Hydrodynamic flow of non-Newtonian power-law fluid past a moving wedge or a stretching sheet: a unified computational approach

Abstract

A unified mathematical equation that combines two different boundary-layer flows of viscous and incompressible Ostwald-de Waele fluid is derived and studied. The motion of the mainstream and the wedge is approximated in the power-law manner, i.e, in terms of the power of the distance from the leading boundary-layer edge. It is also considered that the wedge can move in the same and opposite direction to that of the mainstream. The governing partial differential equations are transformed into the nonlinear ordinary differential equation using a new set of similarity variables. This transformed equation subjected to the boundary conditions describing the flow is then solved using the Chebyshev collocation method. Further, these numerical results are then validated by determining the flow behaviour at far-field by performing asymptotics. The velocity ratio parameter effectively captures and distinguishes two boundary-layer flows. The boundary layer thickness for shear-thinning fluid is thinner compared to corresponding parameters for shear-thickening fluids and is markedly separated by the Newtonian fluid. Further, the boundary-layer flow of the non-Newtonian fluid predicts an infinite viscosity for shear-thinning fluid quite away from the surface. The hydrodynamics of the obtained results is explained thoroughly.