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 Nu number. In this regard, we investigated entropy generation and Nu 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 Nu number and, at the same time, decrease entropy generation. The results showed that the circular cross-section performs better in Nu 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 Nu for the circular cross-section was 26% greater than that of the square. The average Nu 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.

Hitherto, a considerable amount of research has been carried out to investigate the equilibrium condition of adsorption process; nevertheless, there is no comprehensive study to evaluate the surface adsorption properties of MOFs. Therefore, the adsorption mechanism and equilibrium capacity of MOFs have not been fully understood. Furthermore, the mass transfer mechanism is still unknown and so it is not possible to predict the adsorption process using MOFs. In this work, a new metal–organic framework (MOF) named UIO-66–MnFe₂O₄ was synthesized as an adsorbent for oily wastewater treatment. In this way the effects of temperature, amount of adsorbent, adsorption time, pH, and pollutant initial concentration were studied in the treatment of oily wastewater using the UIO-66-MnFe₂O₄ MOF through the adsorption process. Furthermore, to examine the process of surface adsorption, different adsorption kinetic models (pseudo-first-order, pseudo-second-order, and Elovich) have been performed for the removal of oily pollutants on MOF adsorbents and the surface adsorption mechanism has been discussed carefully. Moreover, to investigate the mass transfer mechanism of oily pollutants in the surface adsorption process, different mass transfer models (Weber and Morris, liquid film diffusion, and Bangham and Burt) have been investigated on porous adsorbents, and finally the mass transfer mechanism of the adsorption process has been proposed.

The authors would like to make the following corrections about the published paper