Analytical solution of non-Darcian forced convection in an annular duct partially filled with a porous medium

Abstract An analytical solution is obtained for a fully developed, forced convection in a gap between two concentric cylinders. The inner is exposed to a constant heat flux and the outer is thermally insulated. A porous layer is attached to the inner cylinder. The effects of the permeability, thermal conductivity and the thickness of the porous material are investigated using a Brinkman-extended Darcy model. It is shown that there exists a critical thickness of the porous layer at which heat transfer is minimum in the case of low thermal conductivity materials, while this does not show for highly conducting materials. The obtained results show that increasing either the permeability or the thermal conductivity improves the heat transfer. Further, for highly permeable and conducting porous media, it may not be necessary to fill the gap completely to attain the maximum heat transfer.

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