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The present paper aims to analyze the thermal convective heat transport and generated irreversibility of water-Cu-Al₂O₃ hybrid nanosuspension in an odd-shaped cavity. The side walls are adiabatic, and the internal and external borders of the enclosure are isothermally kept at high and low temperatures of <i>T_h</i>and <i>T_c</i>, respectively. The control equations based on conservation laws are formulated in dimensionless form and worked out employing the Galerkin finite element technique. The outcomes are demonstrated using streamlines, isothermal lines, heatlines, isolines of Bejan number, as well as the rate of generated entropy and the Nusselt number. Impacts of the Rayleigh number, the hybrid nanoparticles concentration (<i>ϕ_hnf</i>), the volume fraction of the Cu nanoparticles to <i>ϕ_hnf</i> ratio (<i>ϕ_r</i>), width ratio (<i>WR</i>) have been surveyed and discussed. The results show that, for all magnitudes of Rayleigh numbers, increasing nanoparticles concentration intensifies the rate of entropy generation. Moreover, for high Rayleigh numbers, increasing <i>WR</i> enhances the rate of heat transport.