MHD flow and heat transfer over stretching/shrinking sheets with external magnetic field, viscous dissipation and Joule effects

The present article considers the steady magnetohydrodynamic (MHD) laminar boundary layer flow of a viscous and incompressible electrically conducting fluid near the stagnation point on a horizontal stretching or shrinking surface, with variable surface temperature and a constant magnetic field applied normal to the surface of the sheet. The governing system of partial differential equations is first transformed into a system of ordinary differential equations by introducing an appropriate similarity transformation, which is then solved numerically using a finite-difference scheme known as the Keller-box method. The effects of the governing parameters on the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles are determined and discussed. Results indicate that for the stretching sheet, solution exists and is unique for all values of the stretching/shrinking parameter $\lambda $, while for the shrinking sheet, solutions only exist up to some critical values $\lambda = \lambda _{{\rm c}} $, and these solutions may be unique, dual and sometimes triple. (c) 2011 Canadian Society for Chemical Engineering