Existence and uniqueness theorem due to non-Newtonian flow past a stretching sheet: Revisited

Abstract

Steady laminar boundary layer flow over a stretching sheet has received considerable attention due to its immense theoretical and practical applications in the engineering and technology field. Couple of highly nonlinear differential equations arise due to the laminar boundary layer flow and heat transfer of a non-Newtonian viscoelastic, electrically conducting second grade fluid past a stretching sheet. After boundary layer approximation and similarity transformation, the governing equations reduce to the following couple of highly nonlinear ordinary differential equations (4) and (5), with the boundary conditions given by equation (6).

Fortunately equation (4) admits a simple closed form solution. In this work a simple mathematical analysis is carried out to study the existence, uniqueness and behavior of exact solutions of the fourth order nonlinear coupled ordinary differential equations (4) and (5). The ranges of the parametric values are obtained for which the system has a unique pair of solutions, a double pair of solutions and infinitely many solutions.