State space formulation for boundary-layer magneto-hydrodynamic free convection flow with one relaxation time

Abstract

We introduce a magnetohydrodynamic model of a boundary-layer equation for a conducting viscous fluid. The state space approach is adopted for one-dimensional problems including heat sources with one relaxation time. 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 induced-electric-field distributions are given and illustrated graphically for both problems. PACS No.: 47.65+a