The significant role of Darcy–Forchhiemer with integrated hybrid nanoparticles (Graphene and TiO₂) on dusty nanofluid flow subjected to heat conduction

The thermal analysis of two-phase models that deal with the fluid and dusty phases has been considered. This study instigates the flow of a non-miscible, dusty hybrid nanofluid over a stretching cylinder with Darcy–Forchheimer permeability in the presence of thermal radiation. The mathematical model is based on the single-phase nanofluid model, which features modified thermophysical characteristics. This innovative flow model explores how important it is to enhance the concentration of dust particles in fluid dynamics. Hybrid nanoparticles are substituted for nanoparticles in a conventional case to accelerate the heat transfer rate of the fluid. Therefore, in this study, the magnetohydrodynamic flow of hybrid nanofluids and heat transfer of non-Newtonian dusty fluids with suspensions of hybrid nanoparticles have been examined. The appropriate dimensionless variables are used to convert the governing periodic model into a non-dimensional form. The finite-difference-based bvp5c algorithm is used through Matlab for numerical analysis of the set of obtained ordinary differential equations. The graphs explored the influences of relatable factors over the profiles of mass, heat, and velocity transfers. It is observed that with intensifying values of Eckert number (Ec) and Biot number (Bi), the temperature of both phases increased at a significant level, and the velocity decreased with increasing intensity of the magnetic field. The computational results of velocity, core temperature, and intensity dispersion are significant for both aspects. Furthermore, it is observed that both the fluid and dust phases exhibit declining behavior as a result of the impact of porosity, mass concentration, and magnetism on the flow stream. Moreover, it is noticed that both the dust phase temperature (Formula presented.) and fluid phase temperature (Formula presented.) intensified with the high intensity of magnetic field and thermal radiation. The missile nozzles, nuclear power plants for aerospace and gaseous-core nuclear rocket systems, and the radiation are considered for evaluating heating significance.