In this study, the thermal performances of optimized finned annuli with various fin shapes were compared. A thermal model based on volume averaging theory was developed for finned tube annuli to realize thermal optimization and perform the comparison. The developed model was used to show that thermal performance improves in the order of straight-finned annuli, circular-sectored-finned annuli, finned annuli with linearly decreasing porosity, finned annuli with linearly increasing fin thickness, and finned annuli with variable fin thickness. Furthermore, contour maps that enable the calculations of the optimal shapes and optimal thermal resistances of the finned annuli based on the information provided on the cooling space and pumping power are presented. Additionally, the results of the model indicated that branched fins are not ideal for the case of finned tube annuli examined in the study.
