Unsteady Stagnation Flow of Viscoelastic Fluid Through Porous Medium Over Stretching/Shrinking Surface Using Ucm Model

Abstract

In the present paper, Upper-Convected Maxwell model is used for formulation of the problem of two-dimensional unsteady stagnation point flow of viscoelastic fluid which passes through a porous medium over a stretching/shrinking surface. The effect of magnetic field on flow is also considered in the presence of time dependent heat source/sink. Using similarity parameters, we convert the governing non-linear system of partial differential equations into non dimensional system of ordinary differential equations. This system of equations is solved by using Runge-Kutta fourth order method with shooting technique. Effect of different physical parameters e.g. Maxwell parameter(β), permeability parameter(K), unsteadiness parameter(γ), velocity ratio parameter(λ) etc. on flow and heat transfer characteristics are analyzed and discussed graphically. It is observed that for some values of λ, dual solution also exists for both velocity and temperature, and existence and uniqueness of solution also depends upon unsteadiness parameter. For the validation of present study, the results are compared to previous investigations and found in good agreement.