In the present study, unsteady MHD boundary layer flow of a rotating Walters’-B fluid (viscoelastic fluid) over an infinite vertical porous plate embedded in a uniform porous medium with fluctuating wall temperature and concentration taking Hall and ion-slip effects into consideration is discussed. The MHD flow in the rotating fluid system is induced due to the non-torsional oscillations of the plate in its own plane and the buoyancy forces arises from temperature and concentration differences in field of gravity. The partial differential equations governing the fluid motion are solved analytically by using regular perturbation and variable separable methods by assuming very small viscoelastic parameter. Solution for velocity field in the case when natural frequency due to rotation and Hall current is equals to the frequency of oscillations i.e. in the case of resonance is also obtained. In order to note the influences of various system parameters and to discuss the important flow characteristics, the numerical results for fluid velocity in the non-resonance case, temperature and species concentration are computed and depicted graphically versus boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form. An interesting observation recorded that there arises flow reversal in the primary flow direction due to high rotation. When natural frequency is greater than the frequency of oscillations the fluid velocity in the primary flow direction is maximum at the plate whereas incase when natural frequency is smaller than the frequency of oscillations, it is maximum in the neighborhood of the plate.

In the present analytical study, we have considered unsteady hydromagnetic heat and mass transfer natural convection flow of an electrically conducting, heat absorbing and chemically reacting fluid past an exponentially accelerated vertical plate in a uniform porous medium taking Hall current and rotation into account. The species concentration near the plate is considered to be varies linearly with time. Two particular cases for plate temperature are considered i.e. (i) plate temperature is uniform and (ii) plate temperature varies linearly with time and after some time it is maintained at uniform temperature. The coupled partial differential equations governing the fluid flow problem are solved analytically for fluid velocity, temperature and species concentration using Laplace transform method. To examine the physical characteristic of this problem the graphs for velocity, temperature, species concentration, skin friction, Nusselt number and Sherwood number distributions are computed and generated for various values of different pertinent flow parameters. It is observed that for small thermal diffusion, the free stream value of velocity and temperature are achieved nearer to the plate in comparison to that for large thermal diffusion.

A mathematical analysis of unsteady MHD free convective flow of an incompressible, chemically reacting, electrically and thermally conducting fluid past an oscillating vertical plate embedded in a fluid saturated porous medium in a rotating system taking Hall and ion-slip currents into account is presented. The plate temperature is considered to be linear function of time for a certain time interval and thereafter it is kept at a constant temperature while species concentration at the surface of the plate is considered to be linear function of time. The governing coupled partial differential equations are solved by using Laplace transform technique. Two particular cases of interest are considered to obtain the solution of velocity field i.e. (i) when the natural frequency due to rotation and Hall current is different from the frequency of oscillations, and (ii) when the natural frequency due to rotation and Hall current is equal to the frequency of oscillations (i.e. the case of resonance). The expressions for skin friction, Nusselt number and Sherwood number are also derived. To analyze the flow features of the present problem the velocity, temperature and concentration distributions are depicted graphically whereas the skin friction at the plate, Nusselt number and Sherwood number are presented in tabular form for various values of different pertinent flow parameters.

A study on the effects of Hall current, ion-slip and permeability on unsteady Magnetohydrodynamic Couette-Poiseuille flow within porous plates filled with porous medium in the presence of a moving uniform transverse magnetic field which is fixed relative to the moving porous plate is carried out. Flow within the channel is generated due to accelerated movement of the lower plate of the channel along x-axis and by an applied constant pressure gradient acting along x-axis. An exact solution of the governing equations is found by Laplace transform method. Numerical values of analytical solution for fluid velocity and that of shear stress at the moving porous plate of the channel are depicted for various values of pertinent flow parameters. It is noticed from the numerical result that, for the pure fluid regime, suction tends to enhance fluid velocity in the primary flow direction whereas injection has reverse effect on it. For the small permeable regime, suction tends to enhance fluid velocity in the primary flow direction in the upper half of the channel whereas injection has reverse effect on it.