Heat transfer and flow structure in centrally-confined 2-D Rayleigh-Bénard convection

Through direct numerical simulations, we investigated the flow structure and heat transfer of the centrally confined 2-D Rayleigh-B & eacute;nard (RB) convection over the Rayleigh number range 9 x 105 <= Ra <= 109 at a fixed Prandtl number Pr = 4.3. It is found that with increasing Ra, the number of convection rolls in the central vertical channel increases from zero to three. When there is no rolls in the vertical channel, the convective flow in central region is significantly influenced by the boundary layer, whereas when the convection rolls is generated in the vertical channel, the convective flows in central regions is free from the boundary layer limitation, and by defining the characteristic length, one obtains the heat transfer scaling law relation in vertical channel, i.e., Nuvc similar to Ravc0.476 +/- 0.005, which could be the evidence of "ultimate regime".