Magnetohydrodynamic free convection flow above an isothermal horizontal plate

Abstract

In the present study a new similarity theory is developed to study the fluid flow and heat transfer characteristics for the steady laminar natural convection boundary layer flow of an incompressible and electrically conducting fluid past a semi-infinite horizontal plate subjected to a constant wall temperature under the action of transverse magnetic field. The governing parabolic boundary layer PDEs are transformed to ordinary differential equations using similarity transformation. This results in a set of three coupled, non-linear ordinary differential equations with variable coefficients (representing the interaction of the temperature and velocity fields) which are then solved by the shooting method. Asymptotic analyses and series solutions are also constructed to explore the mathematical behaviour of the solutions. The numerical results are obtained for various values of Prandtl number and magnetic field parameter ζ. The effects of various values of Prandtl number and magnetic field parameter ζ on the velocity profiles, temperature profiles, wall shear stress and heat transfer coefficients are presented. The results indicate that the wall shear stress τw decreases whereas the local Nusselt number Nux increases with increase in Prandtl number if the magnetic field parameter ζ is held constant at a particular value. On the other hand, both the wall shear stress and Nusselt number decrease with increase in the magnetic field parameter ζ for a fluid with constant Prandtl number. Generic correlations for Nux and τw have been developed in terms of the fluid Prandtl number Pr and magnetic field parameter ζ. A generic relation for free convection flow with magnetohydrodynamic effects, that is equivalent to the well-known Reynolds analogy for forced convection flow, has also been formulated in the present work.