On similarity solutions of boundary layer problems with upstream moving wall in non-Newtonian power-law fluids

Our purpose is to give a theoretical analysis of similarity solutions for the boundary layer on the flat plate moving opposite to the stream in a power law fluid. The generalized Blasius boundary value problem is considered with non-homogeneous lower boundary conditions f (0) = 0, f′ (0) = λ (λ > 0), where λ is the velocity parameter. The numerical calculations indicate that there is a critical value λc such that solution exists only if λ < λc. For Newtonian fluid, this phenomena was proved by Hussaini and Lakin (1986, Existence and nonuniqueness of similarity solutions of a boundary-layer problem. Q. J. Mech. Appl. Math., 39, 177–191) and λc was found to be 0.3541… . Following the method in Hussaini et al. (1987, On similarity solutions of a boundary layer problem with an upstream moving wall. SIAM J. Appl. Math., 47, 699–709), we give estimation analytically for λc depending on the power-law exponent n, moreover, the existence of analytic solution is proved.