A MATHEMATICAL MODEL OF NON-NEWTONIAN FLUID FLOW THROUGH A POROELASTIC CYLINDER WITH MOVING BOUNDARIES

This paper investigates the radial flow of a non-Newtonian fluid through a poroelastic cylinder with moving boundaries. Some applications of the present work include fluid flow through arteries, pressurization of boreholes, extraction of oil from earth, and filtration processes. A general (i.e., planar, cylindrical, and spherical) one-dimensional nonlinear diffusion equation for dilatation is derived for a power-law fluid, and a relation for the solid displacement is given. Geometrically, two different cases of a poroelastic cylinder, i.e., constrained and unconstrained, are considered and corresponding nonclassical time-dependent integral boundary conditions are presented. The governing nonlinear moving boundary value problem is first nondimensionalized by choosing suitable dimensionless quantities and then transformed to a fixed domain by employing a transformation. The closed form equilibrium solutions for dilatation and solid displacement are given for the constant permeability case. The transient form of the governing equation for dilatation is solved numerically using the method of lines and this solution is then utilized to compute the solid displacement by adopting the trapezoidal rule. Comparisons are made between the linearized and full nonlinear moving domain problems for the constrained as well as unconstrained cylindrical geometry.