| Thermal convection is widely found in non-equilibrium open systems such as atmospheric circulation and mantle convection.Rayleigh-Benard Convection?RBC?is a typical model for studying thermal convection in natural non-equilibrium open systems.Most of the previous studies were carried out under smooth boundary,and the study of Rayleigh-Benard convection under rough boundary is important for natural convection and heat transfer in practical engineering.According to the previous results under smooth boundary,the thickness of the thermal boundary layer is no more than 2 mm.Therefore,we set up two cells with roughness h=3 mm and h=6 mm respectively.In this experiment,under the condition of keeping Pr=5.4,in the range of Ra=3.3×109?1.1×1011,the measurement of Nu and Ra is carried out under h=3 mm,and the corresponding scale-law relationship is obtained:Nu=0.0392Ra0.35±0.01.In the range of Ra=3.3×109?6.5×109,the measurement of temperature fluctuations on the central axis is carried out under h=3 mm and h=6 mm respectively.In the range of Ra=3.3×109?8.1×109,the temperature fluctuations near the side wall was measured under h=6 mm,and the probability density function of the temperature fluctuations was analyzed.We optimize the mathematical model based on the predecessors.The probability density function in the RBC system can be mathematically described,and the change of the corresponding parameters can systematically explain the influence of the plume on the temperature fluctuations in various regions of the RBC system.The time series of temperature fluctuations,temperature gradient,and fluctuations of thermal dissipation rate at the tip of the pyramid near the hot plate with roughness h=3mm and 6mm are analyzed.Near the tip of the pyramid,it is considered that the intensity of the plume with h=6 mm is stronger than that with h=3 mm,further indicating that the increase in roughness can enhance the concentration of the plume.At the cell center,the temperature fluctuations under rough boundary are very similar to those under the smooth boundary.It is considered that the influence of the addition of roughness on the cell center is small. |
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