State space approach to unsteady two-dimensional free convection flow through a porous medium

The equations of magnetohydrodynamic unsteady two-dimensional free convection flow through a porous medium bounded by an infinite vertical porous plate are cast into matrix form using the state space and Laplace-transform techniques. The results obtained can be used to generate solutions in the Laplace-transform domain to a broad class of problems in magnetohydrodynamic free convection flow. The technique is applied to a heated vertical plate problem and to a problem pertaining to a plate under uniform heating. The inversion of the Laplace-transforms is carried out using a numerical approach. Numerical results for the temperature, velocity, and skin friction distributions are given and illustrated graphically for both problems.