Exact solution of span-wise fluctuating MHD convective flow of second grade fluid through porous medium in a vertical channel with heat radiation and slip condition - Dev Krishan Singh (Kragujevac Journal of Science, 2015)
The magnetohydrodynamic (MHD) convective flow of a viscoelastic, incompressible and electrically conducting fluid through a porous medium filled in a vertical channel is analyzed. The channel plate at y*= - d 2 is subjected to a slip-flow condition and the other at y*= + d 2 to a no-slip condition. The temperature of the plate at y*= + d 2 with no-slip condition is assumed to be varying both in space and time. The temperature difference of the walls of the channel is assumed high enough to induce heat transfer due to radiation. A magnetic field of uniform strength is applied perpendicular to the planes of the channel walls. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is optically-thin gray gas, absorbing/emitting radiation and non-scattering. Exact analytical solutions of the non-linear partial differential equations governing the flow problem are obtained. The velocity field, the temperature field, the amplitude and the phase angle of the skin friction and the heat transfer coefficient are shown graphically and their dependence on the various flow parameters is discussed in detail.