Study of Periodic Thermal Exchange in a Cavity Ventilated by Displacement

The lattice Boltzmann method with multiple relaxation times has been used to solve numerically the momentum and the heat transfer governing equations. The laminar convection has been studied in two-dimensional square cavity. The temperature of the left wall varies sinusoidally depending on the time, while the other walls are maintained adiabatic. The cavity is ventilated by two diagonally opposed openings, where the injection is at the bottom of the active wall and the aspiration at the top. The control parameters are the temperature amplitude, varying from 0 to 0.9, the Rayleigh number ranged from 10 to 10 +6 which can be expressed in term of Richardson by the range 0.0056 ≤ Ri ≤ 5.63, the Reynolds number is taken as: 50 ≤ Re ≤ 500, and the number of Prandtl is that of the air (Pr = 0.71). The obtained results in terms of streamlines, isotherms and heat transfer rates, expressed by the averaged Nusselt number, as a function of time and for establishment period are presented for different parameters. It is observed that the control parameters, temperature amplitude, Reynolds and Rayleigh numbers have a significant effect on both the flow and the thermal structure fields. It has been revealed that the optimum heating amplitude presents an important factor in order to minimize the cooling demand, that is for amplitude values greater than 0.4 and low Reynolds number (Re ≤ 200), the transfer rate takes negative values, indicating that the cooling phenomena occur between the hot wall and the fluid (from the fluid to the hot wall).