Equilibrium Temperature Distribution Research Articles

Analysis of the Reactor Experiment Results on Irradiation of Lead-Lithium Eutectic

The paper analyzes the results of reactor studies on tritium generation and release from the lead-lithium eutectic PbLi in conditions of reactor irradiation. In this paper, the initial stage of eutectic irradiation is considered. The dependences of tritium and helium release at a reactor power of 1 MW and the following eutectic temperatures were considered: 573, 673, and 773 K. Using an integrated model based on solving related systems of equations, including heat transfer equations, convective mass transfer equations, and diffusion equations, equilibrium temperature distributions over the eutectic were calculated. The evolution (time variation) of tritium concentration distributions in the volume of the eutectic and in traps at different temperatures of the eutectic is calculated.

COMPUTATIONAL ASPECTS OF RADIATIVE TRANSFER EQUATION IN NON-ORTHOGONAL COORDINATES

Non-equilibrium energy transfer takes place for thin films when thermal disturbance is introduced. In this case, phonon transport inside the film governs the heat transport and temperature distribution in the film. In the present study an attempt is made to formulate and illustrate the phonon transfer in micro-scale silicon film of various shapes incorporating the non-orthogonal coordinate system. Successful application of the discrete-ordinates method to the solution of the equation for phonon radiative transport in non-orthogonal coordinates requires the application of various numerical techniques connected to the finite-difference method. The numerical solution of the equation for phonon transfer in non-orthogonal coordinate is introduced via adapting the discrete ordinate method. Phonon intensity distribution in the thin film is presented in terms of equivalent equilibrium temperature. It is found that film shape has significant effect on equivalent equilibrium temperature distribution inside the film. The validation study demonstrates that the code developed solving the equation for phonon transport is also applicable to the phonon transport in non-orthogonal coordinate system.

Near-field radiative heat transfer in multilayered graphene system considering equilibrium temperature distribution.

In the present work, the near-field radiative heat transfer of a multilayered graphene system is investigated within the framework of the many-body theory. For the first time, the temperature distribution corresponding to the steady state of the system is investigated. Unique temperature steps are observed near both boundaries of the system, especially in the strong near-field regime. By utilizing the effective radiative thermal conductance, the thermal freedom of heat flux in different regions of the system is analyzed quantitatively, and the cause of various temperature distributions is explained accordingly. To characterize the heat transfer ability of the whole system, we evaluate the system with two heat transfer coefficients (HTC), transient heat transfer coefficient (THTC), and steady heat transfer coefficient (SHTC). A unique many-body enhancement is observed, which causes a red-shift of resonance peak corresponding to graphene surface plasmon polaritons. Furthermore, a three-body enhancement of SHTC emerges thanks to the relay effect and the complexity of the system. The regime of heat transport can be tuned by changing the chemical potentials of graphene and undergoes a transition from diffusive to quasi-ballistic transport in the strong near-field regime.

Transient free convection in an inclined square porous cavity filled with a nanofluid using LTNE and Buongiorno’s models

The combined effect of Brownian diffusion, thermophoresis and cavity inclination angle on natural convective heat transfer in an inclined porous enclosure has been studied numerically. Fluid containing nanoparticles of low concentration circulates inside the cavity under the effect of the buoyancy force. Governing equations with corresponding boundary conditions formulated using the non-dimensional stream function and vorticity variables have been solved by the finite difference method. An influence of the cavity inclination angle, Darcy and Nield numbers on nanofluid flow and heat transfer has been investigated. It has been found that high Nield numbers illustrate more equilibrium temperature distribution inside the porous cavity.

