This analysis explores the steady-state momentum and radiation heat transfer flow of hybrid nanofluid flow in a porous medium with melting heat conditions. Furthermore, the analysis of entropy generation via the second law of thermodynamics is used to assess the thermal system. Viscous dissipation and Joule heating are also taken into account. The hybrid nanofluid model's numerical framework is established, and similarity transformations are employed to convert the PDEs into nonlinear ordinary differential equations. The innovative nonlinear thermal radiation effects are added into the constitutive model, and the results for the flow regimes (velocity, thermal behavior, shear stresses, and local Nusselt number) are then provided by modifying the physical constraints. In each case, a comparison between single-walled nanotubes (SWCNTs) + copper oxide and multiwalled nanotubes (MWCNTs) + copper oxide is made. It appears that when the Hartmann number and thermal radiation rise, the magnitude of the local heat flux of the hybrid nanofluid diminishes, whereas the melting heat parameter, porosity parameter, and Eckert number exhibit the opposite pattern. Furthermore, multiple-walled carbon nanotubes exhibit unusual behavior equated to single-walled carbon nanotubes. Furthermore, an appropriate agreement is obtained on comparing the numerical results with previously published results.