Water-based copper-alumina hybrid nanofluid flows over a stretchin/shrinking sheet with dual solutions

Hybrid nanofluid has many real-world applications. Previous studies found hybrid nanofluid possesses better heat transfer efficiency compared to nanofluid with a single type of nanoparticle. However, the characteristics of boundary layer flow and heat transfer rate involving hybrid nanofluid could be further explored using different
geometries and physical assumptions in higher-dimensional space. There are dual solutions to these fluid problems due to the nonlinearity of the governing equations. Nevertheless, solutions are difficult to obtain experimentally. Therefore, the main objective of this study is to examine all possible solutions to five new water-based copper-alumina hybrid nanofluid flow problems numerically, which involved vertical exponential, power-law, and linear rotating stretching/shrinking sheet. The hybrid nanofluid flow problems in this study have been governed by systems of nonlinear
partial differential equations, which were then transformed into their corresponding systems of higher-order nonlinear ordinary differential equations using suitable similarity variables. The systems were then solved numerically. The numerical findings for all five problems were found to agree with those existing solutions in the literature. The effects of physical parameters on reduced skin friction, reduced heat transfer, velocity profile, and temperature profile have been established. Findings also revealed that there were distinct zones for dual, unique, and no solutions for each problem. In conclusion, the addition of hybrid nanoparticles boosted the heat transfer rate of the water-based hybrid nanofluid flow. The findings of this study can serve as a guide to lower the cost of experiments in relevant fields of application.