Natural Convection Heat Transfer From a Vertical Hollow Cylinder With Surface Holes

Abstract

Three-dimensional continuity, momentum, and energy equations have been solved around a perforated vertical hollow cylinder to predict the buoyancy-induced flow field and the temperature distribution around it. Finite volume method (FVM) has been implemented for the discretization of the underlying governing equations. Second-order upwind scheme has been adopted to discretize the convective terms in the momentum and energy equation. Results have been obtained by varying the input parameters like hole diameter to cylinder length ratio (d/L), pitch to length ratio (P/L), angular pitch (θ), cylinder length to diameter ratio (L/D), and Rayleigh number (Ra) spanning from 0.005 to 0.08, 0.1 to 0.3333, 30 deg to 180 deg, 2 to 20, and 104 to 108, respectively. It has been found that the average surface Nusselt number (Nu) for the outer surface increases with the diameter of the hole for Ra of 106, however for Ra of 108, it marginally decreases up to d/L of 0.01 and then increases. Nu for the inner surface increases when d/L is more than 0.04 for all Ra. The cylinder with the staggered holes shows a slightly higher Nu compared to the inline holes. Nu for the inner and outer surface at a lower pitch is less than that of the higher pitch when d/L is less than 0.02 for all Ra. The heat transfer rate of the perforated cylinder is more than the nonperforated cylinder for all the cases when L/D is less than 10 and Ra less than 106. However, for Ra more than 106, the perforated cylinder always loses more heat compared to the nonperforated one for all L/D. Finally, the correlation for Nu has been proposed as a function of the pertinent input parameters for future reference in the academic as well as industrial practices.