State Space Approach to Unsteady FreeConvection Effects on Perfectly Conducting Viscoelastic Fluid

Abstract

In this work, we introduce magneto hydrodynamic model of boundary-layer equations for a perfectly conducting viscoelastic fluid. This model is applied to study the effects of free convection currents with one relaxation time on the flow of a perfectly conducting visco-elastic fluid through a porous medium, which is bounded by a vertical plane surface. The state space approach is adopted for the solution of one-dimensional problems. The resulting formulation together with the Laplace transform technique is applied to a thermal shock problem. A discussion of the effects of cooling and heating on a perfectly conducting viscoelastic fluid is given. Numerical results are illustrated graphically for the problem considered.