Copper oxide makes an excellent nanomaterial for various efficient heat transfer devices because of its high specific surface area, lightweight, high specific heat capacity, and high thermal conductivity. Heat transfer intensification using nanofluids has strong potential to improve innovative cost-efficient chilling technologies. The present study aims to analyze the heat transfer intensifications for various parameter settings in a practical application. In recognition of possible applications, the problem of natural convective heat transfer in a copper oxide nanofluid-filled square vessel having the wavy upper wall in the presence of a uniform magnetic field using a nonhomogeneous dynamic model is analyzed. The temperature of both the bottom and the near walls of the vessel are hot, while the upper wavy surface is cold. The remaining vertical wall is considered adiabatic. A Galerkin finite element method is applied to the governing equations, along with suitable boundary conditions. The effects of a wide range of control parameters, such as the Hartmann number, magnetic field inclination angle, gravity inclination angle, solid-volume fraction, nanoparticle diameter, and dimensionless time, on the flow and thermal fields, are studied. The results show that early steady-state heat transfer occurs and that the flow, thermal, and concentration fields become suitable for enhanced heat transfer with increases in the Rayleigh number, wall wavenumber, nanosolid volumetric ratio, and geometry inclination angle, and with decreases in the Hartmann number and the nanoparticle diameter. A 20% improvement in heat transfer can be achieved by increasing the number of waves on the upper surface of heat transfer devices.