Heat Flux Spectrum Research Articles

Asymptotic expressions describing radiative heat transfer between polar materials from the far-field regime to the nanoscale regime

Heat transfer between two plates of polar materials at nanoscale distance is known to be enhanced by several orders of magnitude as compared with its far-field value. In this article, we derive accurate analytical expressions to quantitatively predict heat fluxes in the near-field. These analytical expressions reveal the physical mechanisms responsible for the enhancement. For two dielectric polar materials and for gaps smaller than 75 nm at room temperature the heat transfer is dominated by the surface phonon polariton contribution. Between 75 nm and 500 nm, the enhancement is mostly due to frustrated total internal reflection. The paper reports accurate analytical expressions for both contributions. Our analytical results highlight two differences between radiation flux at the nanoscale and in the far field: i)the heat flux spectrum depends on the gap distance, ii) the temperature dependence of the heat transfer coefficient deviates strongly from the T3 law valid for gray bodies in the far-field.

Single-Side Conduction Modeling for High Heat Flux Coolant Channels

In the development of plasma-facing components (PFCs), most investigators have erroneously postulated negligible water critical heat flux dependence on the coolant channel length-to-diameter (L/D) ratio above a constant value of L/D. Although encouraging results have been obtained in characterizing peaking factors for local two-dimensional boiling curves and critical heat flux, additional experimental data and theoretical model development are needed to validate the applicability to PFCs. Both these and related issues will affect the flow boiling correlation and data reduction associated with the development of PFCs for fusion reactors and other physical problems that are dependent on conduction modeling in the heat flux spectrum of applications. Both exact solutions and numerical conjugate analyses are presented for a one-side heated (OSH) geometry. The results show (a) the coexistence of three flow regimes inside an OSH circular geometry, (b) the correlational dependence of the inside wall heat flux and temperature, and (c) inaccuracies that could arise in some data reduction procedures.

Turbulence in the stratified atmosphere: Recent theoretical developments and experimental results

Above the boundary layer and outside convective systems, atmospheric turbulence generally occurs within a stably stratified environment. Experimental data clearly reveal that classical ideas about isotropy and inertiality of turbulence may then be questioned. Recent theoretical developments show a wide range of possible turbulent regimes, depending upon different physical hypotheses relating the dominant terms in the momentum and energy balances. The scaling of stratified turbulence proposed by /1/ will be extensively reviewed, such as present views of the tubulent buoyancy subrange. Key measurements appear to be those of temperature, vertical and horizontal velocities along vertical paths and, most of all, estimations of vertical heat flux (or mass flux) spectra. Recent atmospheric measurements acquired by a balloon borne instrumentation in the upper troposphere and lower stratosphere will be presented as they give some insight in these debates. Owing to its great practical importance, the problem of the relationships between temperature and velocities fluctuations will be specifically discussed.

Temperature and heat flux spectra in the turbulent buoyancy subrange

Temperature and heat flux spectra in the turbulent buoyancy subrange

Some remarks on the spectra of stably stratified turbulent shear flow

In this paper, a simple model is proposed to solve the system of spectral equations of turbulent kinetic energy and temperature variance in a thermally stratified turbulent shear flow. The buoyancy (or heat flux) term and the production term are modelled by means of turbulent exchange coefficient (or spectral eddy viscosity). For the terms representing inertial transfer of turbulent kinetic energy and temperature variance, Pao's (1965, 1968) formulations are employed. Analytical expressions for the non-dimensional kinetic energy spectrum φ ( k ), temperature variance spectrum φ T ( k ), the shear stress spectrum φ uw ( k ) and the heat-flux spectrum φ wT ( k ) are obtained within the framwork of similarity theory. The results are computed numerically and discussed.

An Application of the Modified Zero-Fourth-Cumulant Approximation to Homogeneous Axisymmetric Turbulence

Dynamical equations governing the energy, temperature and heat-flux spectra in homogeneous axisymmetric Boussinesq turbulence are formulated by applying the modified zero-fourth-cumulant approximation. For nearly-isotropic turbulence with a weak buoyancy force, it is shown that they are reduced to the equations of turbulent field convecting a passive scalar. For this case, numerical calculations are performed to determine the spectra at the Reynolds number 32, Rayleigh number 100 and Plandtl number unity. The results show that the approach to isotropy seems rather slow. The temperature and heat-flux spectra indicate that there are several subranges of the wavenumbers governed by different similarity laws. Also the heat-flux spectrum is found to have a sharp peak which shifts toward the low-wavenumber range.

An Application of the Modified Zero-Fourth-Cumulant Approximation to Homogeneous Axisymmetric Boussinesq Turbulence

Dynamical equations governing the energy, temperature and heat-flux spectra in homogeneous axisymmetric Boussinesq turbulence are formulated by applying the modified zero-fourth-cumulant approximation. For nearly-isotropic turbulence with a weak buoyancy force, it is shown that they are reduced to the equations of turbulent field convecting a passive scalar. For this case, numerical calculations are performed to determine the spectra at the Reynolds number 32, Rayleigh number 100 and Plandtl number unity. The results show that the approach to isotropy seems rather slow. The temperature and heat-flux spectra indicate that there are several subranges of the wavenumbers governed by different similarity laws. Also the heat-flux spectrum is found to have a sharp peak which shifts toward the low-wavenumber range.

Stochastic climate models, Part II Application to sea-surface temperature anomalies and thermocline variability

The concept of stochastic climate models developed in Part I of this series (Hasselmann, 1976) is applied to the investigation of the low frequency variability of the upper ocean. It is shown that large-scale, long-time sea surface temperature (SST) anomalies may be explained naturally as the response of the oceanic surface layers to short-time-scale atmospheric forcing. The white-noise spectrum of the atmospheric input produces a red response spectrum, with most of the variance concentrated in very long periods. Without stabilizing negative feedback, the oceanic response would be nonstationary, the total SST variance growing indefinitely with time. With negative feedback, the response is asymptotically stationary. These effects are illustrated through numerical experiments with a very simple ocean-atmosphere model. The model reproduces the principal features and orders of magnitude of the observed SST anomalies in mid-latitudes. Independent support of the stochastic forcing model is provided by direct comparisons of observed sensible and latent heat flux spectra with SST anomaly spectra, and also by the structure of the cross correlation functions of atmospheric surface pressure and SST anomaly patterns. The numerical model is further used to simulate anomalies in the near-surface thermocline through Ekman pumping driven by the curl of the wind stress. The results suggest that short-time-scale atmospheric forcing should be regarded as a possible candidate for the origin of large-scale, low-period variability in the seasonal thermocline. DOI: 10.1111/j.2153-3490.1977.tb00740.x

Wind stress over ice and over water in the Beaufort Sea

A sonic anemometer-thermometer has been used in a study of Reynolds stress, sensible heat flux, and velocity and temperature spectra over ice and over water in the Beaufort Sea. The wind-drag coefficient over ice for stable conditions is C10=0.0026, and over water for unstable conditions C10=0.0014.