Transient thermal analysis of semitransparent composite layer with an opaque boundary

Transient coupled radiative and conductive heat transfer in a two-layer, absorbing, emitting, and isotropically scattering non-gray slab is investigated by the ray tracing method in combination with Hottel's zonal method. One outer boundary is opaque, and another is semitransparent. The radiative energy transfer process in a semitransparent composite is divided into two sub-processes, one of which considers scattering, the other does not. The radiative transfer coefficients of the composite are deduced under specular and diffuse reflection and combined specular and diffuse reflection, respectively. The radiative heat source term is calculated by the radiative transfer coefficients. Temperature and heat flux are obtained by using the full implicit control-volume method in combination with the spectral band model. The method presented here needs only to disperse the space position, instead of the solid angle. A comparison with previous results shows that the results are more accurate.     

Model of radiative transfer in fibrous media—matrix method

A matrix model of radiative transfer is presented. Beginning with the radiative properties of a medium, two characteristic matrices representing the transmissive and reflective contributions to energy transfer are written and the intensity distribution is then calculated numerically. Applications to pure radiative transfer and combined transfer with conduction are presented. A case of a material composed of silica fibres is discussed, showing that the model is in good agreement with experimental results. Since no simplifying hypotheses concerning the properties of the medium are incorporated into the model, it can be used to study any fibrous medium.     

Thermal radiation in layered participating cylindrical media using an integral equation method

Radiative transfer in a layered cylindrical medium is analyzed using a newly developed S-type integral equation of transfer in terms of incident radiation and net radiative heat flux. The physical systems in hollow and solid cylindrical geometry are modeled as nonhomogeneous participating media with stepwise variable properties. Thus, the necessity to establish the equation of transfer for each layer and combine these layers through the intensity continuity on interface is avoided. Numerical predictions from a collocation method are presented to illustrate the effects of radiation properties on the radiative transfer for the systems considered. Comparison of the results with other available data in literature shows that highly accurate results are obtainable by current method with simplicity.     

An inverse radiation boundary design problem for an enclosure filled with an emitting,absorbing, and scattering media

This work is an inverse radiative design problem in which the objective is to determine the spatial distribution of heat source strengths which produces a desired temperature and heat flux distribution on the design surface. The furnace whose walls are diffuse-grey is assumed to be filled with an absorbing, emitting, and scattering medium. The function to be minimized is the sum of squares of the differences between the desired and calculated radiative heat fluxes at the design surface. Radiative heat flux calculations are accomplished by means of the Modified Discrete Transfer Method MDTM using the correction factors suggested by Coelho and Carvalho [P.J. Coelho, M.G. Carvalho, Conservative formulation of the discrete transfer method, ASME J. Heat Transfer, 119 (1997) 118–128.] and Cumber [P.S. Cumber, Improvements to the discrete transfer method of calculating radiative heat transfer, Int. J. Heat Mass Transfer, 38 (12) (1995) 2251–2258.]. For inverse design calculations the Conjugate Gradient Method CGM is employed, in which the sensitivity coefficients are defined and used as needed by the algorithm. Our investigation shows that the presented algorithm is able to estimate heater strengths accurately.     

一般气体辐射条件下火焰炉膛内辐射换热的网络分析法

指出了用文献[1]提出的辐射网络单元求解火焰炉膛内辐射换热问题的不足之处，提出了更具普遍性的新的辐射网络单元。并用此分析求解一般气体辐射条件下火焰炉的辐射热交换问题，得到了用文献[1]的网络单元不能导出的传统法的结果。     

Radiative transfer in an absorbing-scattering slab bounded by emitting and reflecting surfaces

An exact integral theory of the planar radiative transfer with isotropic scattering and general boundary conditions is presented in the paper. The analytical solution to the problem is numerically processed for two different specializations of the emissivity and reflectivity properties of the bounding surfaces. Results are given for the total and angular radiation intensities as well as for the net radiative flux.     

Optimum outlet temperature of solar collector for maximum work output for an Otto air-standard cycle with ideal regeneration

The optimum solar collector outlet temperature for maximizing the work output for an Otto air-standard cycle with ideal regeneration is investigated. A mathematical model for the energy balance on the solar collector along with the useful work output and the thermal efficiency of the Otto air-standard cycle with ideal regeneration is developed. The optimum solar collector outlet temperature for maximum work output is determined. The effect of radiative and convective heat losses from the solar collector, on the optimum outlet temperature is presented. The results reveal that the highest solar collector outlet temperature and, therefore, greatest Otto cycle efficiency and work output can be attained with the lowest values of radiative and convective heat losses. Moreover, high cycle work output (as a fraction of absorbed solar energy) and high efficiency of an Otto heat engine with ideal regeneration, driven by a solar collector system, can be attained with low compression ratio.     

