A note on flow geometries and the similarity solutions of the boundary layer equations for a nonlinearly stretching sheet

    Authors

    R. A. Van Gorder;K. Vajravelu

    Comments

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    Abbreviated Journal Title

    Arch. Appl. Mech.

    Keywords

    Similarity solutions; Nonlinear boundary value problems; Existence; results; Ascoli-Arzela theorem; CONTINUOUS SOLID SURFACES; VISCOUS-FLOW; FLUID; DIFFUSION; BEHAVIOR; Mechanics

    Abstract

    In this note we extend the results of Akyildiz et al. [Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet. Mathematical Methods in the Applied Sciences (www.interscience.wiley.com). doi: 10.1002/mma.1181] for any n > 0, where n is a nonlinear stretching parameter. Thus, the proof presented for the existence of the similarity solutions for the boundary layer equation for a nonlinearly stretching sheet presented in Akyildiz et al. hold not only for positive odd integer values of n, but also for any real value of it > 0: That is, n can be any positive real. We accomplish this by defining the stretching velocity of the sheet as u = csgn(x)vertical bar x vertical bar(n), -infinity < x < infinity, at y = 0 (instead of u = cx '', 0 < x < infinity, y = 0) and accordingly modifying the similarity variables. This definition for u at the stretching surface eliminates the restrictions on n in all future research results related to flow and heat transfer over nonlinear stretching surfaces.

    Journal Title

    Archive of Applied Mechanics

    Volume

    80

    Issue/Number

    11

    Publication Date

    1-1-2010

    Document Type

    Article

    Language

    English

    First Page

    1329

    Last Page

    U2

    WOS Identifier

    WOS:000282541100009

    ISSN

    0939-1533

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