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In order to achieve the best performance of a thermal system, two major analyses must be carried out on the system: energy and entropy generation. The best scenario is a mechanism in which the system has minimum entropy generation and the highest <i>Nu</i> number. In this regard, we investigated entropy generation and <i>Nu</i> number of fluid flow through tubes of various cross-sections, namely circular tubes, square channels, and rectangular ducts. Additionally, the addition of nanoparticles was tested, and both analyses were carried out. The results reveal that using nanoparticles could significantly increase <i>Nu</i> number and, at the same time, decrease entropy generation. The results showed that the circular cross-section performs better in <i>Nu</i> number and entropy generation. In most cases, the rectangular cross-section performed better than the square one in terms of energy and entropy. In the best case, the average <i>Nu</i> for the circular cross-section was 26% greater than that of the square. The average <i>Nu</i> of the rectangular cross-section showed that this value is 5% greater than that of the square cross-section. Additionally, the total entropy generation of circular cross-sections, which is the minimum, was 44% and 38% lower than rectangular and square cross-sections, respectively.