LAUSR

In the present paper, we numerically investigated the two-dimensional conjugate heat transfer problems in a unitary computational domain containing both the solid and fluid regions. The physical problem configuration consists of two adiabatic horizontal walls of finite thickness and two vertical walls; the left one is maintained at hot temperature Th and the right one is maintained at cold temperature Tc. The lattice Boltzmann method (LBM) based on the BGK model has been used to simulate laminar natural convection in the partitioned air-filled cavity with a heat-conducting solid. In the interface boundaries of the heat-conducting solid, the continuity of temperature and heat transfer is considered. A series of numerical simulation is carried out over a wide range of the Rayleigh number (Ra = 103–106), the thermal conductivity ratio kr and the solid partition thickness (δ = 1–95℅) and its horizontal position. The results show that the partition reduces the heat transfer rate in the cavity. For a centered partition (Xs = 0.5), the average Nusselt number decreases almost linearly with partition thickness for δ ≤ 0.45; however, it increases for δ ≥ 0.45 due to the confinement in the thin fluid regions. For Ra = 105, the heat transfer rate decreases with the partition position until a critical value close to 0.325 and rises slightly until Xs = 0.5. The critical position value decreases with the Ra number increase and it is close to 0.2 for Ra = 106 where Nu = 3.766. The heat transfer rate is enhanced with the increase in thermal conductivity. Correlations of the average Nusselt numbers are obtained as a function of Rayleigh number.