On transient-flows of the Ostwald-de Waele fluids-transport in the Darcy-Brinkman porous medium

This paper presents the mathematical formulation of the pulsatile motion of an Ostwald-de Waele (OdW) fluid in the circular-annular duct and the rectangular channel filled with the Darcy-Brinkman porous material/medium. The Ostwald-de Waele fluid model, modified for the Darcy-Brinkman medium, is used to get the boundary value problems (BVPs). These BVPs contain non-linear partial differential equations (PDEs). These PDEs are further transformed to the ordinary differential equations (ODEs) on using the pulsatile-transformation. The ODEs are solved numerically for different values of OdW-index. However, the exact solutions are also derived for one of the shear-thickening fluids (e.g., p = 2) and the Newtonian fluids (p = 1) in order to validate the numerical results. The numerical results are also compared with the existing or present-derived-analytical solution for the Newtonian fluids. It is observed that the porosity, the permeability and the frequency influence on the fluid-speed, the discharge and the stresses. The fact of relation of the permeability to the porosity is not only valid for the Darcian but also for the Darcy-Brinkman medium. The permeability decreases as the porosity decreases only for shear thinning fluids (p < 1). The imposed pulsatile pressure-gradient results the oscillatory ambient fluid-flow for both the geometries (circular-annular duct and rectangular channel). The radial normal stress is dominant in annular duct whereas the shear stress is significant in rectangular channel