Hydromagnetic stagnation point flow of a viscous fluid over a stretching or shrinking sheet

    Authors

    R. A. Van Gorder; K. Vajravelu;I. Pop

    Comments

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    Abbreviated Journal Title

    Meccanica

    Keywords

    Stagnation point flow; Similarity solution; Stretching sheet; Shrinking; sheet; Existence theorem; Uniqueness theorem; Analytical solution; HOMOTOPY ANALYSIS METHOD; POWER-LAW FLUIDS; NONLINEAR; DIFFERENTIAL-EQUATIONS; BOUNDARY-LAYER EQUATIONS; MIXED CONVECTION; VISCOELASTIC FLUID; HEAT-TRANSFER; MICROPOLAR FLUID; THERMAL-RADIATION; VERTICAL SURFACE; Mechanics

    Abstract

    We establish the existence and uniqueness results over the semi-infinite interval [0, infinity) for a class of nonlinear third order ordinary differential equations of the form f''' (eta) + f (eta) f" (eta) - (f' (eta))(2) - Mf' (eta) + C(C + M) = 0, f (0) = s, f' (0) = chi, lim(eta - > infinity) f' (eta) = C. Such nonlinear differential equations arise in the stagnation point flow of a hydromagnetic fluid. In particular, we establish the existence and uniqueness results, and properties of physically meaningful solutions for all values of the physical parameters M, s, chi and C. Furthermore, a method of obtaining analytical solutions for this general class of differential equations is outlined. From such a general method, we are able to obtain an analytical expression for the shear stress at the wall in terms of the physical parameters of the model. Numerical solutions are then obtained (by using a boundary value problem solver) and are validated by the analytical solutions. Also the numerical results are used to illustrate the properties of the velocity field and the shear stress at the wall. Some exact solutions are also obtained in certain special cases.

    Journal Title

    Meccanica

    Volume

    47

    Issue/Number

    1

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    31

    Last Page

    50

    WOS Identifier

    WOS:000298999500004

    ISSN

    0025-6455

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