Effect of Length and Inclination of a Thin Fin on Natural Convection in a Square Enclosure

A numerical investigation of steady, laminar, natural convective fluid flow in a square enclosure with an inclined heated thin fin of arbitrary length attached to the hot wall is considered. A transverse temperature gradient is applied on two opposing walls of the enclosure, while the other two walls are adiabatic. Attachment of highly conductive inclined thin fins with lengths equal to 20%, 35%, and 50% of the side, positioned in the middle of the hot left wall of the enclosure, is examined. The problem is formulated in terms of the vorticity–stream function procedure. A numerical solution based on the finite-volume method is obtained. Representative results illustrating the effects of the thin-fin inclination angle and length on the streamlines and temperature contours within the enclosure are reported. In addition, results for the local and average Nusselt numbers at the heated wall of the enclosure are presented and discussed for various parametric conditions. It is found that the Rayleigh number and the thin-fin inclination angle and length have significant effects on the average Nusselt number of the heated wall including the fin of the enclosure.