Flow of an Incompressible Fluid in a Cubical Cavity with a Free Fluid-porous Medium Interface Singh Ashok K.1, Nirmal C. Saeheti2,*, Chandran Pallath2 1Department of Mathematics, Bananas Hindu University, Varanasi-221 005, India 2Department of Miithemntics, Smtistics College of Science, Sultan Qnboos University, PC 123 Al, Khod, Muscat, Sultanate of Oman *Author for Correspondence. E-mail: nirmal@squ.eds.om
Abstract The steady laminar flow of a viscous incomppressible fluis in a layer of finite thickness above a porous medium, has been analysed for flow in a closed cubical cavity. The 3-dimensional flow is assumed to be dominated by buoyancy forces. Using the Brinkman equation to model the flow in the porous medium, we have analysed the flow numerically. Numerical solutions of the governing equations, formulated in terms of the voritcity arid vector potential, and subject to a set of matching and boundary conditions, have been obtained using an altemating direction implicit (ADI) method. The influence of thickness of the fluid layer, buoyancy force and permeability of the porous medium on the physical variables of interest, has been investigated. Top 2000 Mathematics Subject Classification 76R10, 76S05, 76D99. Top Keywords Cavity, Buoyancy, Free fluid region, Porous medium, Brinkman equation, Permeability, Vorticity, Vector potential. Top |