Analysis of three-dimensional flow and heat transfer in a Casson quaternary hybrid nanofluid over a Riga plate in a Darcy–Forchheimer porous medium with variable thermophysical properties

Efficient thermal management has become increasingly important in advanced engineering systems, motivating the development of nanofluids with improved heat-transfer capability. This study investigates the three-dimensional flow and heat-transfer behavior of a Casson quaternary hybrid nanofluid composed of Cu, ZrO 2 , Al 2 O 3 , and Fe 3 O 4 nanoparticles dispersed in ethylene glycol. The analysis considers steady, incompressible, laminar boundary-layer flow over a stretching surface in the presence of a Riga plate, Darcy–Forchheimer porous medium, magnetic field, velocity slip, thermal radiation, convective boundary condition, and temperature-dependent viscosity and thermal conductivity. Appropriate similarity transformations are employed to convert the governing partial differential equations into a system of nonlinear ordinary differential equations. The transformed equations are solved numerically using the Galerkin Weighted Residual Method implemented in Mathematica 11.3. The results show that the magnetic field, porous-medium resistance, slip parameter, and variable viscosity reduce the velocity field, whereas Riga-plate forcing accelerates the near-wall flow. Thermal radiation, Biot number, and variable thermal conductivity significantly influence the thermal boundary layer and heat-transfer behavior. Under the investigated conditions, the quaternary hybrid nanofluid exhibits comparatively enhanced heat-transfer characteristics relative to the corresponding dual- and tri-hybrid nanofluids. These findings suggest that Casson quaternary hybrid nanofluids may provide promising thermal-management capability for advanced cooling and heat-transfer applications, although further hydraulic and experimental assessment is required for practical implementation.