Free convection effects on extracellular fluid in the presence of a transverse magnetic field

The model of the magnetohydrodynamic boundary-layer equations for a perfectly conducting micropolar fluid is established. This model is applied to study the effects of free convection currents with one relaxation time on the extracellular fluid (the internal environment) in the presence of a constant magnetic field. The state space approach developed in [M. Ezzat, Can. J. Phys. 1 (1994) 311; M. Ezzat, J. Appl. Math. Comput. 64 (1995) 191] is adopted for the 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. This method was proposed by Nowacki in the context of coupled thermoelasticity. The Laplace transform technique is used. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the velocity, the induced electric and magnetic field, the electric current and the electric potential distributions are given and illustrated graphically for given problems.