On unsteady gravity flows of a power-law fluid through a porous medium

In this paper we endeavour to present a numerical study of the nonlinear effects on the unsteady gravity flows of a fluid with a non-Newtonian behaviour through a porous media. For the case of radial axisymmetric flow, the governing partial differential equation is converted into an ordinary differential equation by a similarity transformation. Some selected similarity solutions which yield the shape of the free surface are given for both shear-thinning and shear-thickening fluids. The non-Newtonian effects on the shape of the free surface have been discussed. The present procedure enables approximate solutions to be obtained also for highly thinning fluids for n = 0.6.