A mathematical study on thermal performance of aluminum and titanium alloys based hybrid nanofluid using a multiparametric fractional operator

The principal aim of this article is to establish a new fractional model for an all-inclusive analysis of heat transfer and flow dynamics of hybrid nanofluids. For the case study, a hybrid nanofluid composed of kerosene oil and aluminum and titanium alloy nanoparticles is investigated. This work also examines the role of shape factors for blade, lamina, hexahedron, cylinder, and column-like shapes, in addition to evaluating the synergistic properties of preceding particles. Natural convection, generalized thermal slip condition, and ramped velocity function are fundamental factors behind flow instigation. Initially, the mathematical relation for the thermal flux is generalized for the development of a fractional model, and to serve this purpose, Fourier law is exposed to the Prabhakar operator. The partial coupling of heat and velocity equations further leads to the incorporation of generalized thermal flux into the flow equation, which transforms the classical governing system into a fractional one. The acquirement of exact solutions for the formulated fractional system involves two major steps: the inclusion of adequate dimensionless parameters, followed by the application of the Laplace transform. Various graphical illustrations are supplied using these solutions to interpret variations occurring in thermal and flow behaviors of the under-investigation hybrid nanofluid due to several associated parameters. Moreover, the influences of relevant contributing factors such as volume concentration, fractional parameters, and shape constants on shear stress and thermal efficacy are elucidated by tabulating the numerical outcomes. The results indicate that the thermal efficiency of kerosene oil can be enhanced up to 26.5% by hybridizing it with uniform fractions of aluminum and titanium alloys. The velocity of flow reduces as the collective volume concentration of considered alloys increases. It is observed that lamina-shaped nanoparticles are the most significant in terms of improving thermal characteristics. The temperature function is attenuated as a result of positive alterations to fractional parameters. Furthermore, the increase in buoyancy force strength causes the flow to accelerate significantly.