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.     

Analysis of transport of collimated radiation in a participating media using the lattice Boltzmann method

Application of the lattice Boltzmann method (LBM) recently proposed by Asinari et al. [Asinari P, Mishra SC, Borchiellini R. A lattice Boltzmann formulation to the analysis of radiative heat transfer problems in a participating medium. Numer Heat Transfer B 2010; 57:126–146] is extended to the analysis of transport of collimated radiation in a planar participating medium. To deal with azimuthally symmetric radiation in planar medium, a new lattice structure for the LBM is used. The transport of the collimated component in the medium is analysed by two different, viz., flux splitting and direct approaches. For different angles of incidence of the collimated radiation, the LBM formulation is tested for the effects of the extinction coefficient, the anisotropy factor, and the boundary emissivities on heat flux and emissive power distributions. Results are compared with the benchmark results obtained using the finite volume method. Both the approaches in LBM provide accurate results.     

吸收-透射界面下正弦折射率介质内辐射换热

对具有吸收-透射性边界面的梯度折射率半透明介质层,建立了介质内热辐射传递与边界面辐射换热的数理模型,并采用数值弯曲光线跟踪法求解介质内的热辐射传递。通过数值模拟,分析了正弦折射率下,边界面的反射特性、吸收率以及介质层光学厚度对介质内热辐射平衡温度场及热流分布的影响。结果表明,边界面的反射特性与吸收率对介质内辐射换热均有重要影响,吸收率的影响与边界面反射特性、介质层光学厚度及环境条件相关,呈现特征不同的作用。     

A modification of the cumulative wavenumber method to compute the radiative heat flux in non-uniform media

This paper presents a modification of the cumulative wavenumber (CW) method to determine the radiative heat flux in non-uniform participating gases. Previous works in the literature have shown that the CW method renders accurate estimates of the radiative volumetric heat source in the medium. However, as will be shown in this work, the radiative heat flux can present considerable deviation of the correct solution, which results from the radiative energy balance not being satisfied by the CW method. A modification of the method is devised in this work to satisfy the radiative energy balance while keeping the same value of the radiative volumetric heat source. The proposed methodology is applied together with the discrete ordinates method to solve the radiation heat transfer in a one-dimensional slab containing a non-isothermal layer of carbon dioxide. The results are compared to the benchmark line-by-line (LBL) integration, and show that the modified CW method can satisfy the radiative energy balance, improving the estimation of the radiative heat flux in the medium.     

管内耦合换热的辐射热流特征及抽样模式比较

通过数值模拟,研究了圆管层流入口段辐射与对流祸合换热中的辐射热流分布特征,提出并比较了采用蒙特卡罗法计算辐射换热的两种抽样模式。结果表明,在圆管入口段的耦合换热中,同一截面的径向辐射热流密度与轴向辐射热流密度数量级相当,世分布形态差别很大。用蒙特卡罗方法计算辐射换热时,采取等权能束的抽样模式,可消除因抽样能束的能量不同而造成的计算误差、降低计算量、提高计算精度。     

Theoretical analysis of porous radiant burners under 2-D radiation field using discrete ordinates method

This paper describes a theoretical study to investigate the heat transfer characteristics of porous radiant burners (PRBs). In the present work, a 2-D rectangular model is used to solve the governing equations for porous medium and gas flow before the premixed flame to the exhaust gas. The gas and the solid phases are considered in non-local thermal equilibrium and combustion in the porous medium is modeled by considering a non-uniform heat generation zone. The homogeneous porous media, in addition to its convective heat exchange with the gas, may absorb, emit and scatter thermal radiation. The radiation effect in the gas flow is neglected but the conductive heat transfer is taken into account. In order to analyze the thermal characteristics of porous burners, the coupled energy equations for the gas and porous medium in steady condition are solved numerically and the discrete ordinates method (DOM) is used to obtain the distribution of radiative heat flux in the porous media. Finally, the effects of various parameters on the performance of porous radiant burners are examined. The present results are compared with some reported theoretical and experimental results by other investigators and good agreement is found.     

