Channel flow in an inclined circular tube filled with a porous medium

Abstract

The fluid flow in a circular tube filled with a porous medium is important in packed-bed catalytic reactors. Due to gravity the fluid only partially fills the inclined tube. The Darcy-Brinkman equation is solved by two different highly efficient boundary collocation methods. The flow rate depends on the porous medium parameter which quantifies permeability and the level of fill of the fluid. It is found that there exists an optimum level of fill for which the flow rate is maximized. Asymptotic approximation for small permeability is also obtained.