Numerical simulation of mixed convection in a two-sided lid-driven square cavity with four inner cylinders based on diamond arrays

The hydrodynamics and thermal characteristics due to mixed convection in a vertical two-sided lid-driven differentially square cavity containing four hot cylinders in a diamond array are investigated by the lattice Boltzmann equation model. The moving walls of the cavity are cold while the others are adiabatic. The flow in the cavity is driven by both the temperature difference and the moving vertical walls. The influence of different flow governing parameters, including the direction of the moving walls (the left wall moves up and the right wall moves down (Case I), both the left and right walls are moving upward (Case II), both the left and right walls are moving downwards (Case III)), the distance between neighboring cylinders delta (0.3L <= delta <= 0.5L), and the Richardson number Ri (0.1 <= <mml:mstyle>Ri</mml:mstyle><= 10) on the fluid flow and heat transfer are investigated with the Reynolds number in the range of 375 <= <mml:mstyle>Re</mml:mstyle><= 3752, the Grashof number of 1.4x106 and the Prandtl number of <mml:mstyle>Pr</mml:mstyle>=0.71. Flow and thermal performances in the cavity are analyzed in detail by considering the streamlines and isotherms profiles, the average Nusselt number, as well as the total Nusselt number. It is found that the heat transfer efficiency is highest when <mml:mstyle>Ri</mml:mstyle>=1.0 for the cases of the walls moving in the opposite direction. When the walls move in the same directions, the heat transfer efficiency obtained by <mml:mstyle>Ri</mml:mstyle>=0.1 is maximum among the considered values of Ri. On the other hand, compared with the cases of <mml:mstyle>Ri</mml:mstyle>=1.0 and <mml:mstyle>Ri</mml:mstyle>=10, the cylinder positions corresponding to the largest and the smallest Nusselt numbers are very sensitive to the moving direction of the walls for <mml:mstyle>Ri</mml:mstyle>=0.1. Moreover, the results also show that in terms of the value of Nusselt number and the stability the case of both walls moving downwards works well. Besides, the effect of the distance between neighboring cylinders is also discussed, it is found that increasing or decreasing the spacing between cylinders could enhance heat transfer to different degrees for the range of Ri number considered. Finally, the empirical relationships among <mml:mstyle>Nu</mml:mstyle><mml:mstyle>ave</mml:mstyle>, Ri, and the spacing between the cylinders (delta) are given, and predictive results match with the computed values very well.