The natural convection in a compact system with a heat source is a key focus in various engineering applications from electronic cooling to building ventilation, where the optimum position of the heat source and advanced coolants can enhance thermal performance. This study investigates the natural convection heat transfer of a cold square enclosure filled with \({\text{Al}}_{2} {\text{O}}_{3}\) /water-based nanofluid and an internal square heat source. Here, an in-house developed lattice Boltzmann method (LBM)-based solver written in the C programming language is employed to conduct two-dimensional numerical simulations. Novelty of this study lies in the combined assessment of nanoparticle concentration ( \(\varphi\) = 0%, 2%, and 4%), eccentricities of the heat source in both horizontal ( \(\chi_{{\text{h}}}\) = − 0.2 to + 0.2) and vertical ( \(\chi_{{\text{v}}}\) = − 0.2 to + 0.2) direction, and Rayleigh number ( \({\text{Ra}}\) = 103 to 106) on natural convection within the enclosure using the LBM-based solver. These governing parameters significantly influence the streamlines, isotherm distribution, and both local and surface-averaged Nusselt numbers ( \(\overline{{{\text{Nu}}}}\) ) on the enclosure’s surface. The eccentric position of the heat source significantly alters the flow dynamics, mixing, and heat transfer rate. At Ra = 103 and 104, the maximum heat transfer occurs at higher eccentricities owing to the dominance of conduction. For Ra = 105 and 106, where both convection and conduction exist, the maximum heat transfer depends on the eccentricity. Additionally, the concentration of nanoparticles strongly affects the thermal performance of the enclosure. The maximum value of \(\overline{{{\text{Nu}}}}\) is 6.19 found at φ = 4% with Ra = 106, \(\chi_{{\text{h}}}\) = 0.0, and \(\chi_{\nu}\) = − 0.2. Notably, the enhancement of \(\overline{{{\text{Nu}}}}\) (En) varies with \(\chi_{{\text{h}}}\) , \(\chi_{\nu}\) , Ra, and \(\varphi\) . The maximum value of En is 8.83%, noticed at φ = 4%, Ra = 106, \(\chi_{{\text{h}}}\) = 0.2, and \(\chi\) ν= 0. This demonstrates that the effectiveness of nanoparticles is significant at higher Ra. Furthermore, a regression analysis-based correlation equation is proposed to predict \(\overline{{{\text{v}}}}\) as a function of governing parameters, enabling the estimation of \(\overline{{{\text{Nu}}}}\) without performing expensive numerical simulations.
