Flow Mode and Global Transport of Liquid Metal Thermal Convection in a Cavity with F=1/3

We report an experimental study of Rayleigh-Benard convection of liquid metal thermal convection with a Prandtl number of Pr = 0.029 in the cuboid cell of aspect ratios I' = width/height = 1/3. By arranging 48 thermistors and 6 ultrasonic sensors in the sidewall of the cell, the flow mode and corresponding flow and heat transfer characteristics are obtained with Rayleigh number Ra varying from 1.05 x 106 to 4.01 x 107. Three typical flow modes are defined from the results of temperature measurements, showing a double -roll mode (DRM) with two vertically stacked counterrotating rolls, a single -roll mode (SRM) that occupies the entire cell and a distorted single -roll mode existing in the transitions between DRM and SRM. Moreover, by gradually increasing the Ra one can observe the flow transition from DRM to SRM by the statistics of the lifetime for each flow mode. The complete Fourier analysis of temperature data shows that the origin of the flow modes can be attributed to the energy transformation between Fourier modes of different orders. When Ra 1.19 x 107, the first Fourier mode energy has accounted for more than 75% of the total energy which is evidence that the SRM is fully established. Furthermore, the measured temperature profiles along the central axis of the cell follow a linear law in the bulk, and the slopes obey power -law scaling with Ra. Regarding the standard deviation of temperature profiles along the central axis of the cell which bulge in the bulk forming the second peak outside the thermal boundary layers at small Ra due to the complex three-dimensional flow structures. Finally, the similar scaling laws of the global heat and momentum transfer of the liquid metal thermal convection in a slender cuboid cell are observed, showing Nu - Ra0.35 and Re - Ra0.36 for heat and momentum transfer, respectively.