New fractional approach for the simulation of (Ag) and (TiO₂) mixed hybrid nanofluid flowing through a channel: Fractal fractional derivative

This paper presents a novel application of the Fractal Fractional derivative to control the flow of non-Newtonian fluids. The study focuses on the generalized magnetohydrodynamic (MHD) flow of a Casson-type hybrid nanofluid in a micro-channel and its modeling and solution. The hybrid nanofluid mixed with the suspension of copper (Cu) and titanium dioxide (TiO₂) nanoparticles with carboxymethyl cellulose (CMC) and water (H₂O) as base fluids are considered. First, the partial differential equations are converted to a fractional model with the current and new description of fractional derivatives, i.e., Fractal fractional derivatives. Then, ordinary differential equations are resolved numerically using a fractional Laplace transformation. Finally, the results are numerically calculated and shown in various graphs with a physical description to study the physical importance of different relevant factors. As a result, it's computed that the momentum field indicates the decaying behavior with incrementing the Casson fluid parameter. Furthermore, the impact of CMC-based hybrid nanofluid (CMC + Ag + TiO₂) on energy and momentum is slightly more significant than the water-based (H₂O + Ag + TiO₂) hybrid nanofluid. Moreover, due to the impact of volume fraction, the fluid temperature increases while velocity slows down due to increased thermal conductivity.