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

Abstract

The method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, is applied to the nondimensional equations of unsteady free convection boundary layer flow through a porous medium bounded by an infinite vertical plate. The formulation is valid for one-dimensional problems with or without heat sources. The resulting formulation together with the Laplace transform technique is applied to a variety of problems. The solution to a thermal shock problem and to a problem for the flow between two parallel fixed plates, both without heat sources, is obtained. Also a problem with adistribution of heat sources is considered. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the velocity distribution are given and illustrated graphically for each problem.