Analysis of collimated radiation in participating media using the discrete transfer method

A general formulation of the discrete transfer method is provided to analyze radiative heat transfer problems in a participating medium subjected to collimated radiation. The formulation is validated by considering 1-D planar absorbing, emitting and anisotropically scattering gray medium in radiative equilibrium. Anisotropy of the medium is approximated by linear anisotropic phase function. For the purpose of comparison, the problem is also solved analytically. Results are obtained for different angles of incidence of the collimated radiation. At a given angle of incidence, results are obtained for forward, isotropic and backward scattering situations. Heat flux results are compared over a wide range of values of the extinction coefficient. Emissive power distributions in the medium are also obtained for some cases. The discrete transfer method results are found to compare very well with the analytic results.     

Steady state ensembles of thermal radiation in a layered media with a constant heat flux

This paper describes steady‐state ensembles of thermally excited electromagnetic radiation in nano‐scale layered media with a constant non‐vanishing heat flux across the layers. It is shown that Planck's law of thermal radiation, the principle of equivalence, and the laws of wave propagation in layered media, imply that in order for the ensemble of thermally excited electromagnetic fields to exist in a medium consisting of a stack of layers between two half‐space, the net heat flux across the layers must exceed a certain threshold that is determined by the temperatures of the half spaces and by the reflective properties of the entire structure. The obtained results provide a way for estimating the radiative heat transfer coefficient of nano‐scale layered structures.     

Nonlinear radiation analysis in hydrogen plasma

This paper deals with the radiation energy transport within a plasma gas enclosed between two parallel black plates, together with the interaction of radiation and conduction under uniform heat generation. An expression for the radiation heat flux is being obtained in terms of the modified emissivity without resorting to the assumption of linearized radiation previously used. Results for the temperature and radiation heat flux distributions are obtained for various values of heat generation and for different spacings between the plates. The results presented are for hydrogen plasma gas at pressures of 0.43 and 37.5 atm with wall temperatures of 10,000°K. The present results for the centerline temperatures are compared with those utilizing linearized radiation, and it was found that the linearized radiation assumption overestimates the temperature values especially for large heat generations.     

空间光学遥感器热试验外热流模拟及程控实现

以某太阳同步轨道空间光学遥感器为例,阐述了空间外热流分析计算、热平衡试验外热流模拟以及外热流程控加载的全过程.首先,总结了空间光学遥感器外热流模拟的完整流程.其次,简要介绍了太阳辐射、地球反照、地球红外辐射三种空间外热流的计算方法.然后,对该空间遥感器进行了空间综合吸收外热流计算,获得了阳照区及阴影区外热流平均值.最后,确定了热平衡试验外热流的模拟方法和策略,利用LabVIEW语言编写了程控电源开环控制程序,实现了热试验外热流的准确加载.试验结果表明,外热流值加载偏差在±2.5%以内,满足热平衡试验要求.     

圆筒形半透明介质内非稳态复合导热与辐射的研究

本文研究细长电加热体在圆筒形半透明介质中的温度响应，通过对控制非稳态导热与辐射复合传热过程的积分-微分方程直接进行数值求解，分析了热辐射对内部径向热流及温度变化的影响．模拟计算结果对热线法测量半透明介质导热系数的研究具有理论指导意义。     

水雾红外隐身的冷/热目标效应

人工水雾对抗红外成像制导导弹时,会因为蒸发对流强、辐射热流弱而使水雾形成冷目标;也可能因为辐射热流过强、散热弱而形成热目标。为详细揭示该现象,以Mie理论为基础,通过辐射传递方程和能量守恒方程的耦合计算,建立了水雾红外隐身产生冷目标或热目标效应的数学模型。应用蒙特卡洛法与本文算法作对比,验证了模型的正确性;将水雾视为吸收、发射、各向异性散射介质,考虑水雾自身辐射、多重散射和各种换热过程,比如辐射热流、两相流的热传导、热对流、紊流热扩散以及雾滴蒸发等,反映了水雾热遮蔽所产生的冷/热目标效应。     

Radiative heat transfer in a planar medium with anisotropic scattering and directional boundaries

Radiation heat transfer in an absorbing, emitting and scattering medium has been the subject of many previous investigations. Most solutions are numerically complex and the existing analytical solutions are restricted in application by the simplifying assumptions involved. A plane-parallel medium is considered which scatters anisotropically. The boundaries are considered to be specular reflectors, as predicted by Fresnel's relations, while the diffusely incident radiation is refracted according to Snell's law. The emission is restricted to a medium with a uniform temperature distribution. Approximate closed-form solutions for the radiative heat flux and incident intensity are presented for dielectric layers and linear anisotropic scattering. Numerical results are also presented and show that the effects of directional boundaries, anisotropic scattering, scattering albedo and optical depth are accurately predicted by the approximate solution.     

