Many-body radiative heat transfer theory

In this Letter, an N-body theory for the radiative heat exchange in thermally nonequilibrated discrete systems of finite size objects is presented. We report strong exaltation effects of heat flux which can be explained only by taking into account the presence of many-body interactions. Our theory extends the standard Polder and van Hove stochastic formalism used to evaluate heat exchanges between two objects isolated from their environment to a collection of objects in mutual interaction. It gives a natural theoretical framework to investigate the photon heat transport properties of complex systems at the mesoscopic scale.     

Sparse tensor spherical harmonics approximation in radiative transfer

The stationary monochromatic radiative transfer equation is a partial differential transport equation stated on a five-dimensional phase space. To obtain a well-posed problem, boundary conditions have to be prescribed on the inflow part of the domain boundary.     

Near-field radiative heat transfer in mesoporous alumina

The thermal conductivity of mesoporous material has aroused the great interest of scholars due to its wide applications such as insulation,catalyst,etc.Mesoporous alumina substrate consists of uniformly distributed,unconnected cylindrical pores.Near-field radiative heat transfer cannot be ignored,when the diameters of the pores are less than the characteristic wavelength of thermal radiation.In this paper,near-field radiation across a cylindrical pore is simulated by employing the fluctuation dissipation theorem and Green function.Such factors as the diameter of the pore,and the temperature of the material are further analyzed.The research results show that the radiative heat transfer on a mesoscale is 2～4 orders higher than on a macroscale.The heat flux and equivalent thermal conductivity of radiation across a cylindrical pore decrease exponentially with pore diameter increasing,while increase with temperature increasing.The calculated equivalent thermal conductivity of radiation is further developed to modify the thermal conductivity of the mesoporous alumina.The combined thermal conductivity of the mesoporous alumina is obtained by using porosity weighted dilute medium and compared with the measurement.The combined thermal conductivity of mesoporous silica decreases gradually with pore diameter increasing,while increases smoothly with temperature increasing,which is in good agreement with the experimental data.The larger the porosity,the more significant the near-field effect is,which cannot be ignored.     

Coupling heat conduction and radiative transfer

A method to compute combined heat conduction and radiative transfer in a semitransparent medium is proposed. The heat equation is solved by an implicit finite-difference scheme and the radiation is simulated using a ray-tracing method. Stability and convergence for the coupling of both methods is shown. The crucial point for ray-tracing as well as for discrete-ordinate methods is the selection of the transfer directions and their associated weights. Using a model problem different direction sets proposed in the literature are compared with respect to their accuracy and the computational effort.     

Monte Carlo ray-tracing simulation for radiative heat transfer in turbulent fluctuating media under the optically thin fluctuation approximation

The Monte Carlo ray-tracing method (MCRT) based on the concept of radiation distribution factor is extended to solve radiative heat transfer problem in turbulent fluctuating media under the optically thin fluctuation approximation. A one-dimensional non-scattering turbulent fluctuating media is considered, in which the mean temperature and absorption coefficient distribution are assumed and the shape of probability density function is given. The distribution of the time-averaged volume radiation heat source is solved by MCRT and direct integration method. It is shown that the results of MCRT based on the concept of radiation distribution factor agree with these of integration solution very well, but results of MCRT based on the concept of radiative transfer coefficient do not agree with these of integration solution. The solution of time-averaged radiative transfer equation by the concept of radiative transfer coefficient should be treated with caution.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

Abstract

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Mesoscopic description of radiative heat transfer at the nanoscale

We present a formulation of the nanoscale radiative heat transfer using concepts of mesoscopic physics. We introduce the analog of the Sharvin conductance using the quantum of thermal conductance. The formalism provides a convenient framework to analyze the physics of radiative heat transfer at the nanoscale. Finally, we propose a radiative heat transfer experiment in the regime of quantized conductance.     

Tau method approximation for radiative transfer problems in a slab medium

An approximate method for solving the radiative transfer equation in a slab medium with an isotropic scattering is proposed. The method is based upon constructing the double Legendre series to approximate the required solution using Legendre tau method. The differential and integral expressions which arise in the radiative transfer equation are converted into a system of linear algebraic equations which can be solved for the unknown coefficients. Numerical examples are included to demonstrate the validity and applicability of the method and a comparison is made with existing results.     

