Measurements of the instantaneous local heat flux in turbulent Rayleigh–Bénard convection

Abstract

We present measurements of the instantaneous local heat flux in highly turbulent Rayleigh–Bénard (RB) convection in air (Pr=0.7) for aspect ratios in the range 1.13⩽Γ⩽9.00 and for Rayleigh numbers in the range 1.3×109⩽Ra⩽9.6×1011. The measurements have been carried out simultaneously at the surfaces of the heating and the cooling plate using a commercial sensor whose diameter is 360 times smaller than the diameter of the RB facility. We find that for all investigated values of Ra and Γ the time-averaged local heat flux at the centres of the heating and cooling plates is significantly higher than the global heat flux obtained in previous measurements. In particular, for the smallest investigated aspect ratio, Γ=1.13, the scaling exponents of the local heat fluxes as functions of the Rayleigh number are found to be considerably below those of the global heat flux obtained in experiments with cryogenic helium at Γ=1 by Niemela and Sreenivasan (2003 J. Fluid Mech.481 355–84). Our measurements indicate that the spatial distribution of the heat flux at the heating and cooling plates is strongly nonuniform and that this nonuniformity decreases with increasing Ra and Γ. Our investigations of the time dependence of the local heat fluxes show that these quantities undergo fluctuations up to ±15% of their time-averaged values. Our work suggests that local heat flux measurements at different positions along heating and cooling plates are useful for a deeper understanding of the scaling properties of the (global) Nusselt number in RB convection.