Free convection flow of two immiscible viscous liquids through parallel permeable beds: use of Brinkman equation

Singh, Ajay Kumar and Takhar, Harmindar S. (2005) Free convection flow of two immiscible viscous liquids through parallel permeable beds: use of Brinkman equation. International journal of fluid mechanics research, 32 (1). pp. 39-56. ISSN 1064-2277

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Abstract

The present paper deals with an analytical study of free convection in fully developed laminar, free convection flow of two viscous, immiscible, incompressible liquids bounded above and blow by two parallel naturally permeable beds of high porosity and finite thickness. The momentum transfer in the free flow region is governed by Navier-Stokes equations and the flow in the porous medium is governed by Brinkman equation. The flow domain is divided into four regions and exact solutions of the momentum and energy equations are obtained for each region under appropriate matching and boundary conditions. The effects of various parameters on the velocity and temperature fields are discussed with the help of graphs while the effects on skin-friction and heat transfer are discussed with the help of tables.