This study investigates natural convection heat transfer through numerical simulations. The computational domain consists of a cubic enclosure filled with an \(\hbox {Al}_2\hbox {O}_3\) – \(\hbox {H}_2\hbox {O}\) nanofluid, containing a concentric sphere that may be either heated or cooled. Various configurations are analyzed by varying the Rayleigh number ( \(10^3 \le \text {Ra} \le 10^5\) ) and the nanoparticle volume fraction ( \(0.01 \le \phi \le 0.1\) ). The governing equations comprise the unsteady incompressible Navier–Stokes equations coupled with the heat transport equation. The Boussinesq approximation is employed, treating the density as constant except in the buoyancy term. To mitigate numerical instabilities inherent in the classical Galerkin finite element method (GFEM), a stabilized finite element formulation, known as the SUPS, is implemented. This formulation incorporates the streamline-upwind and pressure-stabilizing mechanisms. The proposed computational framework and in-house parallel incompressible flow solvers are validated against established benchmark cases, demonstrating good agreement despite using unstructured tetrahedral meshes without adaptive refinement. For the considered flow domain, the stabilized method ensures accurate solution profiles without significant spurious oscillations while substantially reducing computational cost, as linear interpolation functions are sufficient. Findings indicate that increasing the nanoparticle volume fraction enhances velocity magnitudes and the overall heat transfer rate around the sphere. Additionally, a slight reduction in the average number of nonlinear iterations is observed, suggesting improved computational efficiency. These results emphasize the effectiveness of stabilized finite element formulations in accurately and efficiently simulating convection-driven flow phenomena.
