Dual solutions of three dimensional MHD boundary layer flow and heat transfer due to an axisymmetric shrinking sheet with viscous dissipation and heat generation/absorption

Abstract

An analysis is presented to study the effect of magnetic parameter on the certain range of suction parameter where the similarity solution exists of the three dimensional MHD boundary layer flow and heat transfer due to 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 a shooting method. The numerical results of velocity and temperature profiles as well as skin-friction coefficient and rate of heat transfer at the sheet 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 not only on the suction parameter S but magnetic parameter M also. The dual solutions exist in a certain domain of suction parameter S and an increment in the magnetic parameter M increases the domain of S where the solution exists. Also, the thickness of the momentum boundary layer and thermal boundary layer for the second solution are thicker than that of the first solution.