有限体积法在电站锅炉炉膛辐射换热计算中的应用

辐射换热是大型锅炉炉膛内的主要换热形式,准确的计算炉膛内的辐射换热量对大型锅炉设计和优化有重要意义。本文将有限体积法推广用于求解和分析大型电站锅炉炉膛内的辐射换热。给出了有限体积法对辐射传递方程进行离散和求解的基本过程。评估了有限体积法求解大型电站锅炉炉膛辐射换热的可靠性。将有限体积法用于分析某电厂600MW锅炉炉膛内的辐射换热,结果表明有限体积法可以有效的求解大型电站锅炉炉膛内的复杂辐射换热过程。     

Solution of radiative heat transfer in a semitransparent slab with an arbitrary refractive index distribution and diffuse gray boundaries

On the basis of medium discretization and local linear approximation of refractive index distribution, the curved ray tracing technique is used in combination with the pseudo source adding method to numerically solve the radiative heat transfer in a semitransparent slab with an arbitrary refractive index distribution and two diffuse gray walls. The radiative equilibrium temperature field of a linear refractive index distribution is evaluated by this method and the results show excellent agreement with that of the previous research. For two types of sinusoidal refractive index distributions, the radiative equilibrium temperature field as well as the temperature and heat flux fields of coupled radiation-conduction are investigated in detail. The results show considerable significance of the gradient refractive index effect, and some important conclusions are to be obtained.     

Evaluation of an improved hybrid six-flux/zone model for radiative transfer in rectangular enclosures

An improved model for the calculation of radiative transfer in enclosures filled with an absorbing, emitting and scattering medium is presented. The model is denoted by a hybrid six-flux/zone model since it combines features of both the zone method and (three-dimensional) six-flux models. Compared to the zone method, computation time is considerably reduced and reaches approximately the same order as the faster flux-type models. The accuracy of the hybrid six-flux/zone model presented here is drastically improved without increasing computation time. This is achieved by introducing a correction for the directional characteristics of the propagation of radiation through adjacent zones. The thus improved hybrid model is evaluated for a realistic recognized test problem and found to be an efficient and accurate tool for calculating radiative transfer in enclosures filled with a participating medium.     

Investigation of soot transport and radiative heat transfer in an ethylene jet diffusion flame

Numerical and experimental investigations highlighting the heat and mass transfer phenomena in a laminar co-flowing jet diffusion flame have been carried out. The fuel under consideration is ethylene, with ambient air as the co-flowing oxidizer. The diffusion flame is modeled using a 17-step reduced reaction mechanism with finite rate chemistry and the effects of soot on the radiative heat transfer of the flame have been demonstrated. Soot growth and oxidation processes are studied using a two-equation transport model, while the radiative heat transfer is modeled using the P1 approximation. An in-house finite volume code has been developed to solve the axi-symmetric Navier–Stokes equations in cylindrical coordinates, along with the soot mass fraction, soot number density, energy and species conservation equations. Comparison of predictions with experimental results shows reasonable agreement with regard to the flame height and temperature distribution. A parametric study is also presented, which illustrates the effects of the fuel jet Reynolds number and the flow rate of co-flow air.     

Spectrally correlated radiation and laminar forced convection in the entrance region of a circular duct

The two-dimensional combined radiative and convective transfer in emitting and absorbing real gases in the entrance region of a duct with a jump of wall temperature is studied. The axial propagation of radiation is taken into account in the analysis. The flow field and the energy equations are solved simultaneously and the radiative properties of the flowing gases, CO₂ or H₂O, are modeled by using either the narrow-band correlated-k model or the global absorption distribution function (ADF) model. The results are presented in terms of temperature and radiative power fields, and of the evolution of bulk temperatures and of heat transfer coefficients. Due to the axial component of the radiative flux, the gas is preheated or precooled before the change in wall temperature and this induces a persistent difference between the results of 1-D and 2-D radiation analyses. Some differences between CO₂ and H₂O temperature and radiative power profiles, due to the different structures of their spectra, are put in evidence. The ADF model, only suitable for gray walls, is shown to be less accurate when the gas is heated than when it is cooled.     

