Closed-form solutions for unsteady magnetohydrodynamic flow in a porous medium with wall transpiration

Abstract

This problem deals with an unsteady two-dimensional magnetohydrodynamic flow of incompressible viscous fluid over a flat plate with wall transpiration embedded in a porous medium. Exact solutions corresponding to the Stokes first and second problems are obtained using an extended separation of variable technique together with the similarity arguments. The corresponding starting solutions are presented as the sum of steady state and transient solutions. Further, it is found that for small time t the difference between the steady state and the transient solutions is significant. However, for large values of t, both of these solutions become identical. These solutions do not involve any unevaluated integral and are expressed in terms of exponential and complementary error functions. Effects of the material parameters on the velocity fields are investigated by plotting the graphs. The nature of the wall shear stress engendered due to the flow is also studied by presenting the results in graphical and tabular forms. Some well-known and fundamental solutions existing in the literature are also obtained as the limiting cases of our solutions.