the magnetic parameter M, the stretching/shrinking parameter \(\lambda \) and the two constants \(\alpha \) and \(\beta \) arising in the model. It is found that dual (upper and lower branch) solutions exist and that there is a critical value \(\lambda _c\) of \(\lambda \), dependent on M, with solutions only in \(\lambda \ge \lambda _c\) with the lower solution branch terminating as \(\lambda \rightarrow -(1+M)\). It is shown that the values of \(\lambda _c\) increase as M is increased thus extending the range of similarity solutions in the opposing flow regime. It is also found that the stagnation line is displaced due to the effect of MHD with a region of reversed flow being observed near to the wall for a shrinking surface.

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Authors and Affiliations

  1. Mathematics Division, School of Distance Education, Universiti Sains Malaysia, 11800, USM, Pulau Pinang, Malaysia

    Y. Y. Lok

  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

Authors
  1. Y. Y. Lok
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  2. J. H. Merkin
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  3. I. Pop
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Correspondence to I. Pop.

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Lok, Y.Y., Merkin, J.H. & Pop, I. MHD oblique stagnation-point flow towards a stretching/shrinking surface. Meccanica 50, 2949–2961 (2015). https://doi.org/10.1007/s11012-015-0188-y

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  • DOI: https://doi.org/10.1007/s11012-015-0188-y

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