This investigation presents an analytical study on magnetohydrodynamic (MHD), convective flow of a viscoelastic, incompressible, radiative, chemically reactive, electrically conducting and rotating fluid through a porous medium filled in a vertical channel in the presence of thermal diffusion. A magnetic field of uniform strength is applied along the axis of rotation. The fluid is assumed to act on with a periodic time variation of the pressure gradient in upward direction vertically. One of the plates is maintained at non-uniform temperature and the temperature difference of the walls of the channel is assumed high enough that induces heat transfer due to thermal radiation. The analytical solutions are obtained for velocity, temperature and concentration, by solving the dimensionless governing equations using regular perturbation technique. To assess the effects of various parameters involved in the model

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It is considered the unsteady and incompressible magnetohydrodynamic rotating free convection flow of viscoelastic fluid with simultaneous heat and mass transfer near an infinite vertical oscillating porous plate under the influence of uniform transverse magnetic field and taking Hall current into account. The governing equations of the flow field are then solved by a regular perturbation method for a small elastic parameter. The expressions for the velocity, temperature, and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of graphs. The skin friction on the boundary, the heat flux in terms of the Nusselt number, and the rate of mass transfer in terms of the Sherwood number are also obtained and their behavior discussed. The resultant velocity enhances with increasing Hall parameter and rotation parameter. The reversal behavior is observed with increasing viscoelastic parameters. The resultant velocity enhances and experiences retardation in the flow field with increasing radiation parameters, whereas the secondary velocity component increases with increasing rotation parameters. The temperature diminishes as the Prandtl number and/or the frequency of oscillations. The concentration reduces at all points of the flow field with the increase in the Schmidt number.

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The mode of heat transfer will play an important role in the heat engineering applications. The present work is focused on analytical investigation of unsteady heat and mass transfer rate through porous medium in the presence of uniform transverse magnetic field along with radiation/absorption, heat generation/ absorption and homogeneous chemical reaction effects. The coupled nonlinear partial equations into ordinary differential equations by perturbation method. The effects of various parameters on flow characteristics are investigated .The results are presented through various graphs which are plotted for the effect of different parameters on fluid flow. Impact of Casson parameter leads to decrease the fluid velocity. The heavier species with low conductivity reduces the flow within the boundary layer.The Casson parameter is taken due to the significance of nonNewtonian fluids in real time applications in chemical industries and petroleum refineries.

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