Conjugate natural heat transfer scrutiny in differentially heated cavity partitioned with a conducting solid using the lattice Boltzmann method

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 T-h and the right one is maintained at cold temperature T-c. 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=10(3)-10(6)), the thermal conductivity ratio k(r) and the solid partition thickness (delta=1-95c/o) and its horizontal position. The results show that the partition reduces the heat transfer rate in the cavity. For a centered partition (X-s=0.5), the average Nusselt number decreases almost linearly with partition thickness for delta <= 0.45; however, it increases for delta >= 0.45 due to the confinement in the thin fluid regions. For Ra=10(5), the heat transfer rate decreases with the partition position until a critical value close to 0.325 and rises slightly until X-s=0.5. The critical position value decreases with the Ra number increase and it is close to 0.2 for Ra=10(6) 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.