Analytical analysis and experimental verification of trapezoidal fin for assessment of heat sink performance and material saving

A quick assessment of the performance loss in association with material saving amid rectangular and trapezoidal fin is analytically investigated and experimentally verified. A novel dimensionless parameter - rt representing the ratio of the fin tip to base thickness - is used to simplify the fin equation. A dimensionless differential equation is derived based on the formulation and the corresponding closed form solution of the dimensionless temperature and fin efficiency is presented. It is found that the performance drop depends on various rt ratios, and the most pronounced performance difference occurs in the region between M = 1.7 and 2.5. Yet the performance difference between the rectangular and trapezoidal fin are quite insignificant at low velocity region; with the increasing of velocity, the performance loss ratio is gradually discriminated to reach the maximum performance loss between region of M = 1 and 2, then it begins to converge again toward M = 4. The recovering of the ratio is actually associated with the diverging and converging trend of the fin efficiency. The analytical results are in line with the experimental results. At a frontal velocity of 4 m/s, the predicted difference of heat transfer rate between trapezoidal and rectangular fin profile in terms of total heat transfer ratio is only 0.88%.