Numerical analysis of combined-mode dual-phase-lag heat conduction and radiation in an absorbing,emitting, and scattering cylindrical medium

Combined-mode dual-phase-lag (DPL) heat conduction and radiation heat transfer is analyzed in a concentric cylindrical enclosure filled with a radiatively absorbing, emitting, and scattering medium. The governing energy equation is incorporated with volumetric radiation as a source term, essentially to take the effect of radiative heat flux into account. While the energy equation is solved using the lattice Boltzmann method (LBM), the finite volume method (FVM) is used to calculate the radiative information. To establish the accuracy of the proposed LBM formulation, the governing energy equation is also solved with the finite difference method (FDM). Thermal perturbation is caused by suddenly changing the temperature at the boundaries. Radial temperature distributions during transience as well as steady state (SS) are presented for a wide range of parameters such as lag ratio, extinction coefficient, scattering albedo, conduction–radiation (C-R) parameter, boundary emissivity, and radius ratio. Sample results are benchmarked with those available in the literature, and a good agreement between the present and reported results is found.     

燃烧室内三维温度场的辐射反问题

本文提出了一种在介质辐射特性已知的条件下,由壁面入射辐射热流的测量值反演燃烧室内三维温度场的方法。该方法是在辐射传递方程离散坐标近似的基础上,用求目标函数极小值的共轭梯度法进行反演计算。通过对吸收系数、散射不对称因子、反照率、壁面黑度和燃烧室大小尺寸等参数对反演精度影响的分析,结果表明,即使存在随机测量误差,这些参数对温度场反演精度的影响也不大,本文所提出的方法可较精确地反演燃烧室内三维温度场。     

Experimental research of radiative heat transfer in fluidized beds

A new method to measure the radiative heat transfer in fluidized beds was presented. Experiments were carried out on a 0.8 th⁻¹ fluidized bed combustion boiler. The residual slag of fired coal was operated in a fluidized bed at room temperature. As the radiative heat transfer at room temperature is insignificant, its contribution at high temperatures might be obtained by the comparison of experimental results at high and low temperatures. On experimental study, a radiative contribution was given as a function of bed temperature and particle size. The results were compared with those in other references.     

Inverse radiation analysis of simultaneous estimation of temperature field and radiative properties in a two-dimensional participating medium

An inverse radiation analysis is presented for simultaneous estimation of temperature field and radiative properties including absorption and scattering coefficients in a two-dimensional rectangular, absorbing, emitting and scattering gray medium from the knowledge of the exit radiative energy received by charge-coupled device (CCD) cameras at boundary surfaces. The backward Monte Carlo method was introduced to describe the radiative heat transfer for its efficiency. The inverse problem is formulated as an optimization problem and solved by the least-square QR decomposition (LSQR) method. The effects of measurement errors, optical thickness and search step length on the accuracy of the estimation were investigated and the results show that the temperature field and radiative properties can be reconstructed accurately for the exact and noisy data.     

Finite element solution of radiative transfer across a slab with variable spatial refractive index

To avoid the complicated computation of ray trajectories, a finite element formulation is developed to solve the radiative transfer problem in a one-dimensional absorbing-emitting-scattering semitransparent slab with variable spatial refractive index. A problem of radiative equilibrium is taken as an example to verify this finite element formulation. The predicted temperature distributions are determined by the proposed method and compared with the data in references. The results show that the finite element formulation presented in this paper has good accuracy in solving the radiative transfer in one-dimensional absorbing-emitting-scattering semitransparent medium with variable spatial refractive index.     

Numerical investigation of coupled natural convection and radiation in a differentially heated cubic cavity filled with humid air. Effects of the cavity size

A numerical study of natural convection with surface and air/H₂O mixture radiation in a differentially heated cubic square cavity is presented. The coupled flow and heat transfers in the cavity are predicted by coupling a finite volume method with a spectral line weighted sum of gray gase model to describe gas radiative properties. The radiative transfer equation is solved by means of the discrete ordinate method. Simulations are performed at Ra?=?10⁶, considering different combinations of passive wall and/or gas radiation properties and different cavity length. It was found that in presence of a participative medium representative of building, cavity length has a strong influence on temperature and velocity fields which affect the global circulation and heat transfers in the cavity. For each steady-state solution, the convective and radiative contributions to the global heat transfer are discussed. More specifically, boundary layer thickness, thermal stratification parameter, and three-dimensional effects are compared to pure convective case results. The results suggest that radiative effects, often considered as negligible in view of the relatively low optical thickness, may not be neglected when trying to predict regime transitions.