Dual solutions of three dimensional viscous flow and heat transfer due to a shrinking sheet with slip and suction

Abstract

In the present paper, an analysis is presented to study the effect of slip and suction on the dual nature of the solution of the three dimensional boundary layer flow of an incompressible fluid and heat transfer towards a porous axisymmetric shrinking sheet. The governing equations are transformed into self-similar non-linear ordinary differential equations by using suitable similarity transformations and then the transformed equations are solved numerically using the shooting technique with Runge-Kutta forth order method. The numerical results of velocity and temperature profiles as well as skin-friction coefficient and Nusselt number are obtained and displayed graphically with different pertinent parameters to show interesting aspects of the solution. The investigation explores the conditions of the non-existence, the existence and duality of the similarity solutions which depend on the suction parameter S as well as slip parameter λ. The dual solutions exist in a certain domain of suction parameter S and due to an increment in the slip parameter λ, the domain of S where the similarity solution exists, also increases. Also, for increasing values of S and λ, the thickness of the both momentum and thermal boundary layer is decreasing for the first solution while for second solution it is increasing.