Bounds, monotonicity, uniqueness, and analytical calculation of a class of similarity solutions for the fluid flow over a nonlinearly stretching sheet

    Authors

    R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Math. Meth. Appl. Sci.

    Keywords

    nonlinearly stretching sheet; existence result; uniqueness result; shooting parameter; analytical method; CONTINUOUS SOLID SURFACES; VISCOUS-FLOW; DIFFERENTIAL-EQUATION; SHRINKING SHEET; LAYER EQUATIONS; HEAT-TRANSFER; BRANCH; PLATE; DIFFUSION; EXISTENCE; Mathematics, Applied

    Abstract

    Invoking some estimates obtained in [F.T. Akyildiz et al., Mathematical Methods in the Applied Sciences 33 (2010) 601-606] (which presented an alternate method of proof for the present problem), we correct the parameter regime considered in [R.A. Van Gorder, K. Vajravelu, and F. T. Akyildiz, Existence and uniqueness results for a nonlinear differential equation arising in viscous flow over a nonlinearly stretching sheet, Applied Mathematics Letters 24 (2011) 238-242] and add some details, which were omitted in the original proof. After this is done, we formulate a more elegant method of proof, converting the nonlinear ODE into a first nonlinear order system. This gives us a more natural way to view the problem and lends insight into the behavior of the solutions. Finally, we give a new way to approximate the shooting parameter =f(0) analytically, through minimization of the L-2([0,)) norm of residual errors. This approximation demonstrates the behavior of the parameter we expect from the proved theorems, as well as from numerical simulations. In this way, we obtain a concise analytical approximation to the similarity solution. In summary, from this analysis, we find that monotonicity of solutions and their derivatives is essential in determining uniqueness, and these monotone solutions can be approximated analytically in a fairly simple way. Copyright (c) 2014 John Wiley & Sons, Ltd.

    Journal Title

    Mathematical Methods in the Applied Sciences

    Volume

    38

    Issue/Number

    4

    Publication Date

    1-1-2015

    Document Type

    Article

    Language

    English

    First Page

    685

    Last Page

    690

    WOS Identifier

    WOS:000348847200011

    ISSN

    0170-4214

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