Non-Fourier heat conduction with radiation in an absorbing, emitting, and isotropically scattering medium

This article numerically analyses the combined conductive and radiative heat transfer in an absorbing, emitting, and isotropically scattering medium. The non-Fourier heat conduction equation, which includes the time lag between heat flux and the temperature gradient, is used to model the conductive heat transfer in the medium. It predicts that a temperature disturbance will propagate as a wave at finite speed. The radiative heat transfer is solved using the P₃ approximation method. In addition, the MacCormack's explicit predictor-corrector scheme is used to solve the non-Fourier problem. The effects of radiation including single scattering albedo, conduction-to-radiation parameter, and optical thickness of the medium on the transient and steady state temperature distributions are investigated in detail. Analysis results indicate that the internal radiation in the medium significantly influences the wave nature. The thermal wave nature in the combined non-Fourier heat conduction with radiation is more obvious for large values of conduction-to-radiation parameter, small values of optical thickness and higher scattering medium. The results from non-Fourier-effect equation are also compared to those obtained from the Fourier equation. Non-Fourier effect becomes insignificant as either time increases or the effect of radiation increases.     

Time-dependent radiative transfer using Chapman-Enskog maximum entropy method

The time-dependent problems of radiative transfer involve a coupling between radiation and material energy fields and are nonlinear because of proposed temperature dependence of the medium characteristics in semi-infinite medium with Rayleigh anisotropic scattering. By means of the limited flux, Chapman-Enskog and maximum entropy technique the time-dependent radiative transfer equation has been solved explicitly. The maximum entropy method is used to solve the resulting differential equation for radiative energy density. The calculations are carried out for temperature (normalized dimensionless) Θ(x,τ), radiative energy density and net flux with Rayleigh and anisotropic scattering for different space at different times.     

Numerical prediction of heat transfer by natural convection and radiation in an enclosure filled with an isotropic scattering medium

This paper deals with the numerical solution for natural convection and volumetric radiation in an isotropic scattering medium within a heated square cavity using a hybrid thermal lattice Boltzmann method (HTLBM). The multiple relaxation time lattice Boltzmann method (MRT-LBM) has been coupled to the finite difference method (FDM) to solve momentum and energy equations, while the discrete ordinates method (DOM) has been adopted to solve the radiative transfer equation (RTE) using the S8 quadrature. Based on these approaches, the effects of various influencing parameters such as the Rayleigh number (Ra), the wall emissivity (ε_ι), the Planck number (Pl), and the scattering albedo (ω), have been considered. The results presented in terms of isotherms, streamlines and averaged Nusselt number, show that in absence of radiation, the temperature and the flow fields are centro-symmetrics and the cavity core is thermally stratified. However, radiation causes an overall increase in the temperature and velocity gradients along both thermally active walls. The maximum heat transfer rate is obtained when the surfaces of the enclosure walls are regarded as blackbodies. It is also seen that the scattering medium can generate a multicellular flow.     

Heat transfer in a spherical turbid medium with conduction and radiation

The heat transfer through a spherical media with conduction and radiation is considered. The medium is considered to be turbid and anisotropically scattering with diffusely reflecting boundaries of constant temperatures. The radiative transfer problem is solved using the Galerkin method. An iterative method is used to solve the nonlinear relation between the radiative transfer equation and the conductive energy equation. Calculations are carried out and compared for a homogeneous, isotropically scattering medium with isothermal, transparent boundaries. The results show good agreement with previous work. Calculations are carried out for inhomogeneous media with isotropic, and forward and backward anisotropic scattering. The boundaries of the media are considered to be isothermal and may be transparent or diffusely reflecting boundaries. The calculations are used to study the effects of the single scattering albedo, the anisotropic scattering parameter, the conduction-radiation parameter and the heat source.     

Diffusion approximations for the scattering of resonance-line photons: Interior and boundary layer solutions

