Free convection effects on a viscoelastic boundary layer flow with one relaxation time through a porous medium

Effects of free convection currents with one relaxation time on the flow of a viscoelastic conduction fluid through a porous medium, which is bounded by a vertical plane surface, have been studied. The state space approach developed in Ezzat (Can. J. Phys, Vol. 72, p. 311, 1994; J. Appl. Math. Comput., Vol. 64, p. 1, 1994) is adopted for the solution of one-dimensional problems in magnetohydrodynamic free convection flow with thermal relaxation time. The resulting formulation together with the Laplace transform technique is applied to a variety of problems. The solutions to a problem of an electrically conducting visocelastic fluid in the presence of hydromagnetic free convection flow and to a problem of the flow between two parallel fixed plates are obtained. A discussion of the effects of cooling and heating on a viscoelastic conducting fluid is given. Numerical results are illustrated graphically for both problems considered.