An optimal design problem in determining non-uniform fin heights and widths for an impingement heat sink module

• An optimal design problem in estimating the optimal shape of an impingement cooling heat sink is examined.
• Two optimal heat sink design problems with different design variables are considered.
• The result obtained using the LMM to solve this fin design problem is initially justified numerically.
• Finally, the performances of the fabricated original and optimal heat sinks are verified experimentally.
• For optimal heat sink #2, Rth can be decreased by 10.53% compared to the original fin array.

A three-dimensional optimal design problem is examined in this study using a general purpose commercial code (CFD-ACE+) and the Levenberg–Marquardt Method (LMM) to estimate the optimal shape of an impingement cooling heat sink using different design variables. In optimal heat sink design #1, the non-uniform fin widths are taken as the design variables, and in optimal heat sink design #2, the non-uniform fin widths and heights are chosen as the design variables. The objective of this study is to minimize the thermal resistance (Rth) of the fin array and to obtain the optimal dimensions of optimal heat sinks #1 and #2. The experimental results demonstrated that by utilizing the fabricated heat sinks and operating under the design condition Re = 5000, Rth can be decreased by 4.06% and Nu and COE can be increased by 4.23% and 4.20%, respectively, for optimal heat sink #1 compared to the original fin array. For optimal heat sink #2, Rth can be decreased by 10.53% and Nu and COE can be increased by 11.65% and 11.70%, respectively, compared to the original fin array. Consequently, the thermal performances of optimal impingement heat sinks can be greatly improved.