We explored natural convection of copper oxide-water nanofluid flow within a square domain having two wavy vertical surfaces in existence of the hydro-magnetic field using non-uniform dynamic model. Two vertical surfaces on the left and right are regarded as connecting outlets through which heat can pass and considered as the colder walls, the bottom surface is regarded as a uniform heat source, and the upper boundary line is regarded as an insulating surface through which heat cannot pass. The Galerkin's extension in the finite element analysis has been incorporated to design, transform, and solve the nanofluid equations. The results reveal that when the thermal Rayleigh number upturns, the amplitude of the velocity, streamlining, isotherms efficacy, and uniformity of the isoconcentration labeling increase for a nanofluid with reduced nanoparticle volume percentage. As the magnetic pitch intensifies, the flow strength drops, and effective flow occurs in the vertical magnetic field. Flow convolution develops as more waves are formed on a vertical surface. The average heat transmission rose by 158% as the Rayleigh number grew from 10⁴ to 10⁶. The mean heat transmission increases by 10.18% when the nanoparticle volume segment is increased from 0.025 to 0.05. The heat transmission rate is higher on the vessel's non-wave vertical surface. Heat transfer is reduced by 16.98% when the wave number is augmented to 2 and increased by 3.62% when the wave number is risen from 2 to 4.