Conduction-radiation effects on periodic magnetohydrodynamic natural convection boundary layer flow along a vertical surface

The problem of magnetohydrodynamic natural convection periodic boundary layer flow of an electrically conducting and optically dense gray viscous fluid along a heated vertical plate is analyzed. Here, magnetic field is considered in the transverse direction and taken as a sinusoidal function of x¯. In the analysis radiative heat flux is examined by assuming optically thick radiation limit. Attempt is being made to obtain the solutions valid for liquid metals by taking Pr << 1. Three numerical techniques are adopted to obtain the solutions of the problem, namely, (i) direct numerical simulation (DNS) method which is used to integrate the boundary layer equations directly, (ii) implicit finite difference (Keller-box) method on the reduced boundary layer equations obtained by stream function formulation (SFF) and (iii) finite difference method along with Gaussian elimination technique on transformed equations obtained by applying the primitive variable formulation (PVF). Effects of physical parameters, namely, the magnetic field parameter, M, radiation parameter, Rd and the surface temperature parameter, θw, on the numerical values thus obtained for local skin friction coefficient and local Nusselt number coefficient as well as on the streamlines and isotherm lines are shown graphically for large values of X.