MHD Carreau Hybrid Nanofluid Thin Film Flow over an Unsteady Accelerated Surface with a General Surface Temperature

Abstract

In this study, the magnetohydrodynamic (MHD) flow and heat transfer characteristics of a Carreau hybrid nanofluid thin film over an unsteady accelerated stretching surface are numerically investigated using the MATLAB bvp4c solver. The analysis incorporates a general surface temperature varying in both space and time. The hybrid nanofluid consists of titanium dioxide (TiO₂) and copper (Cu) nanoparticles suspended in a carboxymethyl cellulose (CMC)/water-base fluid. The CMC/water-base fluid is assumed to be uniform and initially quiescent, with the flow generated solely by the unsteady stretching of the surface. The results reveal that increasing the Hartmann number  reduces fluid velocity, film thickness, and skin friction coefficient due to the opposing Lorentz force, whereas negative magnetic field values enhance flow acceleration and convective heat transfer. Compared to the TiO₂–water nanofluid, the hybrid nanofluid consistently exhibits higher dimensionless temperature profiles and larger local Nusselt numbers, signifying improved surface heat transfer performance. Furthermore, increasing the power-law index () and unsteadiness parameter  leads to thicker thermal boundary layers and elevated temperature retention within the thin film, while simultaneously modifying the surface heat transfer rate. Overall, the inclusion of hybrid nanoparticles significantly improves thermal and momentum transport characteristics, demonstrating their effectiveness for controlling heat transfer and flow behavior in unsteady MHD thin film applications.