This paper aims to understand the characteristics of heat transfer and flow by natural convection of Al2O3–Cu/water-based hybrid nanofluid-filled square domain containing various configurations of a corrugated conducting solid under a horizontal magnetic field. The basic equations in their non-dimensional form are numerically solved using the finite volume discretization technique. The Corcione correlations are utilized to estimate the overall heat conductivity and overall viscosity of the hybrid nanoliquid when the nanoparticle’s Brownian motion is taken into account. The dependency of different governing factors of the investigation, namely volume fraction of the combined nanoparticles, Rayleigh and Hartmann numbers, undulation number, undulation amplitude and the fluid/solid heat conductivity ratio, on thermohydrodynamic characteristics are delineated. Results stated that the maximum heat transmission rate was obtained for weak values of Hartmann, undulation number, undulation amplitude and high values of Rayleigh and nanoparticles volumic fraction. In addition, the fluid/solid heat conductivity ratio parameter was found to boost the heat transfer at weak Rayleigh while reducing it at high Rayleigh.