Тепловая конвекция в ячейке Хеле–Шоу при наличии у жидкости зависимости температуропроводности от температуры

The investigation of thermal convection of a fluid with the dependence of thermal diffusivity on temperature in a vertical Hele Shaw cell heated from below has been fulfilled theoretically.The expression for equilibrium temperature distribution in a cavity has been derived analytically. It has been found that the dependence of temperature on the vertical coordinate looks like a square rootlaw.The linear stability of mechanical equilibrium state against small normal perturbations has been investigated by means of Galerkin method. It has been shown that the most dangerous perturbation in a cavity under considerationis described by the mode which corresponds to the two vortexsteady flow. The numerical simulation of overcritical steady and oscillatory flows has been carried out in the approximation of plane trajectories.This simplification of theoretical modelis consistent with all experimental data on thermal convection in similar cavities. It has been shown that the inclusion of the dependence of thermal diffusivity on temperature into the mathematical model leads to the up down symmetry breakdown for the small values of over criticality.

Modeling of heterogeneous heat transfer in fabrics

Thermal comfort, an important factor when designing fabric, is strongly related to heat transfer in the fabric. Fabric is not homogeneous because the constituent yarns are interlaced at a certain weave angle, and the contact area between yarns varies. Therefore, heat transfer along the yarn in the fabric is not yet well understood. In this study, we developed a heterogeneous fabric model in which heat transfer along the longitudinal and transverse directions of the yarn is treated independently, and proposed a method for estimating the contact heat transfer coefficients for yarns. The geometrical fabric structure was constructed based on the cross section of three fabrics observed with a three-dimensional microscope. The parameters used were the mass density, specific heat, and thermal conductivity of the fibers and air. The heat flow calculated using the model was compared with that measured experimentally. Fairly good agreement was observed, verifying the validity of this heterogeneous model. The simulation results indicated that when the anisotropy of the fiber thermal conductivity is high, heat is transferred significantly faster along the longitudinal direction than along the transverse direction of the yarn, and the equilibrium temperature distribution is strongly influenced by heat transfer in the longitudinal direction.

A modified lattice Boltzmann model for conjugate heat transfer in porous media

A modified lattice Boltzmann model for conjugate heat transfer in a system containing simultaneously a porous medium and other media is proposed. In this model, the volumetric heat capacity and a new parameter are introduced to the equilibrium temperature distribution function for satisfying the temperature and heat flux continuities at the interface between two phases with different thermal properties (thermal conductivity and volumetric heat capacity), as well as avoiding any correction of distribution functions neighboring the interface. The macroscopic temperature equations are correctly recovered from the corresponding lattice Boltzmann equations by the Chapman–Enskog procedure. Detailed numerical tests of the proposed model are carried out for several benchmark problems including steady-state conjugate heat conduction within two-layer solid medium, transient conjugate heat conduction in infinite composite solid, conjugate natural convection in a cavity partially filled with porous medium and conjugate heat transfer in porous media with a conducting wall. The present numerical results are in excellent agreement with analytical and numerical solutions reported in previous studies. Therefore, it is verified that the present model can be served as a feasible tool for conjugate heat transfer problems in porous media.

Secondary eclipse observations for seven hot-Jupiters from the Anglo-Australian Telescope

We report detections and constraints for the near infrared Ks band secondary eclipses of seven hot-Jupiters using the IRIS2 infrared camera on the Anglo-Australian Telescope. Eclipses in the Ks band for WASP-18b and WASP-36b have been measured for the first time. We also present new measurements for the eclipses of WASP-4b, WASP-5b, and WASP-46b, as well as upper limits for the eclipse depths of WASP-2b and WASP-76b. In particular, two full eclipses of WASP-46b were observed, allowing us to demonstrate the repeatability of our observations via independent analyses on each eclipse. Significant numbers of eclipse depths for hot-Jupiters have now been measured in both Ks and the four Spitzer IRAC bandpasses. We discuss these measurements in the context of the broadband colours and brightness temperatures of the hot-Jupiter atmosphere distribution. Specifically, we re-examine the proposed temperature dichotomy between the most irradiated, and mildly irradiated planets. We find no evidence for multiple clusters in the brightness temperature - equilibrium temperature distributions in any of these bandpasses, suggesting a continuous distribution of heat re-emission and circulation characteristics for these planets.

