Optimum Fin Parameters of Radial Heat Sinks Subjected to Natural Convection

Free convection from an upward facing radial heat sink with fins at an equal angular gap attached to an isothermal base has been investigated numerically. The governing equations in primitive variables were changed to vorticity-vector potential formulation, and an in-house code was developed using finite difference technique. To close the computational domain, two pseudo boundaries were considered. Length, height, and number of fins strongly influence the rate of heat transfer while the fin thickness has a marginal role. As the fin length increases, the rate of heat transfer first increases and then remains almost unaffected. However, the active length of the fins depends on the strength of buoyancy. Heat transfer continuously increases with fin height but with diminishing effect. Adding more number of fins has two opposing effects. It provides more surface area for convection, but at the same time, the induced air is unable to reach the interior of the heat sink making the inner portion of the fins inoperative. As a result of these two opposing influences, heat transfer increases in the beginning and then decreases as more fins are added. This article suggests various fin parameters to achieve maximum cooling. In addition, one can estimate the rate of cooling to be achieved by any radial heat sink.