We present measurements of the Nusselt number N as a function of the Rayleigh number R and the Prandtl number sigma in cylindrical cells with aspect ratios gamma = 0.5 and 1.0. We used acetone, methanol, ethanol, and 2-propanol with Prandtl numbers sigma = 4.0, 6.5, 14.2, and 34.1, respectively, in the range 3x10(7) less, similarR less, similar10(11). At constant R, N(R,sigma) varies with sigma by only about 2%. This result disagrees with the extrapolation of the Grossmann and Lohse theory beyond its range of validity, which implies a decrease by 20% over our sigma range, but agrees with their recent extension of the theory to small Reynolds numbers.

We present measurements of the Nusselt number N as a function of the Rayleigh number R in cylindrical cells with aspect ratios 0.5 ≤ Γ ≡ D/d ≤ 12.8 (D is the diameter and d the height). We used acetone with a Prandtl number σ = 4.0 for 10 5 < ∼ R < ∼ 4 × 10 10 . A fit of a powerlaw N = N0R γ ef f over limited ranges of R yielded values of γ ef f from 0.275 near R = 10 7 to 0.300 near R = 10 10 . The data are inconsistent with a single powerlaw for N (R). For R > 10 7 they are consistent with N = aσ −1/12 R 1/4 + bσ −1/7 R 3/7 as proposed by Grossmann and Lohse for σ > ∼ 2. 44.25.+f,47.27.Te Since the pioneering measurements by Libchaber and co-workers [1,2] of heat transport by turbulent gaseous helium heated from below, there has been a revival of interest in the nature of turbulent convection. [3] In addition to the local properties of the flow, one of the central issues has been the global heat transport of the system, as expressed by the Nusselt number N = λ ef f /λ. Here λ ef f = qd/∆T is the effective thermal conductivity of the convecting fluid (q is the heat-current density, d the height of the sample, and ∆T the imposed temperature difference), and λ is the conductivity of the quiescent fluid. Usually a simple powerlawwas an adequate representation of the experimental data.[4] Here R = αgd 3 ∆T /κν is the Rayleigh number, α the thermal expansion coefficient, g the gravitational acceleration, κ the thermal diffusivity, and ν the kinematic viscosity. Various data sets yielded exponent valuesγ from 0.28 to 0.31. [5,6] Most recently, measurements over the unprecedented range 10 6 < ∼ R < ∼ 10 17 were made by Niemela et al., and a fit to them of Eq. 1 gaveγ = 0.309; [5] but even these data did not reveal any deviation from the functional form of Eq. 1. Competing theoretical models involving quite different physical assumptions made predictions of powerlaw behavior with exponents γ in the same narrow range. [2,6-8] Here we mention just two of them. A boundary-layer scaling-theory [2,8] which yielded γ = 2/7 ≃ 0.2857 was an early favorite, at least for the experimentally accessible range R < ∼ 10 12 . It was generally consistent with most of the available experimental results. More recently, a competing model based on the decomposition of the kinetic and the thermal dissipation into boundary-layer and bulk contributions was presented by Grossmann and Lohse (GL) [7] and predicts that the data measure an average exponentγ associated with a crossover from γ = 1/4 at small R to a slightly larger γ at much larger R. In the experimental range the effective exponent γ ef f ≡ d(ln(N ))/d(ln(R)), which should be compared with the experimentally determinedγ , is only very weakly dependent upon R and has values fairly close to 2/7. Thus, it has not been possible before to distinguish between the competing theories on the basis of the experimental data.Here we present new measurements of N (R) over the range 10 5 < ∼ R < ∼ 4 × 10 10 for a Prandtl number σ ≡ ν/κ = 4.0. Our data are of exceptionally high precision and a...

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Purpose: To demonstrate the feasibility of Tetrahedron Beam Computed Tomography (TBCT) using a carbon nanotube (CNT) multiple pixel field emission x-ray (MPFEX) tube. Methods: A multiple pixel x-ray source facilitates the creation of novel x-ray imaging modalities. In a previous publication, the authors proposed a Tetrahedron Beam Computed Tomography (TBCT) imaging system which comprises a linear source array and a linear detector array that are orthogonal to each other. TBCT is expected to reduce scatter compared with Cone Beam Computed Tomography (CBCT) and to have better detector performance. Therefore, it may produce improved image quality for image guided radiotherapy. In this study, a TBCT benchtop system has been developed with an MPFEX tube. The tube has 75 CNT cold cathodes, which generate 75 x-ray focal spots on an elongated anode, and has 4 mm pixel spacing. An in-house-developed, 5-row CT detector array using silicon photodiodes and CdWO 4 scintillators was employed in the system. Hardware and software were developed for tube control and detector data acquisition. The raw data were preprocessed for beam hardening and detector response linearity and were reconstructed with an FDK-based image reconstruction algorithm. Results: The focal spots were measured at about 1 Â 2 mm 2 using a star phantom. Each cathode generates around 3 mA cathode current with 2190 V gate voltage. The benchtop system is able to perform TBCT scans with a prolonged scanning time. Images of a commercial CT phantom were successfully acquired. Conclusions: A prototype system was developed, and preliminary phantom images were successfully acquired. MPFEX is a promising x-ray source for TBCT. Further improvement of tube output is needed in order for it to be used in clinical TBCT systems.