State space formulation to viscoelastic fluid flow of magnetohydrodynamic free convection through a porous medium

Abstract

In this work we formulate the state space approach for one-dimensional problems of viscoelastic magnetohydrodynamic unsteady free convection flow through a porous medium past an infinite vertical plate. Laplace transform techniques are used. The resulting formulation is applied to a thermal shock problem and to a problem for the flow between two parallel fixed plates both without heat sources. Also a problem with a distribution of heat sources is considered. A numerical method is employed for the inversion of the Laplace transforms. Numerical results are given and illustrated graphically for the problem considered.