Exact solution of MHD mixed convection periodic flow in a rotating vertical channel with heat radiation

Magnetohydrodynamic (MHD) mixed convection flow of a viscous, incompressible and electrically conducting fluid in a vertical channel is analyzed analytically. A magnetic field of uniform strength is applied perpendicular to the planes of the channel walls. The fluid is acted upon by a periodic variation of the pressure gradient in the vertically upward direction. The temperature of one of the plates is non-uniform and the temperature difference of the walls of the channel is high enough to induce heat transfer due to radiation. The fluid and the channel rotate in unison with an angular velocity about the axis normal to the plates of the channel. An exact analytical solution of the problem is obtained. Two cases of small and large rotation have been considered to assess the effects of different parameters involved in the flow problem. The velocity field, the amplitude and the phase angle of the shear stress are shown graphically and discussed in detail. During analysis it is found that the flow problem studied by Makinde and Mhone (2005) is incorrect physically and mathematically.