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Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

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Abstract

The present article investigates the dual nature of the solution of the magneto-hydrodynamic (MHD) stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting method. It is found that the dual solutions of the flow exist for certain values of the velocity ratio parameter. The special case of the first branch solutions (the classical Newtonian fluid model) is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.

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Authors and Affiliations

  1. Department of Basic Science & Humanities, College of Electrical & Mechanical Engineering (CEME), National University of Sciences and Technology, Islamabad, 46000, Pakistan

    N. S. Akbar

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

    Z. H. Khan

  3. Department of Mathematics, University of Malakand, Khyber Pakhtunktwo, 18800, Pakistan

    Z. H. Khan

  4. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    R. U. Haq & S. Nadeem

Authors
  1. N. S. Akbar
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  2. Z. H. Khan
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  3. R. U. Haq
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  4. S. Nadeem
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Correspondence to Z. H. Khan.

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Akbar, N.S., Khan, Z.H., Haq, R.U. et al. Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet. Appl. Math. Mech.-Engl. Ed. 35, 813–820 (2014). https://doi.org/10.1007/s10483-014-1836-9

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  • DOI: https://doi.org/10.1007/s10483-014-1836-9

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2010 Mathematics Subject Classification

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