The paper attempt to investigate the effect of injection/suction on the flow of electrically conducting fluid through a porous channel filled with porous material. A magnetic field of uniform strength is applied perpendicular to the plane of the porous channel. The effect of heat radiation, heat source and chemical reaction has been taken into consideration. The governing equations are solved analytically by using complex variable notation. The expressions for velocity, temperature, concentration, skin friction coefficient, rate of heat transfer and rate of mass transfer have been obtained. The effect of various parameters entering the governing equation have been evaluated numerically and expressed graphically and in tabular form. A detailed discussion is given in the result and discussion section of the research paper.

An exact solution of span-wise fluctuating magnetohydrodynamic (MHD) convective flow problem of a viscous, incompressible and electrically conducting fluid through a porous medium filled in an infinite vertical channel is obtained. The channel walls at and at are subjected to span-wise cosinusoidally varying species concentration and temperature. y* = -d/2 - d/2 and at y* = +d/2 A magnetic field of uniform strength is applied perpendicular to the planes of the channel plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. The temperature difference between the plates is high enough to induce the heat due to radiation. The Rosseland approximation is used to describe the radiation heat flux for the fluid as optically-thick gray gas, absorbing/emitting but non-scattering medium. The partial differential equations governing the flow are solved exactly under the prescribed boundary conditions for the velocity, temperature and species concentration fields. The velocity, temperature, concentration and the skin-friction, Nusselt number, Sherwood number in terms of their amplitudes and phase angles have been shown graphically to observe the effects of different flow parameters. The final results are then discussed in detail in the last section of the paper with the help of figures.

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 analysis of an unsteady MHD convective flow of a viscoelastic, incompressible and electrically conducting fluid through porous medium in a vertical channel in the presence of chemical reaction is carried out. A magnetic field of uniform strength is applied in the direction normal to the planes of the plates. The Hall currents have been taken into account. The temperature and species concentration of either of the channel plates at zz∗ = ±dd22 varies periodically with time. The temperature difference of the channel plates is high enough to cause heat radiation. A closed form solution of MHD flow is obtained analytically. The effects of different parameters on the flow are discussed with the help of graphs. Keywords---Hall current, viscoelastic, MHD, periodic, reacting, radiating, convective flow.

An analysis of magnetohydrodynamic (MHD) mixed convection flow of a viscous, incompressible and electrically conducting fluid through a porous medium filled in a vertical channel is carried out. The walls of the vertical channel lying in the planes y(*)= +/- d/2 are porous and the fluid is injected through one of the porous plates of the channel with constant velocity and simultaneously sucked through the other plate with the same velocity. The temperature of the plate at y(*) = +d/2 is assumed to be varying in space and time as T*(y*,z*,t*) = T-1 + (T-2 - T-1) cos(pi z*/d - omega*t*). 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. The fluid is acted upon by spanwise sinusoidal fluctuating pressure gradient in the vertically upward direction. It is also assumed that the conducting fluid is optically-thin gray gas, absorbing/emitting radiation and nonscattering. The non-linear partial differential equations governing the flow problem along with its boundary conditions are non-dimensionalized by non-similar transformation and an exact analytical solution of the problem is obtained. The velocity field, the temperature field, the amplitude and the phase angle of the skin friction are shown graphically and discussed in detail.

An investigation of heat and mass transfer effect on incompressible chemically reacting, radiating and electrical conducting viscoelastic fluid through porous medium in porous vertical channel has been carried out. The magnetohydro dynamics (MHD) flow is assumed to be laminar and fully developed. A uniform magnetic field is applied in the direction perpendicular to the plane of the plates. The equations governing the flow are solved by perturbation technique. The velocity, temperature, concentration fields, coefficient of skin friction, rate of heat and mass transfer are evaluated numerically and discussed with the help of graphs and tables.

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.

An oscillatory MHD convective flow of an incompressible, viscoelastic and electrically conducting fluid in a vertical porous channel is analyzed. The two porous plates 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 magnetic Reynolds number is assumed to be very small so that the induced magnetic field is negligible. The entire system rotates about an axis perpendicular to planes of the plates. The temperature difference between the 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 rotation parameter Ω, suction parameter �� , Grashoff number Gr, Hartmann number M, the pressure A, Prandtl number Pr, Radiation parameter N and the frequency of oscillation ��.

