Mathematical results for slipping flows past a cylinder or a sphere embedded in a porous medium
Abstract
Flow past a circular cylinder or a sphere embedded in a porous medium is investigated mathematically
by treating porous matrix as an incompressible fluid. Closed form analytic solutions for the fourth order
scalar boundary-value problems for Ψ (r, θ) - known as the Stokes stream function - are obtained by
using Navier-slip conditions. Our exact results for Ψ (r, θ) capture flow fields prevailing in the vicinity of
a cylinder/sphere suspended in a uniform or a shear flow field. All the physical quantities computed
from our solutions depend on two key parameters, namely, δ (the effective permeability) and ζ (slip
coefficient). Flow separation and velocity overshoot behavior are found for certain values of δ and ζ.
The force acting on the cylinder/sphere is calculated in each case. It is observed that the presence of slip
decreases the force on the boundary. Our results show that in the limit δ -> 0, there is no solution to
the two-dimensional boundary-value problem, confirming the familiar Stokes paradox
Description
A Thesis Submitted in Partial Fulfillment of the Requirements for Degree of MASTER OF SCIENCE in The Graduate Mathematics Program in Applied and Computational Mathematics from Texas A&M University - Corpus Christi.