Seasonal Variability of the Polar Stratospheric Vortex in an Idealized AGCM with Varying Tropospheric Wave Forcing

Abstract The seasonal variability of the polar stratospheric vortex is studied in a simplified AGCM driven by specified equilibrium temperature distributions. Seasonal variations in equilibrium temperature are imposed in the stratosphere only, enabling the study of stratosphere–troposphere coupling on seasonal time scales, without the complication of an internal tropospheric seasonal cycle. The model is forced with different shapes and amplitudes of simple bottom topography, resulting in a range of stratospheric climates. The effect of these different kinds of topography on the seasonal variability of the strength of the polar vortex, the average timing and variability in timing of the final breakup of the vortex (final warming events), the conditions of occurrence and frequency of midwinter warming events, and the impact of the stratospheric seasonal cycle on the troposphere are explored. The inclusion of wavenumber-1 and wavenumber-2 topographies results in very different stratospheric seasonal variability. Hemispheric differences in stratospheric seasonal variability are recovered in the model with appropriate choices of wave-2 topography. In the model experiment with a realistic Northern Hemisphere–like frequency of midwinter warming events, the distribution of the intervals between these events suggests that the model has no year-to-year memory. When forced with wave-1 topography, the gross features of seasonal variability are similar to those forced with wave-2 topography, but the dependence on forcing magnitude is weaker. Further, the frequency of major warming events has a nonmonotonic dependence on forcing magnitude and never reaches the frequency observed in the Northern Hemisphere.

Magnetohydrostatics of a vertical flux tube in the solar atmosphere: Coronal loops, a model of a ring flare filament

The magnetohydrostatic theory of a twisted magnetic flux tube (rope) immersed in a realistic solar atmosphere is presented in a closed analytical form for the first time. General formulas that allow the equilibrium plasma density, pressure, and temperature distributions inside an axisymmetric vertical flux tube to be calculated from its magnetic structure, which is assumed to be known (fixed), have been derived. An analytical model of the external hydrostatic medium free of a magnetic field, the solar atmosphere, where the temperature profile of the semi-empirical tabulated Avrett-Loeser model is used, has been constructed. The distribution of plasma parameters in a twisted magnetic flux tube at small deviations of its internal magnetic structure from the force-free one has been calculated as an example of applying the general theoretical formulas. Since the tube cross section does not change with height, the constructed model can be applied to describe the vertical parts of coronal loops. It has been found that the plasma density in the magnetic flux tube rises when the field twisting exceeds the force-free level and falls with decreasing field twisting compared to the force-free level. This property of a twisted magnetic flux tube is of fundamental importance for justifying the mechanism of flare energy release in magnetic flux ropes. A model of a flare in a ring chromospheric configuration is considered.

Equilibrium temperature distribution and Hadley circulation in an axisymmetric model

Abstract. The impact of the equilibrium temperature distribution, θE, on the Hadley circulation simulated by an axisymmetric model is studied. The θE distributions that drive the model are modulated here by two parameters, n and k, the former controlling the horizontal broadness and the latter controlling the vertical stratification of θE. In the present study, variations in the θE distribution mimic changes in the energy input of the atmospheric system, leaving as almost invariant the Equator–poles θE difference. Both equinoctial and time-dependent Hadley circulations are simulated and the results compared. The results give evidence that concentrated θE distributions enhance the meridional circulation and jet wind speed intensities, even with a lower energy input. The meridional circulation and the subtropical jet stream widths are controlled by the broadness of horizontal θE rather than by the vertical stratification, which is important only when θE distribution is concentrated at the Equator. The jet stream position does not show any dependence with n and k, except when the θE distribution is very wide (n = 3) and, in such a case, the jet is located at the mid-latitudes and the model temperature clamps to forcing θE. Using n = 2 and k = 1, we have the formulation of the potential temperature adopted in the classical literature. A comparison with other works is performed, and our results show that the model running in different configurations (equinoctial, solstitial and time dependent) yields results similar to one another.

