A note on flow geometries and the similarity solutions of the boundary layer equations for a nonlinearly stretching sheet
Abbreviated Journal Title
Arch. Appl. Mech.
Similarity solutions; Nonlinear boundary value problems; Existence; results; Ascoli-Arzela theorem; CONTINUOUS SOLID SURFACES; VISCOUS-FLOW; FLUID; DIFFUSION; BEHAVIOR; Mechanics
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.
Archive of Applied Mechanics
"A note on flow geometries and the similarity solutions of the boundary layer equations for a nonlinearly stretching sheet" (2010). Faculty Bibliography 2010s. 896.