| Summary: | The unsteady free convection flow, with heat and mass transfer, of an electrically conducting viscoelastic fluid, through a porous medium of variable permeability is investigated. The flow domain is a half space, bounded by a vertical porous plate, with the constant heat flux, constant concentration and a rectilinear translation in its plane with constant velocity. The applied magnetic field of uniform strength is perpendicular to the plate and the magnetic lines of force are fixed relative to plate or, to fluid. Permeability of the porous medium decreases exponentially, with respect to time t, relative to a constant mean value. The closed forms of the temperature, concentration and velocity fields are determined by means of the Laplace transform and method of separation of variables. Numerical calculations are carried out and graphically displayed in order to study the effects of several parameters such as Hartmann number, permeability of porous medium, Prandtl number, heat source/sink parameter, Schmidt number, chemical reaction parameter. The numerical results show that, if the applied magnetic field is fixed to the plate the fluid flows more slowly than if the magnetic field is fixed to fluid. If the magnetic field strength is high, the fluid moves more slowly than into weak magnetic fields. Keywords: Viscoelastic fluid, Free convection, Magnetic field, Porous medium, Variable permeability, MSC2010database: 76A10, 76R10, 76 W05, 76S05
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