Resonance-line scattering in static low density media with large optical thickness has a diffusive behavior in both space and frequency because photons belonging to the Lorentzian wings of the line may be scattered almost monochromatically a very large number of times. This diffusive behavior holds on frequency scales and spatial scales, χ_c and τ_c, much larger than the scales associated with one elementary scattering of a wing-photon.A method developed for diffusion approximations in neutron transport theory, suitably generalized to handle diffusion in frequency space, is applied to the case of conservative scattering in a bounded medium with interior sources and zero incoming radiation. The method is to separate the line radiation field into an interior part and a boundary layer part which goes to zero in the interior. Each part is expanded in terms of a small parameter ?, which is the ratio of the mean free-path at frequency χ_c to the characteristic spatial scale τ_c.It is shown that the leading term in the interior asymptotic expansion is isotropic, zero on the boundary, and obeys a space and frequency diffusion equation. In the boundary-layer expansion, the leading term is of order ? and is a solution to a monochromatic transfer equation in a semi-infinite, plane-parallel medium. The emergent radiation field is shown to be of order ? and proportional to the gradient of the interior solution at the boundary. Its angular dependence, in the case of isotropic scattering in the atom frame, is given by the Ambartsoumian H-function. A comparison is presented between numerical solutions of the full transfer equation and asymptotic solutions. Non-conservative scattering and time-dependent problems are briefly discussed.     

Numerical study of heat transfer in an optically thick semi-transparent spherical porous medium

In this paper, heat transfer by simultaneous convection, conduction and radiation in a semi-transparent spherical porous medium is investigated. The ROSSELAND approximation is adopted to take account of radiation in the heat transfer rate. The routine used here to solve the set of differential equations is taken from the IMSL MATH/LIBRARY. Various results are obtained for the dimensionless temperature profiles in the solid and fluid phases, the radiative, conductive, convective and total heat fluxes. The effects of some radiative properties of the medium on the heat transfer rate are examined.     

中段弹头表面温度及辐射特性的计算研究

为研究中段弹头的表面温度及辐射特性,利用Lowtran7计算太阳和地球大气的红外与可见光辐射,依据粗糙表面光散射理论计算弹头对太阳、地球大气和地球反照辐射的吸收和散射。采用控制容积法发展了圆柱坐标系下三维非稳态导热的隐式离散方程,迭代求解得到弹头表面的温度。以一射程4000km的中段弹头为例,计算了发动机关机点后2000s内,弹头表面的温度和辐射的变化。     

Temperature dependence of the electrical resistivity in amorphous metals

In amorphous metals the electrical resistivity increases linearly in the temperature range from 2 to 40 K. This result differs fundamentally from the nonlinear behaviour known for crystalline metals and it suggests the conduction electrons not to be scattered by the vibrations of the amorphous point lattice. The temperature dependent part of the resistivity in amorphous metals is explained with scattering of conduction electrons by fluctuations ofp-electrons.     

Three-dimensional radiative transfer in an isotropically scattering, plane-parallel medium: generalized X- and Y-functions

The topic of this work is the generalized X- and Y-functions of multidimensional radiative transfer. The physical problem considered is spatially varying, collimated radiation incident on the upper boundary of an isotropically scattering, plane-parallel medium. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is used to derive coupled, integro-differential equations for the source functions at the boundaries of the medium. The resulting equations are said to be in double-integral form because the integration is over both angular variables. Numerical results are presented to illustrate the computational characteristics of the formulation.     

Effect of metallic surface microroughness on the probability and spectrum of plasmon excitation by a fast charged particle moving parallel to the surface

The Green’s function of the electric field of plasmons is determined in a semi-infinite medium with an abrupt plasma boundary where nonequilibrium conduction electrons either undergo elastic reflection from the boundary or “stick” to it and give rise to a stationary surface charge. The angular reflection of elastically scattered electrons can be either specular or diffuse. The Green’s function is used to find the singleevent spectrum of energy loss by a fast electron moving parallel to the boundary. The effect of electronboundary scattering parameters on the structure of bulk and surface plasmon resonances is analyzed. The probability of transition radiation of bulk plasmon by an electron moving in vacuum is examined. A new type of surface resonance is found under conditions of perfectly elastic scattering of conduction electrons from the plasma boundary, similar in structure to a tangential surface plasmon.     

Radiative and conductive heat transfer in a nongrey semitransparent medium. Application to fire protection curtains

This paper deals with heat transfer in nongrey media which scatter, absorb and emit radiation. Considering a two dimensional geometry, radiative and conductive phenomena through the medium have been taken into account. The radiative part of the problem was solved using the discrete ordinate method with classical S_n quadratures. The absorption and scattering coefficients involved in the radiative transfer equation (RTE) were obtained from the Mie theory. Conduction inside the medium was linked to the RTE through the energy conservation. Validation of the model has been achieved with several simulation of water spray curtains used as fire protection walls.     

