Dual Solutions for the Magnetohydrodynamic Stagnation-Point Flow of a Power-Law Fluid Over a Shrinking Sheet

    Authors

    T. R. Mahapatra; S. K. Nandy; K. Vajravelu;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    J. Appl. Mech.-Trans. ASME

    Keywords

    dual solutions; stability analysis; stagnation-point flow; power-law; fluid; shrinking sheet; BOUNDARY-LAYER-FLOW; MHD VISCOUS-FLOW; STRETCHING SHEET; HEAT-TRANSFER; ANALYTIC SOLUTION; 2ND-GRADE FLUID; SURFACE; SUCTION; PLATE; Mechanics

    Abstract

    We show that there exist bounded self-similar solutions to the steady state problem of the MHD stagnation point flow of a power-law fluid over a shrinking sheet. We then discuss the stability of the unsteady solutions about each steady solution, showing that one steady state solution corresponds to a stable solution whereas the other corresponds to an unstable solution. The stable solution corresponds to the physically relevant solution. Further, we obtain numerical results for each solution, which enable us to discuss the features of the respective solutions. Our method of finding dual solutions and analyzing stability is of practical application to those interested in engineering analysis, as it provides one with a way to determine whether a given steady state solution is physically meaningful. Hence, our study is useful not only as a discussion of the problem of the MHD stagnation point flow of a power-law fluid over a stretching or shrinking sheet but as a demonstration of the treatment of fluid flow problems with multiple solutions. [DOI: 10.1115/1.4005584]

    Journal Title

    Journal of Applied Mechanics-Transactions of the Asme

    Volume

    79

    Issue/Number

    2

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    6

    WOS Identifier

    WOS:000302580000023

    ISSN

    0021-8936

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