This article reports on the International Nanofluid Property Benchmark Exercise, or INPBE, in which the thermal conductivity of identical samples of colloidally stable dispersions of nanoparticles or "nanofluids," was measured by over 30 organizations worldwide, using a variety of experimental approaches, including the transient hot wire method, steady-state methods, and optical methods. The nanofluids tested in the exercise were comprised of aqueous and nonaqueous basefluids, metal and metal oxide particles, near-spherical and elongated particles, at low and high particle concentrations. The data analysis reveals that the data from most organizations lie within a relatively narrow band ͑Ϯ10% or less͒ about the sample average with only few outliers. The thermal conductivity of the nanofluids was found to increase with particle concentration and aspect ratio, as expected from classical theory. There are ͑small͒ systematic differences in the absolute values of the nanofluid thermal conductivity among the various experimental approaches; however, such differences tend to disappear when the data are normalized to the measured thermal conductivity of the basefluid. The effective medium theory developed for dispersed particles by Maxwell in 1881 and recently generalized by Nan et al. ͓J. Appl. Phys. 81, 6692 ͑1997͔͒, was found to be in good agreement with the experimental data, suggesting that no anomalous enhancement of thermal conductivity was achieved in the nanofluids tested in this exercise.

Measurements of the Nusselt number Nu and of a Reynolds number Re(eff) for Rayleigh-Bénard convection (RBC) over the Rayleigh-number range 10(12)≲Ra≲10(15) and for Prandtl numbers Pr near 0.8 are presented. The aspect ratio Γ≡D/L of a cylindrical sample was 0.50. For Ra≲10(13) the data yielded Nu∝Ra(γ(eff)) with γ(eff)≃0.31 and Re(eff)∝Ra(ζ(eff)) with ζ(eff)≃0.43, consistent with classical turbulent RBC. After a transition region for 10(13)≲Ra≲5×10(14), where multistability occurred, we found γ(eff)≃0.38 and ζ(eff)=ζ≃0.50, in agreement with the results of Grossmann and Lohse for the large-Ra asymptotic state with turbulent boundary layers which was first predicted by Kraichnan.

Non-Oberbeck-Boussinesq (NOB) effects on the Nusselt number Nu and Reynolds number Re in strongly turbulent Rayleigh-Bénard (RB) convection in liquids were investigated both experimentally and theoretically. In the experiments the heat current, the temperature difference, and the temperature at the horizontal midplane were measured. Three cells of different heights L, all filled with water and all with aspect ratio Γ close to 1, were used. For each L, about 1.5 decades in Ra were covered, together spanning the range 10 8 6 Ra 6 10 11 . For the largest temperature difference between the bottom and top plates, ∆ = 40 K, the kinematic viscosity and the thermal expansion coefficient, owing to their temperature dependence, varied by more than a factor of 2. The Oberbeck-Boussinesq (OB) approximation of temperature-independent material parameters thus was no longer valid. The ratio χ of the temperature drops across the bottom and top thermal boundary layers became as small as χ = 0.83, which may be compared with the ratio χ = 1 in the OB case. Nevertheless, the Nusselt number Nu was found to be only slightly smaller (by at most 1.4%) than in the next larger cell with the same Rayleigh number, where the material parameters were still nearly height independent. The Reynolds numbers in the OB and NOB case agreed with each other within the experimental resolution of about 2%, showing that NOB effects for this parameter were small as well. Thus Nu and Re are rather insensitive against even significant deviations from OB conditions. Theoretically, we first account for the robustness of Nu with respect to NOB corrections: the NOB effects in the top boundary layer cancel those which arise in the bottom boundary layer as long as they are linear in the temperature difference ∆. The net effects on Nu are proportional to ∆ 2 and thus increase only slowly and still remain minor despite drastic materialparameter changes. We then extend the Prandtl-Blasius boundary-layer theory to NOB Rayleigh-Bénard flow with temperature-dependent viscosity and thermal diffusivity. This allows calculation of the shift in the bulk temperature, the temperature drops across the boundary layers, and the ratio χ without the introduction of any fitting parameter. The calculated quantities are in very good agreement with experiment. When in addition we use the experimental finding that for water the sum of the top and bottom thermal boundary-layer widths (based on the slopes of the temperature profiles at the plates) remains unchanged under NOB effects within the experimental resolution, the theory also gives the measured small Nusselt-number reduction for the NOB case. In addition, it predicts an increase by about 0.5%

