Numerical analysis of mixed convection at various walls speed ratios in two-sided lid-driven cavity partially heated and filled with nanofluid

Abstract In this study, the problem of laminar mixed convection in a two-sided lid-driven square cavity partially heated and filled with Cu/water nanofluid, is analyzed using a numerical procedure based on the finite volume method with the help of a full multigrid solver. Two heat sources of dimensionless length B maintained at high temperature (T H ) are embedded in the center of the two side walls of the cavity. The top and bottom walls of the enclosure are considered with low temperature (T C ), while the remaining boundary parts of the enclosure are thermally insulated. The top and bottom walls of the cavity can slide in the same or opposite direction with various speed ratios named λ. A parametric study is conducted and a set of graphical results is presented and discussed to illustrate the effects of λ (− 2 ≤ λ ≤ 2), the Richardson number Ri (0.01 ≤  Ri  ≤ 100) and the solid volume fraction ϕ (0 ≤ ϕ ≤ 0.1) on the flow and heat transfer characteristics. The results show that varying the speed ratio has significant effects on both the flow structure and the heat transfer. It is found that heat transfer enhancement can be provided by the presence of nanoparticles and that this is accentuated by decreasing the Richardson number. Special attention has been given to predict a characteristic Richardson number of equilibrium, namely Ri e , leading to an equal heat transfer rate balance between the two opposite sources. Finally, multiple correlations in terms of Richardson number and volume fraction nanoparticles have been established at various speed ratios.