Heat transport in horizontally periodic and confined Rayleigh-Bénard convection with no-slip and free-slip plates

•The periodic sidewall boundary condition influences the heat transport and does not influence the temperature profiles compared with the confined sample.•When zonal flow appears, the heat transport decreases as Ra increases•The zonal flow forms when Ra exceeds a threshold value in the periodic sample We report the results of the direct numerical simulations of two-dimensional Rayleigh-Bénard convection(RBC) in order to study the influence of the periodic (PD) and confined (CF) samples on the heat transport Nu. The numerical study is conducted with the Rayleigh number (Ra) varied in the range 106≤Ra≤109 at a fixed Prandtl number Pr=4.3 and aspect ratio Γ=2 with the no-slip (NS) and free-slip(FS) plates. There exists a zonal flow for Ra≥3×106 with the free-slip plates in the periodic sample. In all the other cases, the flow is the closed large-scale circulation (closed LSC). The striking features are that the heat transport Nu is influenced and the temperature profiles do not be influenced when the flow pattern is zonal flow.