Experimental study of temperature distribution and local heat flux for turbulent Rayleigh–Bénard convection of air in a long rectangular enclosure

Measurements of temperature distribution and local heat flux were performed in a rectangular Rayleigh–Bénard (RB) cell with aspect ratios Γx=5Γx=5 and Γy=1Γy=1 using air as the working fluid. The range of Rayleigh numbers was from Ra≈6×107Ra≈6×107 up to Ra≈6×108Ra≈6×108 and the measurements were taken at four different positions on the cooling and heating plates. The structure of the temperature profiles was analysed with the scaling to the temperature gradient at the wall γγ, calculated from both global Nusselt number (γglob)(γglob) and the measured local heat flux density q  (γloc)(γloc). The measured local Nusselt number in the center of Rayleigh–Bénard cell is found to be significantly higher than the global Nusselt number, which was calculated from a heat transfer law, based on asymptotic considerations from Hoelling and Herwig [M. Hoelling, H. Herwig, Asymptotic analysis of heat transfer in turbulent RB-convection, Int. J. Heat Mass Transfer 49 (2006) 1129–1136]. Profiles scaled with γglobγglob agree very well with the universal asymptotic temperature profile for Ra→∞. Conversely, profiles scaled with γlocγloc have another structure. The results clearly show the difference between the temperature profiles from the theoretical model with walls of infinite extend and from the real RB-cell. In contrast to common opinion the structure of the temperature profile was found to consist of three different behaviors. It has been observed for all profiles a linear behavior in the viscous sublayer directly on the wall, a power law in the boundary layer and a logarithmic function in the overlap layer.