Radiation and thermal diffusion effects on an unsteady MHD free convection mass-transfer flow past an infinite vertical porous plate with the hall current and a heat source

Abstract

UDC 536.25 An analysis is performed to study the effects of radiation and thermal diffusion on an unsteady MHD free convection heat-and mass-transfer flow of an incompressible, electrically conducting, viscous fluid past an infinite vertical porous plate with the Hall current and a heat source. The flow is considered under the influence of a constant suction velocity and a uniform magnetic field applied normally to the flow. The dimensionless governing equations are solved numerically by the Galerkin finite element method. The effects of the flow parameters on the primary and secondary velocities, temperature, species concentration, shearing stresses, Nusselt number, and Sherwood number are calculated and presented in figures and tables. The results obtained show that a decrease in the temperature boundary layer thickness occurs when the Prandtl number and radiation parameter are increased and an increase in the Schmidt number leads to a decrease in the concentration boundary layer thickness.Introduction. The study of the natural convection induced by the simultaneous action of buoyancy forces arising due to thermal and mass diffusion is of considerable interest in many industrial applications, such as geophysics, oceanography, drying process, and solidification of binary alloys. The effects of magnetic field on free convective flows are of importance in liquid metals, electrolytes, and ionized gases. The thermophysics of the MHD problems with mass transfer is of interest in power engineering and metallurgy. Many cross galvano-and thermomagnetic effects occur in the boundary area between the hydraulics and thermophysics which are relevant in the study of semiconductor materials. The conduction mechanism in ionized gases in the presence of a strong magnetic field is different from that in a metallic substance. An electric current in ionized gases is generally carried out by electrons which undergo successive collisions with other charged or neutral particles. In ionized gases, the current is not proportional to the applied potential, except for the cases where the electric field is very weak. However, in the presence of a strong electric field, the electrical conductivity is affected by a magnetic field. Consequently, the conductivity parallel to the electric field is reduced. Hence, the current is reduced in the direction normal to both electric and magnetic fields. This phenomenon is known as the Hall effect.The MHD convective flows of different geometries with account for various processes were studied in a number of works [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The Hall current effect on the MHD convective flows has been considered in [1-4, 9, 12-15].In the present paper, the effects of radiation and thermal diffusion on an unsteady MHD free convective heatand mass-transfer flow past an infinite vertical porous plate with the Hall current and a heat source is studied. The flow is subjected to a constant suction velocity and to a uniform magnetic field applied normally to the flow. The problem is d...

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