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Non-linear Oberbeck-electroconvection (OBEC) in a poorly electrically conducting fluid through 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 analytical results agree well with numerical results 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.

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Nonlinear oberbeck convection of a couple stress fluid in a vertical porous channel in the presence of transverse magnetic field is investigated in this paper. Analytical solution is obtained using the perturbation technique for vanishing values of the buoyancy parameter. Numerical solution of the nonlinear governing equations is obtained using the finite difference technique to validate the results obtained from the analytical solutions. The influence of the physical parameters on the flow, such as couple stress parameter, Hartmann number, temperature parameter, porous parameter and buoyancy parameter are evaluated and presented graphically. A new approach is used to analyse the flow for strong, weak and comparable porosity cases. It is found that increase in porous parameter, couple stress parameter, Hartmann number and temperature parameters decrease the velocity considerably.Kathmandu University Journal of Science, Engineering and Technology Vol. 12, No. I, June, 2016, Page: 49-62