Lattice-Boltzmann modelling of natural convection in an inclined square enclosure with partitions attached to its cold wall

In the present work, a numerical study of the effect of a single and multiple partitions on heat transfer phenomena in an inclined square cavity, differentially heated, is carried out for Pr = 0.71 and Rayleigh numbers of Ra = 103–106. The partitions are attached to the cold wall of the cavity. Numerical coupling between the lattice Boltzmann equation and finite-difference for the temperature is used to solve this problem. The investigation is performed for various inclination angles and gap widths W. At lower Ra (Ra ⩽ 105), the average hot wall Nusselt number Num is higher in inclined cavities than in vertical ones; while at larger Ra (Ra = 106), the opposite occurs. In vertical cavities, Num decreases with decreasing W. However in inclined ones, this trend is found only at lower Ra whereas at higher Ra, Num shows a maximum at about W = 0.5. Num also decreases when the number of partitions (Np) attached to the cold wall of the enclosure increases; however beyond a certain value of (Np), which depends of Ra, Num becomes almost constant.