Numerical investigation of MHD stagnation point flow and heat transfer over a permeable shrinking sheet with external magnetic field, viscous dissipation and Joule heating

Abstract

The present study considers the steady laminar magnetohydrodynamic (MHD) boundary layer flow of a viscous and incompressible electrically conducting fluid near the stagnation point on a horizontal continuously shrinking surface, with variable wall temperature and a constant magnetic field applied normal to the surface of the sheet. The surface is assumed to be permeable, allowing either suction or injection at the wall. By introducing an appropriate similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using an implicit finite-difference scheme known as the Keller-box method for some values of the selected parameters. The effects of the governing parameters, namely the shrinking parameter λ, the suction parameter f0 and the magnetic parameter M on the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles are determined and discussed. For the present study, the analysis is limited to the case where the Prandtl number is fixed at unity, i.e. Pr = 1 and the Eckert number, Ec = 0.5. It is found that solutions for the shrinking sheet only exist when the magnitude of the shrinking parameter is less than some limiting critical value λc. Where solutions do exist, they are either a unique solution or dual solutions, and for large enough suction at the wall, there may even be triple solutions. For the shrinking sheet, in the presence of viscous dissipation and Joule heating, the magnetic field increases the surface shear stress and slightly increases the surface heat transfer rate.