Darcy-Forchheimer dynamics of Cu-TiO2/H2O hybrid nanofluid flow over a nonlinearly stretching sheet with shape effect

The current study presents the physical perspectives on 3D hydromagnetic Darcy-Forchheimer stream of composite ($\mathrm{Ti}{O}_2-\mathrm{Cu}/H_{2}O$) and mono ($\mathrm{Cu}-H_{2}O$) nanofluids over a nonlinear-elastic inclined sheet with the effects of the shape factor of nano materials and the convective heating. Previous research has looked at the effects of mixed nanofluid dynamics and porous media on their own, but not much has been done on how shape factor, Lorentz force, nonlinear stretching, and inclined geometry all work together in a Darcy–Forchheimer structure.The resulting ODEs are solved using the shooting mechanism in combination with the Runge-Kutta Fehlberg methodology. The influence of various emerging parameters on the velocity and temperature fields, frictional drag, and heat transfer rate is examined and illustrated graphically. The results reveal that the two-phase hybrid nanofluid exhibits higher velocity compared to that in the single-phase flow. The $x$ and $y$ components of the drag force on the surface in both phases decrease with the Grashof number, while an opposite trend occurs with the magnetic parameter. Moreover, the hybrid nanofluid demonstrates enhanced heat transfer rates and elevated temperature fields relative to the mono nanofluid. Among the nanoparticle shapes considered, blade-shaped nanomaterials produce higher temperatures and greater heat transfer rates in both fluids. When particles are blade-shaped, the Nusselt number increase is 7.6 % higher than when particles are spherical. These implications have practical relevance towards thermal design in the fields of biomedical thermal control devices, electronic cooling systems and industrial heat exchangers.