A Bingham fluid flow through a channel filled with a Darcy-Brinkman medium(*)
A.Y. Gunawan(1), A.A.F. van de Ven(2)

(1) Industrial and Financial Mathematics Research Group
Institut Teknologi Bandung
Jln. Ganesa 10 Bandung-Indonesia

(2) Department of Mathematics & Computer Sciences Eindhoven Universtiy of Technology
5600 MB Eindhoven-The Netherlands

Abstract

An analytical solution for a one-dimensional non-steady pressure-driven flow of a Bingham fluid in a channel filled with Darcy-Brinkman medium is derived. Two dimensionless time scales are introduced, i.e. a viscosity-related time scale and a permeability-related one. Solutions are fully determined by two dimensionless parameters, i.e. a fluid parameter and a permeability parameter. The effects of porous medium on the flow are specifically investigated. How velocity decreases with decreasing permeability of the porous medium is specified. For the start-up flow case, it evolves in time monotonously into a steady state. The time in which this state is reached is shorter for media of lower permeability. A simple hand-on formula for the total flow rate is derived and compared with the exact solution- good correspondence is found.

(*) This article has already been published in J Eng Math: (2022) 137:5

Keywords: Pressure-driven flow, Bingham fluid, Darcy-Brinkman medium

Topic: MATHEMATICS AND STATISTICS