An analysis of the unsteady flow of a dusty viscous, incompressible, electrically conducting fluid in a vertical porous channel rotating with constant angular velocity under the influence of periodic pressure gradient is presented. The left porous plate of the channel is subjected to a uniform injection and the right porous plate to same uniform suction respectively. A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed to be small enough so that the induced magnetic field is negligible. The whole system rotates in unison about the axis normal to the planes of the plates. Analytical solutions for the velocities and temperatures of the fluid and the dust particles are obtained. The influence of the various parameters appearing in the equations of velocities and temperatures of the fluid and the dust particles have been numerically evaluated and expressed graphically.

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

A theoretical analysis of an oscillatory viscoelastic, incompressible and electrically conducting fluid in an infinite vertical porous channel is presented. The entire system rotates about the axis normal to the plane of the plate with uniform angular velocity \( \Upomega \). A closed form solution for the velocity, temperature and skin friction are obtained. Results are presented through graphs and table for the various values of rotation, viscoelastic, permeability and frequency of oscillation parameter and discussed in detail.

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.

The effects of Hall current and rotation on MHD free convection flow in a vertical rotating channel filled with porous medium have been studied. A uniform magnetic field is applied in the direction normal to the planes of the plates. The entire system rotates about an axis normal to the planes of the plates with uniform angular velocity Omega*. The temperature of one of the plates varies periodically and the temperature difference of the plates is high enough to induce radiative heat transfer. The effects of various parameters on the velocity profiles, the skin friction, temperature field, rate of heat transfer in terms of their amplitude and phase angles are shown graphically.

In this paper, an analytical study on unsteady MHD free convective viscous incompressible flow of electrically-conducting fluid with periodic heat and mass transfer past an infinite vertical porous flat plate in slip flow regime is presented. A uniform magnetic field perpendicular to the plate is applied. The effects of thermal radiation and chemical reaction are included. The effects of flow parameters and thermo physical properties on the flow, temperature and concentration fields across the boundary layer are investigated. The forms of the wall shear stress, Nusselt number and Sherwood number are derived. The results are shown in figures and tables followed by a quantitative discussion.

The flow of viscous incompressible fluid in an infinite horizontal channel has been analysed. The lower portion of the channel is filled with porous medium while upper portion is filled with clear fluid. The lower stationary porous plate of the channel is subjected to a transverse sinusoidal injection velocity. The upper porous plate moving with uniform velocity is subjected to a constant suction velocity. Due to this type of injection velocity the flow becomes three-dimensional. The analytic expressions for velocity, temperature, skin friction and rate of heat transfer are obtained by using series expansion method. The effects of different parameters on the velocity field, temperature field, skin friction and the rate of heat transfer are discussed with the help of graphs.

An analysis of an oscillatory free convective flow of a viscous incompressible and electrically conducting fluid with radiative heat in a vertical porous channel is carried out. The stationary plate and the plate in motion are subjected to a constant injection and suction velocity respectively. A uniform magnetic field is applied in the direction normal to the plates. The entire system rotates about an axis normal to the planes of the plates with uniform angular velocity Omega*. For small and large rotations the dependence of the steady and unsteady resultant velocities and their phase differences on various parameters are discussed in detail.

An analytical study is performed to examine an oscillatory heat and mass transfer mixed convection flow in the presence of heat source/sink and Soret effect (thermal diffusion effect). The entire system rotates about an axis normal to the planes of the plates with a constant angular velocity Omega*. The dimensionless governing equations are solved using two term harmonic and non-harmonic functions. The dependence of the steady and un-steady resultant velocities, skin frictions and their phase differences on various parameters are discussed in detail for small and large rotations.

The present analysis examines the free convective magnetohydrodynamic (MHD) flow of a viscous incompressible and electrically conducting fluid past a hot vertical porous plate. The temperature of the plate varies both in space and time. The non-linear coupled partial differential equations are solved by the series expansion method. The dependence of the important flow characteristics i.e the skin friction and the Nusselt number on various parameters are discussed.