CFD solutions for magnetohydrodynamic natural convection over horizontal and vertical surfaces

This paper investigates the effects of a magnetic field on the natural convective boundary layer flow of an electrically conducting fluid adjacent to horizontal as well as vertical surfaces. This has allowed us to establish overall similarities and several subtle differences between the two cases. Previously published studies concentrated on obtaining self-similar solutions at the cost of assuming very restrictive variation of the magnetic field along the surface. In the present work, a numerical model and an in-house computer program have been developed to solve directly the non-linear boundary layer equations which can accommodate any arbitrary variation of the magnetic field. Special emphasis is given to the case of uniform magnetic field which perhaps represents the most practical case and which cannot be solved by the similarity theory. Computations show that the Nusselt number and the skin-friction coefficient decrease as the magnetic field increases. It is shown that the detailed characteristics of the velocity profiles and the values of Nusselt number and skin-friction coefficient for the case of a magnetic field which admits similarity are significantly different from those when a uniform magnetic field is applied, thus showing the importance of the present model.