Forchheimer model and generalized Fourier and Fick heat flux in water based Williamson hybrid nanofluid flow over stretched surface under Lorentz force

Abstract This research provides a comprehensive understanding of water-based Williamson MoS 2 / H 2 O nanofluid and MoS 2 − Go / H 2 O hybrid nanofluid flow, considering various physical parameters. The study investigates a two-dimensional, time-independent boundary layer flow over a stretching sheet, addressing the critical challenge of optimizing heat transfer efficiency and stabilizing nanoparticle dynamics. These challenges are essential for applications in chemical processing, material coating, and advanced electronic cooling systems. Governing equations are modeled and analyzed, incorporating the generalized Fourier and Fick heat flux to account for heat transfer time delay, magnetic field effect, diffusion, Forchheimer flow, and chemical reaction parameters. The converted coupled system of ordinary differential equations is solved numerically using the shooting method. The findings reveal that the generalized Fourier and Fick heat flux, together with the magnetic field effects, significantly enhance the heat transfer, thereby improving the thermal diffusion. The diffusion and Forchheimer flow are observed to have a substantial impact on velocity, temperature, and concentration profiles and their rates of change. Heat transfer is observed to decrease by 4.32% in nanofluid and 3.42% in hybrid nanofluid with a 33.3% rise in the radiative heat parameter. Additionally, an initial transient behavior in nanoparticle concentration is observed near the surface which is reversed a bit away from the surface. Understanding this behavior is crucial for improving the performance and efficiency of thermal systems in diverse engineering applications.