Effect of fin thickness, grooves depth, and fin attachment angle to the hot wall on maximum heat transfer reduction in a square enclosure

Abstract

This study investigates the effect of optimal thickness, position, and length of a thick fin, optimal groove depth, position, and length of a horizontally grooved thin fin, and optimal position and length of an obliquely fin (at ±45° to the horizontal) attached to the hot wall of a square enclosure in reduction of free convection heat transfer through this enclosure. The results are analyzed for Rayleigh numbers of 104 and 106 and thermal conductivity ratios of 1, 10, and 1000. The continuity, momentum and energy equations of the enclosure are discretized by the finite volume method and then solved with SIMPLER algorithm. The particle swarm optimization (PSO) algorithm is used to optimize the fin size and position and groove depth so that heat transfer through the enclosure is minimized. The results are compared to determine the effects of aforementioned fin characteristics on heat transfer reduction performance. The results obtained with Rayleigh numbers of 104 and 106 show that, as can be expected, for the fins with thermal conductivity ratios of 1 and 1000, the optimal thickness values are, respectively, the upper and lower bounds set by problem definition (defined geometry). But for the fin with thermal conductivity ratio of 10, the optimal thickness varies with Rayleigh number. The results also show that after widening the range of allowed thickness values, the optimal values no longer stick to the upper and lower bounds of that interval. It is also shown that at low thermal conductivity ratios, the fin with horizontal grooves has the same heat transfer reduction performance as a solid thick fin, but allows some degree of conservation in materials. Moreover, the results show that at all thermal conductivity ratios in Ra = 106, the heat transfer reduction performance of the obliquely fin is better than both of the straight thick fin and horizontally grooved fin. However, at all thermal conductivity ratios, the straight thick and obliquely fin slightly underperform rather than horizontally grooved fin in Ra = 104. Overall, the obliquely fin and horizontally grooved fin can be confidently recommended for heat transfer reduction at all thermal conductivity ratios in high Rayleigh number Ra = 106 and low Rayleigh number Ra = 104, respectively.