<p>This study numerically investigates natural convection around an elliptical–circular composite cylinder placed in a square enclosure under the assumptions of two-dimensional, unsteady, and incompressible flow. The simulations were performed using an in-house Fortran code based on the finite volume method with the immersed boundary approach. The effects of the major axis length (<i>b/L</i>), cylinder radius (<i>R/L</i>), and inclination angle (<i>φ</i>) on flow structure and heat transfer characteristics were analyzed for various Rayleigh numbers. The results reveal that increasing the dimensionless major axis length <i>b/L</i> and the cylinder radius <i>R/L</i> narrows the upper gap, intensifies plume circulation and recirculation zones, and enhances heat transfer on the enclosure walls while slightly reducing that on the cylinder surface due to thinner boundary layers. The inclination angle mainly causes local asymmetry but has a negligible effect on the overall heat transfer at high Rayleigh numbers. Furthermore, the correlation equations were derived using a polynomial form that incorporates not only the linear terms of each variable but also their quadratic terms and interaction terms.</p>