Analytical Solution of Unsteady MHD Periodic Flow of a Non-Newtonian Fluid Through a Porous Channel

The unsteady magnetohydrodynamic (MHD) periodic flow of a non-Newtonian fluid through a porous channel analytically has been investigated. The unsteady one-dimensional equations of motion and energy considering the MHD, Darcian porous media, and radiation terms are used. The constitutive equation for generalized Maxwell fluids is considered. After nondimensionalizing the governing equations, an analytical solution has been developed. The effects of the rheological behavior of fluid on velocity and shear stress profiles along channel width at different time periods have been discussed and depicted. The effect of porosity on velocity and shear stress profiles and the combined effect of viscoelasticity and porosity has been studied. Results show that by increasing the Deborah number for generalized Maxwell fluid, the average velocity through the porous media increases. It is found that the fluid maximum velocity point could be changed along the channel width by normalized relaxation time variations of the fluid. It also could be seen that the effect of Darcy number variations on the velocity and shear stress is more considerable in the generalized Maxwell fluids than in Newtonian fluids.