Finite difference solutions of magneto hydrodynamic free convective flow with constant suction and variable thermal conductivity in a Darcy-Forchheimer porous medium

This paper presents the study of the effects of variable thermal conductivity and Darcy-Forchheimer on magnetohydrodynamic free convective flow in a vertical channel in the presence of constant suction. The resulting governing equations are non-dimensionalised, simplified and solved using Crank Nicolson type of finite difference method. To check the accuracy of the numerical solution, steady-state solutions for velocity, temperature and concentration profiles are obtained by using perturbation method. Numerical results for the velocity, temperature and concentration profiles are illustrated graphically while the skin friction, Nusselt number and Sherwood number are tabulated and discussed for some selected controlling thermo physical parameters involved in the problem to show the behavior of the flow transport phenomena. It is found that the velocity and temperature increased due to increase in variable thermal conductivity parameter and there is decrease in concentration due to increase in Darcy-Forchheimer number. It is also observed that the numerical and analytical solutions are found to be in excellent agreement.