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This paper investigates unsteady hydromagnetic flow of a viscous fluid in a rotating frame. The fluid is bounded by an oscillating porous plate embedded in a porous medium. The Laplace transform and Fourier sine transform methods are employed to find the exact solutions. They satisfy all imposed initial and boundary conditions and as special cases are reduced to some published results from the literature. The graphical results are plotted for different values of pertinent parameters and some interesting conclusions are made.

Stokes’ problem for the flow of an incompressible, viscous fluid over an oscillating plane serves as a benchmark in the literature of fluid dynamics [

On the other hand, flow through porous media is very prevalent in nature and, therefore, has become a principal interest of researchers in many scientific and engineering studies. For example, one can refer to the books of Pop and Ingham [

In order to further discuss the work of Jana et al. [

Consider the unsteady flow of an incompressible viscous fluid occupying the upper porous half-space of the

Geometry of the problem.

The corresponding initial and boundary conditions are

Defining

Taking the Laplace transform of (

Now, applying Fourier sine transform to (

Now, we take the inverse Fourier sine transform of (

Taking the inverse Laplace transform of (

In order to verify the correctness of our obtained solutions, it is important to note that (

The exact solutions for the unsteady hydromagnetic flow of viscous fluid bounded by a porous plate in a porous medium are obtained. The analytical results are displayed for various values of emerging parameters such as Hartmann number

Profiles of velocity for different values of

Profiles of velocity for different values of

Profiles of velocity for different values of

Profiles of velocity for different values of

Profiles of velocity for different values of

Figure

Figure

The unsteady hydromagnetic rotating flow of viscous fluid bounded by an oscillating porous plate embedded in a porous medium is studied. The Laplace transform and Fourier sine transform methods are used for finding the solutions of the problem. The analytical results for nondimensional velocity and skin friction are obtained. The graphical results are plotted. The results show that velocity increases with increasing rotation parameter and permeability parameter whereas it decreases with increasing Hartmann number, suction parameter, and phase angle. Moreover, as the permeability of the medium increases, the velocity field increases in the boundary layer. Thus we can control the velocity field by introducing porous medium in a rotating system.