Unsteady Fluid Flow and Heat Transfer Through a Porous Medium in a Horizontal Channel with an Inclined Magnetic Field

This paper investigates the unsteady flow and heat transfer of a viscous, incompressible, and electrically conducting fluid through a porous medium in a horizontal channel. The basic physical properties of the fluid and the porous medium are constant. The fluids considered are those with the Prandtl number less than 1. The channel walls are made of horizontal permeable plates, which are at constant but different temperatures. Fluid suction/injection through the plates occurs at a velocity perpendicular to the plates, whose intensity is a cosine function of time. The applied external magnetic field is homogeneous and inclined in relation to the transverse plane of the channel. The problem is dealt with through an inductionless approximation. Fluid flow is instigated by constant pressure drops along the channel. The equations used to describe the problem are transformed to dimensionless forms and solved analytically using the perturbation method. Approximate analytical expressions for dimensionless fluid flow velocity and dimensionless temperature are determined as functions of the following physical parameters: Prandtl number, Hartmann number, porosity factor, frequency, amplitude, and magnetic field inclination angle. Numerical results are presented as diagrams and tables and are used to analyse the influence of physical parameters on the fluid flow velocity and temperature.