Simultaneous radiative and conductive heat transfer in non-gray media

Steady-state energy transfer through non-gray radiating and conducting media enclosed by black walls of unequal temperature is studied. A rectangular Milne-Eddington type relation is used to describe the frequency dependence of the absorption coefficient. Temperature distributions and total heat transfer results are presented for materials which absorb radiation (a) of low frequency, (b) of high frequency, (c) within a finite band width, and (d) of all frequencies (gray). The influence of optical thickness (τ₀) and conduction to a radiation interaction parameter (N) are examined and the results for non-gray materials are compared with those for a gray analysis. Exact results are compared with those determined by using the optically-thin and the optically-thick approximations, as well as with those evaluated for purely conductive and purely radiative transfer.     

Calculation of radiative heat transfer in argon arc plasmas

Radiation emission and absorption in arc plasmas are important energy transfer processes. Exact calculations, though possible in principle, are usually impossible in practice because of the need to treat a large number of spectral lines and also the continuum radiation in the whole spectrum range. Recently, we have used an approximate method of partial characteristics to evaluate the radiation intensities, radiation fluxes and the divergence of radiation fluxes for SF₆ arc plasma with cylindrical symmetry. In this paper, we have extended our calculations toargon arc plasmas for the plasma pressures of 0.1, 0.5 and 1.0 MPa. We have calculated the coefficients of absorption for Ar plasmas at temperatures from 300 to 35 000 K, and have used these coefficients to calculate the partial characteristics. Both the continuum and the line spectra have been included in calculations. We have taken into account the radiative photo-recombination and bremsstrahlung for the continuous spectrum, and over 500 spectral lines for the discrete spectra.The method of partial characteristics has been applied to three-dimensional calculations of radiative heat transfer — i.e. radiation intensity, radiation flux and its divergence — in simplified temperature profiles. Conclusions have been made concerning validity and utilization of the method of partial characteristics in general gas dynamics problems.     

Role of fluctuational electrodynamics in near-field radiative heat transfer

The objective of this paper is to discuss the role of fluctuational electrodynamics in the context of a generalized radiative heat transfer problem. Near-field effects, including the interference phenomenon and radiation tunneling, are important for applications to nanostructures. The classical theory of radiative transfer cannot be readily applied as the feature size approaches the dominant wavelength of radiative emission. At all length scales, however, propagation of radiative energy is properly represented by the electromagnetic wave approach, which requires the solution of the Maxwell equations. Fluctuational electrodynamics provides a model for thermal emission when solving a near-field radiation heat transfer problem, and the fluctuation-dissipation theorem provides the bridge between the strength of the fluctuations of the charges inside a body and its local temperature. This paper provides a complete and systematic derivation of the near-field radiative heat flux starting from the Maxwell equations. An illustrative example of near-field versus far-field radiation heat transfer is presented, and the length scale for transition from near- to far-field regime is discussed; the results show that this length scale can be as large as three times than predicted from Wien's law.     

Near-field radiative heat transfer between macroscopic planar surfaces

Near-field radiation allows heat to propagate across a small vacuum gap at rates several orders of magnitude above that of far-field, blackbody radiation. Although heat transfer via near-field effects has been discussed for many years, experimental verification of this theory has been very limited. We have measured the heat transfer between two macroscopic sapphire plates, finding an increase in agreement with expectations from theory. These experiments, conducted near 300?K, have measured the heat transfer as a function of separation over mm to μm and as a function of temperature differences between 2.5 and 30?K. The experiments demonstrate that evanescence can be put to work to transfer heat from an object without actually touching it.     

Adsorbate vibrational mode enhancement of radiative heat transfer

We show that radiative heat transfer between two solid surfaces at short separation may increase by many orders of magnitude when the surfaces are covered by adsorbates. In this case, the heat transfer is determined by resonant photon tunneling between adsorbate vibrational modes. We propose an experiment to check the theory.     

Application of the modified differential approximation for radiative transfer to arbitrary geometry

The first-order spherical harmonics method (or P₁ approximation) has found prolific usage for approximate solution of the radiative transfer equation (RTE) in participating media. However, the accuracy of the P₁ approximation deteriorates as the optical thickness of the medium is decreased. The modified differential approximation (MDA) was originally proposed to remove the shortcomings of the P₁ approximation in optically thin situations. This article presents algorithms to apply the MDA to arbitrary geometry—in particular, geometry with obstructions, and inhomogeneous media. The wall-emitted component of the intensity was computed using a combined view-factor and ray-tracing approach. The Helmholtz equation, arising out of the medium-emitted component, was solved using an unstructured finite-volume procedure. The general procedure was validated for both two-dimensional (2D) and three-dimensional (3D) geometries against benchmark Monte Carlo results. The accuracy of MDA was found to be superior to the P₁ approximation for all optical thicknesses. Its accuracy, when compared with the discrete ordinates method (both S₆ and S₈), was found to be clearly superior in optically thin situations, but problem dependent in optically intermediate and thick situations. For 3D geometries, calculation and storage of the view-factor matrix was found to be a major shortcoming of the MDA. In addition, for inhomogeneous media, calculation of optical distances requires a ray-tracing procedure, which was found to be a bottleneck from a computational efficiency standpoint. Several strategies to reduce both memory and computational time are discussed and demonstrated.     

