: An analytical study of magnetohydrodynamic (MHD) mixed convection flow of a viscoelastic, incompressible and electrically conducting fluid through a porous medium filled in a vertical channel is carried out. A magnetic field of uniform strength is applied perpendicular to the planes of the channel walls. The fluid is acted upon by periodic time 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 rotations 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 skin friction are shown graphically and discussed in detail.