A new efficient method of solution to radiation transfer in absorbing,emitting, isotropically scattering,homogeneous, finite or semi-infinite,plane-parallel media

A new efficient method of analysis, which utilizes the natural eigenfunctions of the problem, is developed for solving radiation transfer in an absorbing, emitting, gray, isotropically scattering, homogeneous, finite or semi-infinite, plane-parallel medium. Expressions for the forward and backward radiation intensities, the incident radiation and forward and backward radiation heat fluxes are included. Since the physical aspects of the problem are well documented, attention is focused on the presentation of the method of analysis and discussion of its convergence and accuracy. For the test case involving uniform incident radiation on the boundary surface at x = 0, it is shown that the solution converges extremely rapidly to the exact results, and that lower-order approximations are highly accurate. For example, the first-order solution predicts values of the incident radiation, reflectivity and transmissivity that are less than 1% in error in almost all cases, for optical thicknesses in the range 0.1 ⩽ L ⩽ 10 and single-scattering albedos in the range 0.1 ⩽ ω ⩽ 0.99. The present method of solution has an excellent potential for generalization to anisotropic scattering and to radiation transfer in spherical and cylindrical geometries.     

Heat transfer by radiation and conduction in fibrous media without axial symmetry

Coupled radiative and conductive heat transfer in a fibrous medium formed by silica fibres is investigated in this paper by not taking account of the axial symmetry for the distribution of fibres or the boundary conditions. Radiative properties of the medium are calculated by using the Mie theory. The model obtained depends only on optical parameters (indices of silica) and on morphological parameters (diameter and orientation of the fibres, density of the medium). Simulations make it possible to study the strongly anisotropic behaviour of the scattering of the radiation by a fibre and to study the influence of various parameters on the radiative properties of the medium. The results of the Mie theory make possible the simulation of the heat transfer coupled by radiation and conduction. To do this, we introduce a new numerical scheme able to simulate heat transfer in the lack of axial symmetry. With this model, we can show the effects of distribution of fibres and temperature on the thermal behaviour of the medium as well as showing the importance of the phenomenon of scattering in fibrous media.     

开口/封闭薄壳体声辐射和散射的统一边界积分方程解法

推导了在二维和三维空间下开口和封闭薄壳体在任意阻抗边界条件下声辐射和散射的统一边界积分方程.相对于以前的求解方法,该方程求解声辐射和散射问题具有相同的影响矩阵,能够同时求解薄壳体气动和振动噪声的辐射和散射现象,以及分析壳体声阻抗对声波传播的影响.推导的方程可以应用于叶轮机械、管道等噪声和消声器消声性能的预测等方面.在此方程基础上,可以进一步考虑运动边界和运动介质对声辐射和散射的影响. 关键词： 薄壳体 声阻抗 积分方程 边界元方法     

Simultaneous solution of Kompaneets equation and radiative transfer equation in the photon energy range 1-125 keV

Radiative transfer equation in plane parallel geometry and Kompaneets equation is solved simultaneously to obtain theoretical spectrum of 1-125 keV photon energy range. Diffuse radiation field are calculated using time-independent radiative transfer equation in plane parallel geometry, which is developed using discrete space theory (DST) of radiative transfer in a homogeneous medium for different optical depths. We assumed free-free emission and absorption and emission due to electron gas to be operating in the medium. The three terms n, n² and (∂n/∂x_k) where n is photon phase density and x_k=(hν/kT_e), in Kompaneets equation and those due to free-free emission are utilized to calculate the change in the photon phase density in a hot electron gas. Two types of incident radiation are considered: (1) isotropic radiation with the modified black body radiation I^MB[1] and (2) anisotropic radiation which is angle dependent. The emergent radiation at τ=0 and reflected radiation τ=τ_max are calculated by using the diffuse radiation from the medium. The emergent and reflected radiation contain the free-free emission and emission from the hot electron gas. Kompaneets equation gives the changes in photon phase densities in different types of media. Although the initial spectrum is angle dependent, the Kompaneets equation gives a spectrum which is angle independent after several Compton scattering times.     

Analysis of radiative transport in a cylindrical enclosure—An application of the modified discrete ordinate method

Application of the modified discrete ordinate method (MDOM) proposed by Mishra et al. [Mishra SC, Roy HK, Misra N. Discrete ordinate method with a new and simple quadrature scheme. J Quant Spectrosc Radiat Transfer 2006;101:249-262.] has been extended for calculation of volumetric radiative information in a cylindrical enclosure. Radiatively, the medium inside a diffuse gray 1-D concentric cylinder is absorbing, emitting and scattering. Three types of problems, viz., an isothermal medium representing non-radiative equilibrium case, a non-isothermal medium representing radiative equilibrium situation and the case of a combined mode conduction and radiation heat transfer have been used to test the robustness of the MDOM. Temperature/emissive power and heat flux/energy flow rate distributions in the medium have been found for the effects of various parameters like the extinction coefficient, the scattering albedo, the boundary emissivity and the conduction-radiation parameter. To check the accuracy of the results of the MDOM, results have been compared with those available in the literature and also by obtaining the radiative information using the finite volume method. MDOM has been found to provide accurate results.     

