Unsteady Mixed Convection of Opposing Flow: Dual Solution Report of Two-Particle Nanofluid Behavior Around a Vertical Cylinder

This research endeavors to conduct a comprehensive numerical investigation into the unsteady mixed convection phenomenon observed in the flow of a stagnation point Cu–Al 2 O 3 /H 2 O hybrid nanofluid past a vertical cylinder under an opposing regime. Initially, the nanofluid’s complex behavior is analytically characterized, and leveraging suitable similarity variables, the equations are changed into a set of ODEs. These equations are subsequently tackled, utilizing the bvp4c function available in MATLAB. To ensure the reliability and validity of the study, the obtained numerical results are meticulously compared with existing research findings, demonstrating a noteworthy degree of alignment. The numerical analysis uncovers the presence of dual solutions within a specific range of the mixed convection parameter. However, due to the inherent instability associated with the second solution, the present attention is focused solely on exploring the stability and characteristics of the primary solution. Moreover, the investigation reveals intriguing insights into the behavior of the primary solution. Specifically, it can be observed that both the skin friction coefficient and the heat transfer rate exhibit a significant response to changes in the volume fraction of nanoparticles and Reynolds number, demonstrating an enhancement with increasing them. For the analyzed case, in the absence of free convection effects, the results indicate that as the nanoparticle volume fraction increases from 0 to 0.2, the skin friction coefficient rises from 1.707 to 3.468, while the Nusselt number enhances from 2.151 to 3.269. Furthermore, a detailed examination of the velocity and temperature profiles associated with the primary solution elucidates that the thickness of both the hydrodynamic boundary layer and the thermal boundary layer experiences a discernible reduction as the volume fraction of nanoparticles decreases and the Reynolds number increases. This study can offer valuable insights for engineering applications and scientific inquiry alike.