Transmission of radiation through an aerosol medium

The properties of radiation through an aerosol medium have been achieved. This has been done by employing Mie scattering theory to calculate the radiation transfer scattering parameters in the form of extinction, absorption and scattering efficiencies. The equation of radiative transfer for the heat flux through a plane parallel atmosphere of aerosol has been solved. The aerosol size distributions are found in practical systems. Average efficiencies over size distribution for spherical particles of complex refractive index are calculated. Therefore, the radiative properties of stratospheric aerosols have been done. The obtained results found to be in a good agreement with the previous work.     

Radiative transport in a planar medium exposed to azimuthally unsymmetric incident radiation

An analytical solution is developed for the radiation field engendered by illuminating an absorbing/anisotropically scattering planar medium with an azimuthally unsymmetric incident flux. The boundaries of the medium are allowed to possess both specular and diffuse reflection characteristics. The problem is mathematically reduced to solving a system of azimuthally independent equations which may be analyzed by many existing techniques. A solution scheme is formulated in terms of singular eigenfunctions and solved using a modified F_N method. Computations are performed for the azimuthally symmetric case of irradiation by parallel rays at oblique incidence. Several different phase functions are considered and results are presented for the discrete eigenvalues, the heat flux distributions within the medium, the reflectance and transmittance of the slab and the angular distribution of the intensities at the boundaries.     

Transient radiation and conduction heat transfer inside a plane-parallel participating gray medium with boundaries having different reflecting characteristics

A hybrid ray-tracing method is developed for the solution to the radiative transfer in a plane-parallel participating medium having one specular surface and another diffuse surface. By this method, radiative transfer coefficients (RTCs) for specular–diffuse (S–D) surfaces are deduced. The medium surfaces are considered to be semitransparent. The effects of convection–radiation parameter, conduction–radiation parameter and refractive index on transient coupled heat transfer are investigated. Results show that the temperature curves of the medium having S–D surfaces is higher than those of the medium having S–S surfaces (two specular surfaces); the total heat flux at steady state for the S–D surfaces is lower than that for the S–S surfaces.     

IR thermography heat flux measurement in fire safety applications

The paper deals with heat flux measurement possibilities in fire safety applications. The paper presents two methods for radiation heat flux measurement – the thermography source-target measurement method, and the radiation contact target measurement method. Both the methods were used simultaneously for radiation heat flux measurement during a fire experiment on a high-density polyethylene plastic box storage stack. The theoretical background, experimental set-up, application example, and comparison of both methods are presented in this paper. Dependence of heat flux magnitude on a distance and direction from a heat source is evaluated. The possible safety risks ensuing from high temperatures inside the burning stack, and therefore high heat fluxes near the stack, are discussed.     

Equilibrium ensembles of electromagnetic thermal radiation in layered media

This paper describes equilibrium ensembles of thermally excited electromagnetic fields in layered media. The obtained results complement Planck's law of thermal radiation that determines the spectrum of the radiation but supplies little information about the ensemble of eigenfields (normal modes) excited in the medium. The developments regarding these ensembles presented in this paper make it possible to apply perturbation techniques for the analysis of the ensembles of radiated fields in layered media with a steady heat flux.     

Simulation of radiative heating of snow and ice coating

Numerical simulation of thermal state was performed for semitransparent medium; the thermal state is formed under impact of incident radiation and convective heat transfer to the ambient medium. The model takes into account the heat transfer to the semi-infinite opaque substrate below the layer of semitransparent material. Computation was performed for governing parameters typical of snow and ice coating during winter period. Solving the radiative part of problem uses the modified average flux method. This method takes into account the dependence of optical properties on the wavelength of incident radiation, scattering, and reflective properties of the layer boundaries.