The influence of anisotropic scattering on the radiative intensity in a gray, plane-parallel medium calculated by the DRESOR method

Even though there have been many ways to treat complex anisotropic scattering problems, in most of the cases only the radiation flux or its dimensionless data were provided, and radiative intensity with high directional resolution could merely be seen. In this paper, a comprehensive formulation for the DRESOR method was proposed to deal with the anisotropic scattering, emitting, absorbing, plane-parallel media with different boundary conditions. The method was validated by the data from literature and the integral formulation of RTE. The DRESOR value plays an important role in the DRESOR method, and how it is determined by the anisotropic scattering was demonstrated by some typical results. The intensities with high directional resolution at any point can be given by the present method. It was found that the scattering phase function has little effect on the intensity for thin optical thickness, for example, 0.1. And there is the largest boundary intensity for the medium with the largest forward scattering capability, and the smallest one with the largest backward scattering capability. An attractive phenomenon was observed that the scattering of the medium makes the intensity at boundary can not reach the blackbody emission capability with the same temperature, even if the optical thickness tends to very large. It was also revealed that the scattering of the medium does not mean it cannot alter the magnitude of the energy; actually, stronger scattering causes the energy to have more chance to be absorbed by the medium, and indirectly changes the energy magnitude in the medium. Finally, it is easy to deduce all the associated quantities such as the radiation flux, the incident radiation and the heat source from the intensity, just as done in literature.     

Low-temperature hopping conduction over the upper Hubbard band in p-GaAs/AlGaAs multilayered structures

The low-temperature 2D variable range hopping conduction over the states of the upper Hubbard band is investigated in detail for the first time in multilayered Be-doped p-type GaAs/AlGaAs structures with quantum wells of 15-nm width. This situation was realized by doping the layer in the well and a barrier layer close to the well for the upper Hubbard band (A ⁺ centers) in the equilibrium state filled with holes. The conduction was of the Mott hopping type in the entire temperature range (4?0.4 K). The positive and negative magnetoresistance branches as well as of non-Ohmic hopping conduction at low temperature are analyzed. The density of states and the localization radius, the scattering amplitude, and the number of scatterers in the upper Hubbard band are estimated. It is found that the interference pattern of phenomena associated with hopping conduction over the A ⁺ band is qualitatively similar to the corresponding pattern for an ordinary impurity band, but the tunnel scattering is relatively weak.     

The effect of scattering-medium parameters on signal magnitude under acousto-optic tomography

We have experimentally studied the influence of scattering anisotropy parameter g of a medium on the magnitude of signal S (visualization parameter) at an ultrasonic frequency that is registered upon acoustooptic tomography. Aqueous solutions of mixtures of cream and skimmed milk with different ratios between them were used as scattering media. The optical properties of media (absorption coefficient μ_a and reduced scattering coefficient μ′ _S ) have been measured on a spectrophotometer (Perkin-Elmer Lambda 950 UV-VIS-NIR) using the inverse adding-doubling technique. As a result of the investigation, we have found that there is a certain correlation between the value of the scattering anisotropy parameter g of aqueous solutions of investigated mixtures and the percentage of the mixture in the aqueous solution, which ensures the required small value of extinction coefficient μ of the scattering medium. An increase in signal S has been revealed with increasing anisotropy parameter g of the medium at a invariable value of extinction coefficient μ. We have concluded that, to solve an inverse problem on the acousto-optic tomography, it is necessary to take into account possible changes in the g factor in scattering media, including biological ones.     

The thermodynamic properties and special features of spectra of elementary excitations of unstable valence Sm-and Ce-based compounds

The experimental data on the spectra of elementary excitations measured by inelastic neutron scattering and on the heat capacity and the coefficient of thermal expansion are used to analyze the correlation between the spectral characteristics of the electron and phonon subsystems and the special features of the temperature dependence of the thermodynamic properties of a number of unstable valence Sm-and Ce-based compounds. The anomalous behavior of the thermodynamic properties of these compounds is defined by the special features of their phonon and electron (4f and conduction electrons) spectra. The rearrangement of the 4f-electron spectrum as a result of temperature variation plays a decisive part in the formation of temperature dependences of the heat capacity and the coefficient of thermal expansion of unstable valence systems.