Exploration of generalized two-phase free convection magnetohydrodynamic flow of dusty tetra-hybrid Casson nanofluid between parallel microplates

Dusty Casson fluids and tetra-hybrid nanofluids are complex phenomena that find their extensive uses in engineering and industrial applications. For instance, dusty fluids are used in gas-freezing systems and nuclear power reactors. The main objective of this article is to focus on the characterization of generalized two-phase free convection magnetohydrodynamic flow of dusty tetra-hybrid Casson nanofluid among parallel microplates: dusty Casson fluid and tetra-hybrid nanofluid exhibit free movement and electrical conductivity. The Caputo–Fabrizio fractional derivative recently discovered generalizes the partial differential equations governing the flow. Highly accurate temperature and velocity distributions can be obtained using finite sine Fourier and Laplace transform together. This study examines the relationships between temperature, dust particle velocity, and Casson fluid velocity, along with the effects of magnetic parameter, Grashof number, dusty fluid parameter, Peclet number, Reynold number, and particle mass parameter. The Mathcad-15 software provides Casson, dusty, and temperature profiles graphically. The Nusselt number and skin friction are also examined for the tetra-hybrid nanofluid. The fractional Casson fluid model is more accurate than the classical model in terms of velocity, temperature, heat transfer, and skin friction. Graphical results conclude that the fractional Casson fluid model describes a more realistic aspect of both (fluid and dust particle) velocities and temperature profiles, heat transfer rate, and skin friction than the classical Casson fluid model. Furthermore, the heat transfer rate enhanced from 0 to 39.3111% of the tetra-hybrid nanofluid.