Analysis of heat transfer and stability of magnetohydrodynamic natural convection above a horizontal plate with heat flux boundary condition

A boundary layer analysis is performed for the steady laminar natural convection of an electrically conducting viscous incompressible fluid above a horizontal plate in the presence of a transverse magnetic field. The governing boundary layer equations are transformed to a set of non-linear ordinary differential equations which are then solved numerically using the shooting method. The effects of Prandtl number Pr and magnetic field parameter ζ on the velocity profiles, temperature profiles, skin friction coefficients and heat transfer coefficients are presented and discussed. A linear stability analysis based on the parallel flow model is also carried out to study the vortex instability of such flow. The present results indicate that the skin friction coefficient cfx decreases whereas the local Nusselt number Nux increases with increase in Pr if ζ is held constant. On the other hand, both the skin friction coefficient and Nusselt number decrease with increase in ζ for a fluid with constant Pr. Generic correlations for Nux and cfx have been developed in terms of Pr and ζ. A generic relation for magnetohydrodynamic free convection flow, equivalent to the Reynolds analogy for forced convection, has also been formulated.