A single-scattering approximation for infrared radiative transfer in limb geometry in the Martian atmosphere

We present a single-scattering approximation for infrared radiative transfer in limb geometry in the Martian atmosphere. It is based on the assumption that the upwelling internal radiation field is dominated by a surface with a uniform brightness temperature. It allows the calculation of the scattering source function for individual aerosol types, mixtures of aerosol types, and mixtures of gas and aerosol. The approximation can be applied in a Curtis-Godson radiative transfer code and is used for operational retrievals from Mars Climate Sounder measurements. Radiance comparisons with a multiple scattering model show good agreement in the mid- and far-infrared although the approximate model tends to underestimate the radiances in realistic conditions of the Martian atmosphere. Relative radiance differences are found to be about 2% in the lowermost atmosphere, increasing to ∼10% in the middle atmosphere of Mars. The increasing differences with altitude are mostly due to the increasing contribution to limb radiance of scattering relative to emission at the colder, higher atmospheric levels. This effect becomes smaller toward longer wavelengths at typical Martian temperatures. The relative radiance differences are expected to produce systematic errors of similar magnitude in retrieved opacity profiles.     

Evaluation method for radiative heat transfer in polydisperse water droplets

Simplifications of the model for nongray radiative heat transfer analysis in participating media comprised of polydisperse water droplets are presented. Databases of the radiative properties for a water droplet over a wide range of wavelengths and diameters are constructed using rigorous Mie theory. The accuracy of the radiative properties obtained from the database interpolation is validated by comparing them with those obtained from the Mie calculations. The radiative properties of polydisperse water droplets are compared with those of monodisperse water droplets with equivalent mean diameters. Nongray radiative heat transfer in the anisotropic scattering fog layer, including direct and diffuse solar irradiations and infrared sky flux, is analyzed using REM². The radiative heat fluxes within the fog layer containing polydisperse water droplets are compared with those in the layer containing monodisperse water droplets. Through numerical simulation of the radiative heat transfer, polydisperse water droplets can be approximated by using the Sauter diameter, a technique that can be useful in several research fields, such as engineering and atmospheric science. Although this approximation is valid in the case of pure radiative transfer problems, the Sauter diameter is reconfirmed to be the appropriate diameter for approximating problems in radiative heat transfer, although volume-length mean diameter shows better accordance in some cases. The CPU time for nongray radiative heat transfer analysis with a fog model is evaluated. It is proved that the CPU time is decreased by using the databases and the approximation method for polydisperse particulate media.     

Resistance-network representation of radiative heat transfer with particulate scattering

The resistance-network representation for radiative heat transfer is developed for a planar absorbing-scattering medium on the basis of the two-flux model and the linear anisotropic scattering model. Particular attention is given to the scattering effect due to particulates such as flame soot or smoke particles. Limiting relations for various radiative regimes are derived and the physical significance of the resistances are discussed. An illustrative example is presented for thermal radiation from a smoke layer. Extension to two-phase dispersed systems is also demonstrated.     

Regularization of inverse boundary design radiative heat transfer problems

Inverse boundary design heat transfer problems, including only radiation, are considered. Variational methods of regularization are used for solving these (mathematically ill-posed) problems, they give possibility to take into account various a priori information about the desired solution. For minimizing the discrepancy functional we use the adjoint problem method; however, we use it not only in iterative regularization, but in Tikhonov and parametric ones as well. We use all the available a priori information about desired solutions in all the techniques; this allows to obtain physically feasible solutions in all the cases.     

轻介质传输中辐射热传导近似成立的判别因子

 从辐射输运方程出发,通过递推的方法,推导并得到了包含高级修正的辐射能流表达式。利用这个表达式,分析了辐射在轻介质中传输时,辐射热传导近似的成立条件。热传导近似的成立条件总是要求温度空间变化尺度与自由程之比远大于某个值,该值即判别因子,它表征热传导近似条件满足的苛刻程度,其值越大,热传导近似就越难满足。讨论得出：当同时考虑轫致和散射过程时,这一判别因子的值在3~60之间。并进一步分析了密度的空间变化以及1维球坐标下的半径对判别因子的影响。