Effect of two sinusoidal protuberances on natural convection in a vertical concentric annulus

A numerical study is presented for laminar flow and heat transfer in a vertical concentric annulus with two sinusoidal protuberances on the external and internal surfaces of the inner and external cylinders, respectively. The basis of the method used is an algebraic nonorthogonal coordinate transformation that maps the complex fluid domain onto a rectangle. The transformed equations and the entire discretization procedure were solved by a finite volume methodology. Representative results were found for laminar flow, uniform wall temperature (case I), uniform heat flux (case O), a range of Rayleigh numbers, Prandtl number, various values of aspect ratio, and the height of the sinusoidal protuberances. As seen from the streamlines, the flow patterns are highly perturbed by the presence of the protuberance, including recirculation zones. It is also noted that the presence of the protuberance leads to an increase in heat transfer rates in the location of the obstruction along the wall. The pressure drops and thermal correlation results are higher than the corresponding values for the cylinders without protuberances.