Low Rayleigh number flow in a heat generating porous media |
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Affiliation: | University of Missouri-Kansas City Department of Mechanical and Aerospace Engineering Energy Research Laboratory Truman Campus Independence, Missouri 64050, USA |
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Abstract: | A numerical analysis has been performed for the steady-state temperature and stream function distributions in a short cylinder, having an isothermal side and top, an insulated bottom, for a uniform heat generating porous medium. The analysis uses the stream function formulation of Darcy's equation in cylindrical coordinates and the Boussinesq approximation. A single energy equation was used for the fluid and solid, since conduction was the expected mode of heat transfer at low heat generation rates for a lead sphere air porous media system. The solution of the non-dimensionalized momentum and energy equations resulted in small Rayleigh numbers (2×10−6 to 0.2) indicating the heat transfer is by conduction. Solutions for the stream lines and isotherms were obtained using a transient explicit finite-difference approximation using a mean bed thermal conductivity. |
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