Effects of slip boundaries on thermal convection in 2D box using lattice Boltzmann method

This work studied the thermal convection under various slip boundary conditions in a 2D box with aspect ratio equal to two. The slip parameter is the normalized tangential momentum accommodation coefficient (TMAC, 0 ⩽ σ ⩽ 1). The results show that the slip boundary conditions of vertical side walls (σv) and horizontal plates (σh) will affect the pattern selections of the flow and temperature fields. When σh < 0.02, the pattern is the one-roll mode for all σv. When σh ⩾ 0.02 and σv ⩽ 0.1, the fluids prefer the two-roll mode where two rolls make the fluids to move upwards in the middle of the box. While σh ⩾ 0.02 and σv ⩾ 0.2, the fluids prefer the other two-roll mode which makes the fluid to move downwards in the middle of the box.