Prabhakar fractional simulations for natural convective hybrid nanofluid mixed with Cu and Al2O3 nanoparticles flowing through a channel

This study seeks to investigate the heat transfer analysis of hybrid nanofluids containing fractionalized water and kerosene oil, which flow through a vertical channel via convection. To represent the problem in terms of fractional partial differential equations, we utilized the Prabhakar time-fractional derivative, a recent advancement in the concept of fractional derivatives. The governing equations were then solved using physical initial and boundary conditions that include momentum, concentration, and energy equations. Stehfest and Tzou's Laplace inversion techniques are used to provide semi-analytical solutions for governed equations, such as temperature, concentration, and momentum profiles, and we applied the fractional Laplace transformation to find solutions in the transform domain. Furthermore, the resultant solutions in tabular form are also derived using Tzou and Stehfest's numerical methods for Laplace inversion to ensure the accuracy of our findings. According to our research, an increase in volumetric fraction causes a reduction in fluid velocity. Due to the physical properties of the investigated nanoparticles, the water-based hybrid nanofluid has a bigger effect on the temperature and momentum profile than the kerosene oil-based hybrid nanofluid.