Maximal heat transfer density from cross-flow heat exchanger with tapered fins using constructal design method

Tapered fins are widely used in heat sinks cooled by forced convection. In this study, maximal forced convective heat transfer from a set of tapered fins in cross-flow is investigated based on the constructal design method. The tapering of the fins is done for a three-fin base-to-tip ratio (taper ratio). The first taper ratio is TR = 0.5 (fin base < fin tip), the second taper ratio is TR = 1 (fin base = fin tip, straight fin), and the third taper ratio is TR = 2 (fin base > fin tip). In all these cases, the fin length is constant. The fins are heated at constant surface temperature and they are cooled by cross-flow. A constant pressure difference pushes the cross-flow toward the fins. The Bejan number ranges from 10⁵ to 10⁷. The forced convective heat transfer density is maximized from the fins for the three taper ratios, and a comparison between them is carried out. The maximization is conducted by numerical and scale analysis. In the numerical analysis, the pressure-driven flow equations (continuity, momentum, and energy) are solved by means of the finite volume method. In the scale analysis, two extremes are considered. The first extreme is for TR < 1, and the second extreme is for TR > 1. These two extremes are intersected to find the maximal forced convective heat transfer density. The results obtained from numerical and scale analysis confirmed that the maximal forced convective heat transfer density occurs for straight fins (TR = 1) in the whole range of the Bejan number. The heat transfer density from straight fins (TR = 1) is higher than that of tapered fins (TR = 2) by 45.2%, and it is higher than that of tapered fins (TR = 0.5) by 52.7% at Be = 10⁷.