A numerical investigation is performed to study conjugate natural convection heat transfer in a square cavity coupled with a copper–graphene nanocomposite solid wall. The cavity is filled with a Newtonian fluid and subjected to a constant heat flux applied over a finite portion of the bottom wall, while the vertical sidewalls are maintained at a constant cold temperature, and the remaining boundaries are adiabatic. Heat conduction in the solid wall and convection in the fluid domain are simultaneously considered. The Lattice Boltzmann Method (LBM) with the Bhatnagar–Gross–Krook (BGK) collision model is employed to solve the governing equations. The effective thermal conductivity of the copper–graphene nanocomposite is evaluated using a micromechanical model accounting for graphene nanoplatelet waviness, alignment, and Interfacial Thermal Resistance (ITR). The numerical model is validated against well-established experimental correlations for natural convection, showing excellent agreement.Parametric analyses are conducted to examine the effects of Rayleigh number, constant heat flux length, and solid wall thickness on flow structure and heat transfer characteristics. The results indicate that the copper–graphene nanocomposite significantly enhances heat transfer compared to pure copper by reducing surface temperature and increasing local and average Nusselt numbers. Increasing Rayleigh number intensifies buoyancy-driven convection, while larger heat flux lengths reduce heat transfer efficiency. Thicker nanocomposite walls improve conductive heat spreading and overall thermal performance.