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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 ≤ Ra ≤ 107, the Darcy number (Da), 10−7 ≤ Da ≤ 1, the porous layer thickness (S), 0 ≤ S ≤ 1, the modified conductivity ratio (γ), 10−1 ≤ γ ≤ 104, the interphase heat transfer coefficient (H), 10−1 ≤ H ≤ 1000, the heat source length (B), 0.2, 0.4, 0.6, 0.8 and 1, and the nanoparticle volume fraction (ϕ), 0 ≤ ϕ ≤ 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 ≤ 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 γ and H can strongly enhance the heat transfer rate and satisfy the thermal equilibrium case. [ABSTRACT FROM AUTHOR]

Graphical abstract Physical domain of case 1 in the vertical direction and case 2 in the horizontal direction of the composite nanofluid-porous medium layers. Highlights • Natural convection in a composite cavity filled with porous nanofluid was performed. • The effect of a linearly heated left sidewall for two cases 1 & 2 was utilized. • Effects of S , Ra , Da and K r on the flow distributions are investigated. • Increasing Ra caused the intensity of the streamlines in case 2 > case 1. • At low values of K r especially at Da < 10 - 3 , Nu av increased in case 2 > case 1. Abstract The effect of a linearly heated left sidewall on natural convection flows in a cavity filled with nanofluid-superposed porous layers is investigated numerically using the Galerkin finite element method. Two cases, which use the vertical and horizontal directions for the porous–nanofluid layers, are considered to investigate the natural convection in the flow inside a square enclosure. In both cases, the left wall is linearly heated, whereas the right wall is isothermally cooled. The horizontal walls are assumed to be thermally insulated. The Darcy–Brinkmann model is used to solve the governing equations in the porous layer. The results show that the nanofluid produces more enhancement of heat transfer compared to the base fluid. Increasing the Rayleigh number (R a) values caused the intensity of the streamlines in case 2 to be stronger than that in case 1. Lower values of the thermal conductivity ratio (K r) imply greater heat transfer enhancement than for the high thermal conductivity ratios. At the low values of the thermal conductivity ratio (K r < 1) and Darcy number values (D a < 10 - 3 ) , the heat transfer is more enhanced for case 2 compared to case 1 while higher Darcy number produced case 1 overcome case 2. [ABSTRACT FROM AUTHOR]