The flow of hybrid alumina–copper/water nanofluid with mixed convection heat transfer from multiple square cylinders arranged in three different types of arrays, namely equilateral triangle (ET), rotated square (RS), and rotated rhombus (RR) in a heat exchanger, has never been studied before the present study. Navier–Stokes and energy equations with a periodic boundary condition in the transverse direction for all three array types having the same porosity are solved with the finite volume methodology. The combined effect of aiding buoyancy (Richardson number 0–2), the configuration of square cylinders, and hybrid nanoparticle volume fraction (0-0.06) on the flow dynamics and their impact on the overall heat transfer phenomenon through three different array configurations is thoroughly elucidated. The arrays’ overall drag and friction coefficient increases with an increase in the strength of aiding buoyancy and nanoparticle volume fraction. An increment in Richardson number, and nanoparticle volume fraction, causes thermal boundary layer thinning and results in higher heat transfer rates across all three arrays. With an increase in Ri from 0 to 2 at a nanoparticle volume fraction of 0.06, the mean Nusselt number of ET, RS, and RR arrays is increased by 161%, 5%, and 32%, respectively. While, with an increase in nanoparticle volume fraction from 0 to 0.06 at Ri = 2, the mean Nusselt number of ET, RS, and RR arrays is augmented by 17%, 6%, and 9%, respectively. Finally, the efficient array configuration in terms of fluid-thermal behavior is proposed to design various heat-exchange systems under differing operating conditions.