Consideration of the effects of intense tissue heating on the RF electromagnetic fields during MRI: simulations for MRgFUS in the hip

Due to the strong dependence of tissue electrical properties on temperature, it is important to consider the potential effects of intense tissue heating on the RF electromagnetic fields during MRI, as can occur in MR-guided focused ultrasound surgery. In principle, changes of the RF electromagnetic fields could affect both efficacy of RF pulses, and the MRI-induced RF heating (SAR) pattern. In this study, the equilibrium temperature distribution in a whole-body model with 2 mm resolution before and during intense tissue heating up to 60 °C at the target region was calculated. Temperature-dependent electric properties of tissues were assigned to the model to establish a temperature-dependent electromagnetic whole-body model in a 3T MRI system. The results showed maximum changes in conductivity, permittivity, and SAR of about 25%, 6%, 2%, and 20%, respectively. Though the B1 field and SAR distributions are both temperature-dependent, the potential harm to patients due to higher SARs is expected to be minimal and the effects on the B1 field distribution should have minimal effect on images from basic MRI sequences.

Thermal Postbuckling of Imperfect Circular Functionally Graded Material Plates: Examination of Voigt, Mori–Tanaka, and Self-Consistent Schemes

Thermal postbuckling of solid circular plates made of a through-the-thickness functionally graded material (FGM) is analyzed in this paper. Initial imperfection of the plate is also taken into account. Each thermomechanical property of the plate is assumed to be a function of the temperature and thickness coordinate. Equivalent properties of the FGM media are obtained based on three different homogenization schemes, namely, Voigt rule, Mori–Tanaka scheme, and self-consistent estimate. Temperature profile is assumed to be through-the-thickness direction only. The solution of the heat conduction equation is obtained using an iterative central finite difference scheme. Various types of thermal loadings, such as uniform temperature rise, temperature specified at surfaces, and heat flux, are considered. Nonlinear equilibrium equations of the plate are obtained by means of the conventional Ritz method. Solution of the resulting nonlinear equilibrium equations and temperature distribution are obtained simultaneously at each step of heating. It is shown that response of a perfect clamped FGM plate is of the bifurcation type of buckling with stable postbuckling equilibrium branch, whereas imperfect clamped and perfect/imperfect simply supported FGM plates do not reveal the bifurcation type of instability through the nonuniform heating process. Furthermore, amplitude of initial imperfection is an important factor on the equilibrium path of FGM circular plates, especially for simply supported ones.

Can the Delay in Antarctic Polar Vortex Breakup Explain Recent Trends in Surface Westerlies?

Abstract The authors test the hypothesis that recent observed trends in surface westerlies in the Southern Hemisphere are directly consequent on observed trends in the timing of stratospheric final warming events. The analysis begins by verifying that final warming events have an impact on tropospheric circulation in a simplified GCM driven by specified equilibrium temperature distributions. Seasonal variations are imposed in the stratosphere only. The model produces qualitatively realistic final warming events whose influence extends down to the surface, much like what has been reported in observational analyses. The authors then go on to study observed trends in surface westerlies composited with respect to the date of final warming events. If the considered hypothesis were correct, these trends would appear to be much weaker when composited with respect to the date of the final warming events. The authors find that this is not the case, and accordingly they conclude that the observed surface changes cannot be attributed simply to this shift toward later final warming events.

Local and nonlocal anisotropic transport in reversed shear magnetic fields: Shearless Cantori and nondiffusive transport

