On the thermal performance of an internally finned three-dimensional cubic enclosure in natural convection

Abstract

The present paper evaluates the effect of the aspect ratio and horizontal length of a high conductivity rectangular fin attached to the hot wall of a three-dimensional differentially heated cubic enclosure in laminar natural convection. The objective is the augmentation of the heat transfer delivered from the heated wall to the fluid when the volume fraction of the fin is fixed. Two different values for the fin volume were considered: (i) a large fin that occupies 10 percent of the cubic enclosure, and (ii), a much smaller fin that occupies only 0.1 percent of the enclosure total volume. The finite element technique was applied for solving the coupled steady-state velocity and temperature fields in the 3-D domain in the range 10 3 < Ra < 10 5 , where Ra is the Rayleigh number based on the enclosure height. The numerical results showed that for an enclosure assisted by a large volume fraction fin, the fin aspect ratio does not play an important role, and the average heat flux transferred to the fluid increases monotonically with the fin horizontal length. For a cubic enclosure assisted by a small volume fraction fin, the average heat flux delivered to the fluid increases with the aspect ratio of the fin, and with the horizontal length of the fin. A scale analysis was used to predict the domain in which the fin geometry plays a significant role, i.e., when optimization opportunities are present.