An impingement heat sink module design problem in determining optimal non-uniform fin widths

A three-dimensional inverse design problem is examined in this study for estimating the optimal non-uniform fin widths of an impingement heat sink module using a general purpose commercial code (CFD-ACE+) and the Levenberg-Marquardt Method (LMM). The optimal heat sink was designed based on the original 10 by 10 squared fin array with a fixed fin volume and height. The objective of this study is to minimize the thermal resistance (R_th) of the fin array and to obtain the optimal dimensions of non-uniform fin widths. The results obtained using the LMM to solve this three-dimensional fin design problem were initially justified numerically. Under the design operating condition Re = 5000, R_th can be decreased by 12.98% and 4.81% compared to the original and to Yang and Peng's optimal heat sinks, respectively. At the same time, the thermal performances of the optimal heat sink can be improved significantly. For instance, the Nusselt number (Nu) and the Coefficient of Enhancement (COE) can be increased by 14.92% and 15%, respectively, compared to the original heat sink, and these parameters can be increased by 5.06% and 3%, respectively, when compared to the optimal heat sink proposed by Yang and Peng. Finally, prototypes of the original and optimized heat sinks were fabricated and used to experimentally verify the validity of this work. The experimental results demonstrated that by utilizing the fabricated heat sinks and operating under the design condition Re = 5000, R_th can be decreased by 12.49% and Nu and COE can be increased by 14.21% and 14%, respectively, compared to the original fin array. Consequently, the thermal performances of optimal impingement heat sinks can be greatly improved.