Study of buoyancy-induced flow and heat transfer in a cylindrical annulus with geometric perturbations

A numerical study is performed to analyze the natural convection fluid flow and heat transfer in a horizontal cylindrical annulus in the presence of geometric perturbations. The effect of inclusion of a single geometric perturbation on the inner cylinder is done for varying sizes of the perturbation. Also, the effects of multiple perturbations on the inner and outer cylinders are studied in this work. The flow fields for the annulus with multiple perturbations were found to be qualitatively similar, and the addition of each perturbation was found to alter the flow field in a regular and recurring manner. For the case of an annulus with a porous perturbation, the flow in the porous region is modeled using the Brinkman-Forchheimer Darcy model. The numerical scheme used in the present study is based on the Galerkin method of the finite element formulation. The nature of the three-dimensional flow field for the different cases have been analyzed in detail and the local and average Nusselt numbers have been obtained for a range of Rayleigh numbers of practical interest. It is observed that the presence of multiple perturbations on the inner and outer cylinders substantially increase the overall heat transfer rate as compared to the regular annulus without any perturbation.