Power law fluid flow through a bundle of regular fibers

The numerical predictions of the velocity field and the component of longitudinal permeability in the filtration equation for the steady incompressible flow of power law liquids through the assemblages of cylindrical fibers are presented in this paper. The fibers are arranged regularly in triangular, square, and hexagonal arrays. Flow is longitudinal with respect to the fibers. The non-linear governing equation in the repeated element of the array is solved using Picard iteration. At each iteration step the method of fundamental solutions and the method of particular solutions are used. The advantage of the proposed meshless approach is that it does not require the generation of a mesh in the domain or its boundary, but uses only a cloud of arbitrarily located nodes. The non-homogenous term is interpolated by radial basis functions. The next bundle of fibers is treated as a porous media and on the base of velocity field the permeability coefficients are calculated as functions of porosity.