Asymptotic Behaviour and Existence of Similarity Solutions for a Boundary Layer Flow Problem
Keywords:
Asymptotic behaviour, Boundary layer flow, Existence of solutions, Power law fluid, Singular non-linear boundary value problem.Abstract
The problem of boundary layer flow of a non-Newtonian power-law fluid (which is assumed to be incompressible) is considered. Existence and uniqueness of similarity solutions are considered for all values of the power-law index $n>0$. Conditions are determined (values of $n$ and various parameters within the problem) where existence and uniqueness of solutions hold and where they do not hold. Exact solutions in some cases are exhibited. The asymptotic behaviour of solutions is also determined for all values of $n>0$ of the non-Newtonian fluid.References
Acrivos, A., Shah, M.~J. ,Petersen, E.~E. Momentum and heat transfer in laminar boundary-layer flow of non-Newtonian fluids past external surfaces. {em AIChE Journal}. {bf 6}(2), 312--317 (1960)
Pakdemirli, M. Similarity analysis of boundary layer equations of a class of non-Newtonian fluids. {em International Journal of Non-Linear Mechanics}. {bf 29}(2), 187--196 (1994)
Astarita, G., and Marrucci, G. {em Principles of Non–Newtonian Fluid Mechanics} McGraw-Hill (1974)
Schlichting, H. {em Boundary layer theory}, McGraw-Hill Press, New York (1979)
Bohme, G.~{em Non–Newtonian Fluid Mechanics}, North-Holland Series in Applied Mathematics and Mechanics, Amsterdam (1987)
Nachman, A., and Taliaferro, S. Mass transfer into boundary-layers for power-law fluids. {em Proceedings of the Royal Society of London A}, {bf 365}, 313--326 (1979)
Guedda, M., and Hammouch, Z. Similarity flow solutions of a non-Newtonian power-law fluid flow. {em International Journal of Nonlinear Science} {bf 6}(3), 255--264 (2008)
Guedda, M. Boundary-layer equations for a power-law shear driven flow over a plane surface of non-Newtonian fluids. {em Acta Mechanica}, {bf 202}(1), 205--211 (2009)
Wei, D., and Al-Ashhab, S. Similarity Solutions for a non-Newtonian power-law fluid flow. {em Applied Mathematics and Mechanics (English Edition)}, {bf 35}(9), 1155--1166 (2014) DOI 10.1007/s10483-014-1854-6
Ece, M.~C., and B"{u}y"{u}k, E. Similarity solutions for free convection to power-law fluids from a heated vertical plate. {em Applied Mathematics Letters}, {bf 15}, 1--5 (2002)
Denier, J.~ P., and Dabrowski P. On the boundary-layer equations for power–law fluids. {em Proceedings of the Royal Society of London A}, {bf 460}, 3143--3158 (2004)
Blasius, H.~ Grenzschichten in Fl"{u}ssigkeiten mit kleiner Reibung. {em Z. Math. Phys.}, {bf 56}, 1--37 (1908)
Marin, M., and Lupu,M.~ On harmonic vibrations in thermoelasticity of micropolar bodies. {em Journal of Vibration and Control}, {bf 4}, 507--518 (1998)
Howell, T.~G., JENG, D.~R., and De Witt, K.~J. Momentum and heat transfer on a continuous moving surface in a power-law fluid. {em International Journal of Heat Mass Transfer}, {bf 40}(8), 1853--1861 (1997)
