On three models of magneto-hydrodynamic free-convection flow

Abstract

In this work, we introduce a model of the boundary-layer equations of a generalized thermofluid for an electrically conducting pourous medium in the presence of a constant magnetic field. This model is applied to each generalization, Cattaneo theory with one relaxation time, Chandrasekharaiah–Tzou theory, as well as classical Fourier law. The state space approach developed by Ezzat (Can. J. Phys. 86, 1241 (2008)), is adopted for the one-dimensional problems including heat sources. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semi-space problem with a plane distribution of heat sources located inside the fluid. Numerical results for the velocity, temperature, and induced-magnetic and electric field distributions are given and illustrated graphically for both problems. The comparisons are made for all functions with the results obtained in the three theories.