Direct measurements of the thermal dissipation rate in turbulent Rayleigh–Bénard convection

We report measurements of the thermal dissipation rate in turbulent Rayleigh-Bénard convection using a four-thermistor temperature gradient probe. The measurements have been undertaken in a Rayleigh-Bénard cell filled with air (Prandtl number P r = 0.7 ). The focus of this work is on large aspect ratios Γ (ratio between the horizontal and vertical extension of the cell), for which reason four datasets in the range of Rayleigh number R a = 3.9 × 10 6 to R a = 1.8 × 10 9 were taken at Γ ≥ 8. In order to extend the range toward higher Rayleigh numbers, two smaller aspect ratios were also investigated ( Γ = 4 with R a = 1.7 × 10 10 and Γ = 2 with R a = 1.6 × 10 11). We present highly resolved, vertical profiles of the thermal dissipation rate in the central vertical axis and discuss how these profiles change with the Rayleigh number. With its maximum near the wall and at the highest Rayleigh number, the thermal dissipation rate decreases monotonically with the distance from the plate. Moreover, the normalized, volume-averaged thermal dissipation rate, which effectively results in the Nusselt number N u, scales with an exponent of about 0.29 with the Rayleigh number. In the Rayleigh number range investigated here, the dissipation is always higher in the boundary layer than in the bulk region. However, by means of an extrapolation of the considered Rayleigh number range to larger Rayleigh numbers, the intersection point between the dissipation in the boundary layer and the bulk region can be estimated as R a ≈ 3 × 10 12.