996 Words4 Pages

Abstract: The effect of thermal and hydrodynamics boundary conditions on electroconvection in saturated porous medium with temperature dependent viscosity (TDV) has been studied in the present paper. Thermal boundary conditions are considered at either at constant temperature or at fixed heat flux of lower surface, while the upper surface is considered to be general convective-radiative exchange. The electrohydrodynamic conditions are included namely, (i) both rigid surfaces (R-R), (ii) lower-rigid and upper-free (R-F), (iii) lower and upper free surfaces (F-F). The eigenvalue problem is computed numerically the Galerkin weighted residual method. It is found that the criticalthermal or electric Rayleigh number making the onset of electroconvection is greatest for the thermal boundary condition of fixed temperature and least for fixed heat flux condition. It is observed that increase in critical thermal Rayleigh number, is to hasten the onset of electroconvection, while increase in Biot number, temperature dependent viscosity and permeability parameter is to delay*…show more content…*

Mathematical Formulation

Consider an incompressible dielectric fluid-saturated Brinkman porous in the presence of uniform AC electric field is perpendicular to the horizontal layer between the surfaces and The constant temperatures of lower surface at and the upper surface at ( ). A Cartesian coordinates (x, y, z) are chosen. Gravity is present . The schematic of the geometry of electroconvection problem is presented in Fig. 1. In this paper, we consider the viscosity as linearly with temperature: where and are positive constants.

The following the governing equations are: Mass conservation: , (1) Momentum conservation: (2)

Energy conservation: , (3) Electrical equation: ,

Mathematical Formulation

Consider an incompressible dielectric fluid-saturated Brinkman porous in the presence of uniform AC electric field is perpendicular to the horizontal layer between the surfaces and The constant temperatures of lower surface at and the upper surface at ( ). A Cartesian coordinates (x, y, z) are chosen. Gravity is present . The schematic of the geometry of electroconvection problem is presented in Fig. 1. In this paper, we consider the viscosity as linearly with temperature: where and are positive constants.

The following the governing equations are: Mass conservation: , (1) Momentum conservation: (2)

Energy conservation: , (3) Electrical equation: ,

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