Unsteady Stokes Flow of a non-Newtonian Fluid Between Two Parallel Porous Plates with Periodic Suction and Injection

Unsteady Stokes Flow of non-Newtonian Fluid Between Two Parallel Porous Plates

Abstract

Unsteady Stokes flow of a non-Newtonian fluid is the time-dependent motion of a fluid where inertial forces are negligible and the fluid exhibits non-Newtonian behaviour, which means that its viscosity is not constant and can depend upon factors such as the rate of strain, time, or fluid history. Non-Newtonian fluids, including viscoelastic and shear-thinning, are used in many applications, particularly in the flow of blood, synovial fluids, and mucus, as well as in industry like polymer extrusion and oil recovery. The current research is based on the unsteady Stokes flow of a non-Newtonian fluid in parallel porous plates with periodic injection and suction at the plates under no slip conditions. The governing equations are solved analytically using the stream function, and the velocity components and pressure distribution are examined. The findings demonstrate that non-Newtonian fluids behave very differently from Newtonian fluids in porous channels. The graphical representations of the physical outcomes provide valuable insights into the behavior of non-Newtonian fluids in porous channels. The main finding of this research indicates that the volume flow rate is not affected by the different parameters. This result provides a useful guideline for designing channels with porous walls for the transport of non-Newtonian fluids. The exact solution obtained in this research represents a generalization of previous studies when a non-Newtonian parameter approaches zero.