A study of anisotropic heat transport in reversed shear (nonmonotonic q-profile) magnetic fields is presented. The approach is based on a recently proposed Lagrangian-Green's function method that allows an efficient and accurate integration of the parallel (i.e., along the magnetic field) heat transport equation. The magnetic field lines are described by a nontwist Hamiltonian system, known to exhibit separatrix reconnection and robust shearless (dq/dr=0) transport barriers. The changes in the magnetic field topology due to separatrix reconnection lead to bifurcations in the equilibrium temperature distribution. For perturbations of moderate amplitudes, magnetic chaos is restricted to bands flanking the shearless region. As a result, the temperature flattens in the chaotic bands and develops a very sharp radial gradient at the shearless region. For perturbations with larger amplitude, shearless Cantori (i.e., critical magnetic surfaces located at the minimum of the q profile) give rise to anomalous temperature relaxation involving widely different time scales. The first stage consists of the relatively fast flattening of the radial temperature profile in the chaotic bands with negligible flux across the shearless region that, for practical purposes, on a short time scale acts as an effective transport barrier despite the lack of magnetic flux surfaces. In the long-time scale, heat starts to flow across the shearless region, albeit at a comparatively low rate. The transport of a narrow temperature pulse centered at the reversed shear region exhibits weak self-similar scaling with non-Gaussian scaling functions indicating that transport at this scale cannot be modeled as a diffusive process with a constant diffusivity. Evidence of nonlocal effective radial transport is provided by the existence of regionswith nonzero heat flux and zero temperature gradient. Parametric flux-gradient plots exhibit multivalued loops that question the applicability of the Fourier-Fick's prescription even in the presence of a finite pinch velocity.

Phonon Transport in Two-Dimensional Silicon–Diamond Film Pair

Phonon transport in a two-dimensional silicon–diamond film pair is investigated. The frequency dependent Boltzmann equation is solved numerically while introducing the transient effect. Equivalent equilibrium temperature distribution in the silicon and the diamond films is predicted to assess the ballistic contribution of phonons on energy transport. Thermal boundary resistance is introduced at the interface of the silicon–diamond films to account for the acoustic speeds and phonon frequencies mismatch between the films. The study is extended to include the frequency independent solution of the Boltzmann transport equation for comparison. It is found that ballistic contribution of phonons on energy transport is significant in the film pair, and thus ballistic phonons suppress equivalent equilibrium temperature increase in both films.

On the nature of the transition region between the solar corona and chromosphere

We have calculated an equilibrium temperature distribution over the column depth of plasma in the transition region between the solar corona and chromosphere by assuming the plasma in the transition region and the chromosphere to be heated by the heat flux from the corona and the energy fluxes from the convective zone, respectively. The corona-chromosphere transition region is shown to be actually a stable, very thin layer in which, however, the standard collision approximation is well applicable for describing the heat flux. The solution we found explains well the currently available results of satellite observations of extreme ultraviolet (EUV) radiation from the transition region.

FREQUENCY DEPENDENT PHONON TRANSPORT IN TWO-DIMENSIONAL SILICON AND DIAMOND THIN FILMS

Phonon transport in two-dimensional silicon and aluminum films is investigated. The frequency dependent solution of Boltzmann transport equation is obtained numerically to account for the acoustic and optical phonon branches. The influence of film size on equivalent equilibrium temperature distribution in silicon and aluminum films is presented. It is found that increasing film width influences phonon transport in the film; in which case, the difference between the equivalent equilibrium temperature due to silicon and diamond films becomes smaller for wider films than that of the thinner films.

Temperature Distribution in Silicon-Aluminum Thin Films with Presence of Thermal Boundary Resistance

Phonon transport in two-layer films, consisting of silicon and aluminum, is considered. Phonon radiative energy transfer is incorporated to predict equilibrium temperature distribution in the silicon film, while the modified two-equation model is used to predict electron and phonon temperatures in the aluminum film. The thermal boundary resistance is introduced at the interface of both films. Equilibrium temperature decay is found to be sharp in the early heating period in the silicon film. Phonon temperature remains higher than electron temperature in the vicinity of the interface of aluminum film. Electron and phonon temperature become the same at mid-thickness of the aluminum film.

Local temperature pattern in plasmonic gold nanoshell: tuning the heat generation

Under quasi-steady-state conditions, we investigated the photo-heat conversion in a gold nanoshell by calculating the local equilibrium temperature distribution. In a thinner gold shell, the hot spots take place near the poles of both shell-surrounding and core-shell interface, perpendicularly to the incident field. In a thicker gold shell, the hot spots only take place near the core-shell interface. The maximum local temperature also depends greatly on the core media and shell thickness. Optimal heat generation can be obtained with small core dielectric constant and thin shell thickness. The mechanism of this local heating distribution is explained by the local field enhancement that is induced by the plasmon coupling.