We used the time correlation of shadowgraph images to determine the angle Θ of the horizontal component of the plume velocity above (below) the center of the bottom (top) plate of a cylindrical Rayleigh-Bénard cell of aspect ratio Γ ≡ D/L = 1 (D is the diameter and L ≃ 87 mm the height) in the Rayleigh-number range 7 × 10 7 ≤ R ≤ 3 × 10 9 for a Prandtl number σ = 6. We expect that Θ gives the direction of the large-scale circulation. It oscillates time-periodically. Near the top and bottom plates Θ(t) has the same frequency but is anti-correlated.PACS numbers: 44.25.+f,47.27.Te Turbulent Rayleigh-Bénard convection (RBC) is an important process that occurs in the oceans, the atmosphere, the outer layer of the sun, the Earth's mantle, and in many industrial processes.[1] Despite the seeming simplicity of the idealized laboratory experiment, i.e. a fluid between horizontal parallel plates heated from below and cooled from above, our understanding of the physical mechanism of turbulent RBC remains incomplete. [2,3,4] Much of the heat transport is mediated through the emission of hot (cold) plumes of fluid from a thin boundary layer adjacent to the bottom (top) plate, and these plumes are carried by a large-scale circulation [5,6,7,8,9,10,11] known as the "wind of turbulence". For systems with aspect ratio Γ ≡ D/L = O(1) (D is the diameter and L the height of a cylindrical cell) this wind, when time averaged, takes the form of a single convection roll filling the entire cell. The plume interaction with this circulation is a central component of the turbulent RBC problem, and yet only little is known quantitatively about plume motion and the wind. To a large extent we expect that at least the horizontal motion of the plumes is slaved to the wind velocity, since the only independent force acting on the plumes is the buoyancy force in the vertical direction. Here we present a quantitative study of plume motion and thus, by inference, of the wind direction above (below) the center of the bottom (top) plate. The measured horizontal direction oscillates time periodically, and the oscillations persist with a unique frequency over hundreds of cycles. The oscillations at the top and bottom have the same frequency but a phase which is displaced by half a cycle. We conclude that the wind is a significantly more complicated dynamical system than a simple Rayleigh-Bénard convection cell.Numerous measurements of the speed of the fluid and/or of the temperature at distinct points (i.e. of scalar quantities) were made before and revealed a timeperiodic component. [6,7,8,9,10,11] In some instances these results were interpreted as indicative of a timeperiodic plume emission from the plates. Where direct comparison is possible, we find that the measured frequencies agree quantitatively with our determination of the oscillation frequency of the horizontal wind direction. It has been shown [9] that the corresponding oscillation period is commensurate with the period of circulation of the wind. It had been suggested that periodic plu...

We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of water (Prandtl number σ = 4.38) with diameters D = 49.7, 24.8, and 9.2 cm, all with aspect ratio Γ ≡ D/L ≃ 1 (L is the sample height). In addition, we present data for D = 49.7 and Γ = 1.5, 2, 3, and 6. For each sample the data cover a range of a little over a decade of R. For Γ ≃ 1 they jointly span the range 10Where needed, the data were corrected for the influence of the finite conductivity of the top and bottom plates and of the side walls on the heat transport in the fluid to obtain estimates of N ∞ for plates with infinite conductivity and sidewalls of zero conductivity. For Γ ≃ 1 the effective exponent γ ef f of N ∞ = N 0 R γ ef f ranges from 0.28 near R = 10 8 to 0.333 near R ≃ 7 × 10 10 . For R < ∼ 10 10 the results are consistent with the Grossmann-Lohse model. For larger R, where the data indicate that N ∞ (R) ∼ R 1/3 , the theory has a smaller γ ef f than 1/3 and falls below the data. The data for Γ > 1 are only a few percent smaller than the Γ = 1 results.