Title

A Note On Flow Geometries And The Similarity Solutions Of The Boundary Layer Equations For A Nonlinearly Stretching Sheet

Keywords

Ascoli-Arzela theorem; Existence results; Nonlinear boundary value problems; Similarity solutions

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 n > 0: That is, n can be any positive real. We accomplish this by defining the stretching velocity of the sheet as u = csgn(x)|x| n, -∞ < x < ∞, at y = 0 (instead of u = cx n, 0 < x < ∞, 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. © 2009 Springer-Verlag.

Publication Date

11-1-2010

Publication Title

Archive of Applied Mechanics

Volume

80

Issue

11

Number of Pages

1329-1332

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00419-009-0370-6

Socpus ID

77957862117 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/77957862117

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