Strong coupling between height of gaps and thickness of thermal boundary layer in partitioned convection system

A direct numerical simulation (DNS) method is used to calculate the partitioned convection system with Ra number ranging from 10⁷ to 2×10⁹. Using the boundary layer thickness to normalize the height of gaps d, we find a strong consistency between the variation of the TD number (the average value of the temperature in each heat transfer channel is averaged after taking the absolute values) with the change of the height of gaps and the variation of the TD number with the change of Ra number in partitioned convection. For a given thickness of partition, heights of gaps are approximately equal to 0.5 or 1 time of the thermal boundary layer thickness λ_θ at different Ra numbers. TD number representing temperature characteristics is almost the constant value, which means that TD number is a function of d/λ_θ only. Analysis of local temperature field of area in gaps shows that the temperature distribution in the gaps are basically the same when d/λ_θ is certain. The heat transfer Nu number of the system at d/λ_θ≈ 0.5 is larger than that of d/λ_θ≈ 1, both of them have the same scaling law with Ra number and Nu~Ra^0.25.