This present work concerns the study of laminar mixed convection in lid-driven cavities filled with Cu-water nanofluid. Each cavity is heated by two heat sources placed on vertical walls at a constant heat flux q. The top wall moved with uniform velocity of U0. The top and bottom walls of the cavity are maintained at a local cold temperature TC, respectively. The continuity, Navier-Stokes, and energy equations are all solved by using the finite volume method. A computer program is developed and compared with the numerical results found in the literature. Results are presented in terms of streamlines, isotherms, vertical velocity profile, and average Nusselt numbers at a fixed Reynolds number (Re=10) and for Rayleigh numbers in the range (Ra=10 3 -10 6 ), solid volume fractions of nanoparticles (=0-0.20) and different aspect ratios (AR=0.5-4). It is found that the average Nusselt number increases with the increase of the Rayleigh number, solid volume fraction and aspect ratio of the cavity.

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A numerical simulation was performed in four geometries with different boundary conditions; two geometries have top walls moving with a constant horizontal velocity U0 in two opposite directions, while the other geometries have vertical walls moving in two opposite directions with a constant vertical velocity V0. These cavities are filled with hybrid nanofluid Al2O3-Cu/water, and heated by two constant flow heat sources placed on the left vertical wall. The moving wall and the other walls are respectively maintained at a local cold temperature Tc. The interest of this work is to see the effects generated by incorporation of hybrid nanofluids on the mixed convection flow, and to make an analysis of the entropy production in the mixed convection problem in order to be able to choose the geometry with different boundary conditions among the four geometries with different boundary conditions that will ensure energy efficiency. The finite volume method was used to solve the heat transfer flow equations across the physical domain with the SIMPLER algorithm. The influence of relevant parameters such as Richardson and Reynolds numbers and volume fraction of nanoparticles on entropy generation and heat transfer rate were studied. It was found that entropy generation decreases with increasing Richardson number, Reynolds number and that incorporation of a hybrid Al2O3-Cu/water nanofluid in the base fluid improves the high heat transfer rate.

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