STABILITY OF COUPLE STRESS FLUID FLOW THROUGH A HORIZONTAL POROUS LAYER

Abstract

The stability of pressure-driven parallel shear flow in a horizontal layer of couple stress fluid saturated porous medium is investigated using a classical linear stability theory. A modified Orr-Sommerfeld equation is derived and solved numerically using the Chebyshev collocation method. The critical Reynolds number, the critical wave number, and the critical wave speed are computed for various values of the porous and couple stress parameters. The equilibrium is always stable if the convective inertial term is omitted, but with its inclusion the basic state becomes unstable depending on the choices of physical parameters. It is found that an increase in the couple stress parameter has a destabilizing effect on the fluid flow, while an opposite trend is observed with increasing porous parameter. The streamlines presented herein demonstrate the development of complex dynamics at the critical state. Individual components of the kinetic energy spectrum are analyzed and presented for different parametric values in order to obtain detailed information at the critical state of fluid flow.