Natural convection in a vertical annulus driven by a central heat generating rod

A numerical study of the conjugate natural convection in a vertical annulus with a centrally located vertical heat generating rod is performed. The formulation in primitive form is solved using a pressure-correction algorithm. A parametric study is conducted by varying the heat generation based Grashof number, aspect ratio and the solid-to-fluid thermal conductivity ratio over wide ranges with the Prandtl number fixed at 0.7. Results are presented for the temperature distributions and Nusselt numbers. The average Nusselt numbers on the inner and outer boundaries show an increasing trend with the Grashof number. Correlations are presented for the Nusselt number and the dimensionless temperatures of interest in terms of the parameters of the problem.