An analysis of an oscillatory magnetohydrodynamic (MHD) convective flow of a second order (viscoelastic), incompressible, and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel porous plates is presented. The two porous plates with slip-flow condition and the no-slip condition are subjected respectively to a constant injection and suction velocity. The pressure gradient in the channel varies periodically with time. A magnetic field of uniform strength is applied in the direction perpendicular to the planes of the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature of the plate with no-slip condition is non-uniform and oscillates periodically with time and the temperature difference of the two plates is assumed high enough to induce heat radiation. The entire system rotates in unison about the axis perpendicular to the planes of the plates. Adopting complex variable notations, a closed form solution of the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters of the problem. The velocity, temperature and the skin-friction in terms of its amplitude and phase angle have been shown graphically to observe the effects of the viscoelastic parameter γ, rotation parameter Ω, suction parameter λ , Grashof number Gr, Hartmann number M, the pressure A, Prandtl number Pr, radiation parameter N and the frequency of oscillation ω .

An oscillatory MHD convective flow of an incompressible, viscoelastic (Walter's liquid model-B) and electrically conducting fluid through porous medium filled in a vertical porous channel is analyzed. The two porous plates of the channel are subjected to a constant injection and suction velocity as shown in Fig.1. A magnetic field of uniform strength is applied perpendicular to the plates of the channel. The temperature of one of the plates varies periodically and the temperature difference between the two plates is high enough to induce the heat due to radiation. A closed form solution of the purely oscillatory flow is obtained. The velocity, temperature and the skin-friction in terms of its amplitude and phase angle have been shown graphically to observe the effects of viscoelasticity γ, injection/suction parameter λ, Grashof number Gr, Hartmann number M, Hall parameter H, the pressure A, Prandtl number Pr, Radiation parameter N and the frequency of oscillation ω.

Hall current effect on visco-elastic MHD oscillatory convective flow through a porous medium in a vertical channel with heat radiation is investigated.An oscillatory MHD convection flow of visco-elastic, incompressible, electrically conducting fluid in a vertical channel filled with porous medium in the presence of Hall currents is studied analytically.A magnetic field of uniform strength is applied in the direction normal to the planes of the plates.The temperature of one of the plates varies periodically and the temperature difference of the plates is high enough to induce heat transfer due to radiation.A closed form solution of the problem is obtained.The effects of various parameters on the velocity profiles, the skinfriction in terms of the amplitude and the phase angle are shown graphically and discussed in detail.

In this paper the magnetohydrodynamic (MHD) mixed convection flow of an electrically conducting, viscoelastic and incompressible fluid through a porous medium filled in a vertical porous channel is analyzed. The fluid is injected into the channel with a constant velocity through one of the plates and simultaneously removed through the other porous plate of the channel The flow is generated by a periodic pressure gradient varying with time. A magnetic field of uniform strength is also applied perpendicular to the plates. Closed form solution of the problem is obtained for the velocity, temperature, skin friction and the rate of heat transfer in terms of their amplitude and phase.

In this paper an oscillatory flow of a viscoelastic, incompressible and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel plates is discussed. One of these plates is subjected to a slip-flow condition and the other to a no-slip condition. The pressure gradient in the channel oscillates with time. A magnetic field of uniform strength is applied in the direction perpendicular to the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature difference of the two plates is also assumed high enough to induce heat transfer due to radiation. A closed form analytical solution to the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters entering into the problem. A number of particular cases have been shown by dotted curves in the figures. During the analysis it is found that the physical and the mathematical formulations of the problems by Makinde and Mhone (2005), Mehmood and Ali (2007), Kumar et al. (2010) and Choudhury and Das (2012) are not correct. The correct solutions to all these important oscillatory flow problems are deduced.