Buoyancy-driven flow inside a superposed enclosure filled with composite porous-hybrid nanofluid layers was investigated numerically using a local thermal nonequilibrium model for the heat transfer between the fluid and the solid phases. The bottom wall of the enclosure was partly heated to provide a heat flux, while the other parts of the wall were thermally insulated. The top and vertical walls of the enclosure were maintained at constant cold temperatures. The Darcy-Brinkman model was adopted to model the flow inside the porous layer. The Galerkin finite element method was used to solve the governing equations using the semi-implicit method for pressure linked equations algorithm. The selected parameters are presented for the Rayleigh number (Ra), 103 B Ra B 107, the Darcy number (Da), 10?7 B Da B 1, the porous layer thickness (S), 0 B S B 1, the modified conductivity ratio ( kf), 10?1 & 104, the interphase heat transfer coefficient (H), 10?1 B H B 1000,the heat source length (B), 0.2, 0.4, 0.6, 0.8 and 1, and the nanoparticle volume fraction (), 0 B  B 0.2. It has been concluded that the rate of heat transfer of hybrid nanofluid (Cu?Al2O3/water) is higher than with the pure fluid. Furthermore, at Ra B 105, the heat transfer rate maintains its maximum value when S reaches the critical value (S = 0.3). The values of S, Da, and B were found to have a significant effect on the heat removal from the heat source. Increasing the values of and H can strongly enhance the heat transfer rate and satisfy the thermal equilibrium case.