Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface

The development of velocity and temperature fields of an incompressible viscous electrically conducting fluid, caused by an impulsive stretching of the surface in two lateral directions and by suddenly increasing the surface temperature from that of the surrounding fluid, is studied. The partial differential equations governing the unsteady laminar boundary-layer now are solved numerically using an implicit finite difference scheme. For some particular cases, closed form solutions are obtained, and for large values of the independent variable asymptotic solutions are found. The surface shear stresses in x- and y-directions and the surface heat transfer increase with the magnetic field and the stretching ratio, and there is a smooth transition from the short-time solution to the long-time solution.