It is a recognized hard task for the traditional thermal design of compact heat exchangers to obtain the optimal geometric parameters efficiently and effectively, owing to its complex trial-and-error process. In response to this issue, a simplified conjugate-gradient method (SCGM) combined with a sequential unconstrained minimization technique (SUMT) as a favorable optimization technique is incorporated with the traditional thermal design in this study, and then the key geometric parameters of fin-and-tube heat exchangers (FTHEs) are investigated and optimized successfully. In this method, the minimum total weight of FTHEs as the final objective is discussed, involving two geometric parameters, diameter of tube and height of shape as search variables. Aiming to minimize the objective function, SCGM is introduced to the SUMT to update the search variables continually with the fixed search steps and the search directions. Meanwhile, with the known geometric parameters from the SUMT, the log-mean temperature difference method (LMTD) is applied to determine the heat transfer area under the combined structure sizes for a given heat duty. Additionally, optimization results for three different heat duty is discussed in this work. The results show that it is effective to obtain the optimal sets of geometric parameters of FTHEs by the present method, and there are some guidance values for the thermal designs of compact heat exchangers.

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