Theoretical and numerical study of enhanced heat transfer in partitioned thermal convection

It was recently discovered that a partitioned Rayleigh-Bénard convection (PRBC) by vertical adiabatic boards leaving a narrow horizontal channel (HC) open between partition boards and the cooling/heating plates, may remarkably enhance the overall heat transfer (Bao et al., 2015). This phenomenon is thoroughly investigated by both numerical and analytic study. Numerically, we perform a series of two-dimensional (2-D) direct numerical simulations (DNS) of PRBC for the same set of Rayleigh and Prandtl numbers (Ra=1×108,Pr=0.7and5.3) and two aspect ratios (Γ=1 and 5). The DNS confirm that when the number of partition boards n is large enough, the flow in PRBC becomes coherent and laminar, and the wall jet in HC forms a thinner thermal boundary layer and hence enhances the heat flux from/to conducting plates. A thermosiphoning mode (TS-mode) is used to characterize this laminar forced convection state, which yields an analytic description of the relation between geometrical parameters and the heat transfer coefficient, including two asymptotes for small and large board-to-plate spacing d, where the Nusselt number (Nu) varies with d as d3 and d-1, respectively. The analytical model then predicts an optimal partition spacing maximizing the heat transport, in good agreement with the DNS. More interestingly, the model yields an optimal width of the vertical channel (VC) between two partition boards, in the range 0.01⩽s/H⩽1.00 for Γ=1, as also validated by DNS. For large VC width, we develop a convection-adaptive (CA) model describing the interplay between turbulent bulk flow in VC and the TS-mode, which yields a prediction of Nu in close agreement with DNS for a wide range of n (n=0-35 for Γ=5). Therefore, we have developed an analytic understanding of the PRBC enhanced heat transfer, which provides useful relations for engineering design in industrial applications.