The authors of the present paper sought to conduct a numerical study on the convection heat transfer, along with the radiation and entropy generation (EGE) of a nanofluids (NFs) in a two and three-dimensional square enclosure, by using the FVM. The enclosure contained a high-temperature blade in the form of a vertical elliptical quadrant in the lower corner of the enclosure. The right edge of the enclosure was kept at low temperature, while the other edges were insulated. The enclosure was subjected to a magnetic field (MGF) and could be adjusted to different angles. In this research, two laboratory relationships dependent on temperature and volume fraction were used to simulate thermal conductivity and viscosity. The variables of this problem were Ra, Ha, RAP, nanoparticle (NP) volume fraction, blade aspect ratio, enclosure angles, and MGF. Evaluating the effects of these variables on heat transfer rate (HTR), EGE, and Be revealed that increasing the Ra and reducing the Ha could increase the HTR and EGE. On the other hand, adding radiation HTR to the enclosure increased the overall HTR. Moreover, an augmentation of the volume fraction of magnesium oxide NPs led to an increased amount of HTR and EGE. Furthermore, any changes to the MGF and the enclosure angle imposed various effects on the HTR. The results indicated that an augmentation of the size of the blade increased and then decreased the HTR and the generated entropy. Finally, increasing the blade always increased the Be.

In the current numerical study, various wall shape effects are investigated on the thermal-hydraulic characteristics of different channels filled with water-based graphite-SiO₂ hybrid nanofluid. In this work, the performance evaluation criteria (PEC) index is employed as the target parameter to attain optimum geometry. Six different cases are studied in this research, and each case has different geometrical dimensions. The inlet temperature for the fluids in the channel is 300 K, over a range of different flow velocities. According to the obtained results, an increase in the volume fraction of nanoparticles results in higher PEC values. In addition, an increase in Reynolds number to Re = leads to an increase in the PEC index. The results clearly show that increasing the Reynolds number has two consequences: on the one hand, it increases the pressure drop penalty; on the other hand, it improves heat transfer. Therefore, the maximum value of the PEC index occurs at Re = 15,000.

In this paper, the free convective heat transfer of nanofluids in a square cavity is simulated using a numerical method. The angle of the cavity could be changed in the horizontal axis from 0 to 90 degrees. The cavity is exposed under a constant magnetic field. Two opposite walls of the cavity are cold and warm, and the rest of the walls are insulated. On the hot wall, there are two fins with the same wall temperature. The equations were discretized by the finite volume method (FVM) and then solved using the SIMPLE algorithm. Three different fin configurations (straight, inclined and curved) were studied in terms of heat transfer rate and generation of entropy. According to the simulation results, the heat transfer rate was improved by tilting the fins toward the top or bottom of the cavity. At Ra = 10⁵ and Ha = 20, the maximum heat transfer rate was achieved at a cavity inclination of 90° and 45°, respectively, for straight and curved fins. In the horizontal cavity, heat transfer rate could be improved up to 6.4% by tilting the fins and up to 4.9% by warping them. Increasing the Hartmann number from 0 to 40 reduced the Nusselt number and entropy generation by 37.9% and 33.8%, respectively.