Mixed convection flow of an electrically conducting fluid in a vertical channel using Robin boundary conditions with heat source/sink

A numerical study of steady, mixed convection of electrically conducting fluid in a vertical channel with heat source/sink is analyzed using Robin boundary conditions. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperature of the external fluid are considered. The governing equations are solved analytically using regular perturbation method and numerically by Runge–Kutta fourth order method with shooting technique. The graphs illustrating the effects of various parameters involved in the problem on the flow as well as average velocity and Nusselt number are presented and discussed. It is found that the effect of negative electric field load parameter is to aid the flow while the effect of positive electric field load parameter is to oppose the flow as compared to the case of short circuit. The analytical and numerical solutions agree very well for small values of perturbation parameter.