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

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.