Effects of permeability and electric field on nonlinear Oberbeck Electro-convection in a vertical poorly conducting fluid saturated porous channel

Abstract

The effects of permeability on nonlinear Oberbeck Electro-convection in a poorly conducting fluid saturated porous medium in a vertical channel, when the walls are held at different temperatures with temperature difference perpendicular to gravity, is studied using the modified Navier stokes equation in the presence of both induced and an applied electric field. Both analytical and numerical solutions for the non-linear coupled equations governing the motion are obtained and found that analytical solutions agree well with numerical solutions for values of the buoyancy parameter N <1. It is shown that OBEC can be controlled by maintaining the temperature difference either in the same direction or opposing the potential difference with a suitable value of electric number W. The effect of W on velocity, temperature, rate of heat transfer, skin friction and mass flow rate are computed and the results are depicted graphically. We found that the analytical solutions for velocity and temperature distributions are in close agreement with those obtained from the numerical method for small values of N. We also found that an increase in W accelerates the flow and hence increases linearly the skin friction and mass flow rate. Further, the velocity and temperature have the same behavior for different values of porous parameter when the temperature difference and the potential difference are in the same or in the opposite directions.