Inverse Radiation problem in One—Dimensional Semitransparent plane—Parallel Media

The discrete ordinates method is used to develop a solution to an inverse radiation problem of source term in one-dimensional semitransparent plane-parallel media with opaque and specularly reflecting boundaries. It is assumed that, with the exception of the inhomogeneous source term, all aspects of the radiation transport problem are known. A method is developed to determine the inhomogeneous source term from specified incident radiation intensities on the boundaries. The inverse problem is solved using conjugate gradient method that minimizes the error between the incident radiation intensities calculated and the experimental data. The effects of single-scattering albedo, scattering asymmetry parameter, wall emissivity, the diffuse fraction of reflectivity, and the optical thickness on the accuracy of the inverse are investigated. The results show that the source term can be estimated accurately, even with noisy data.     

Simultaneous radiation and conduction heat transfer in a graded index semitransparent slab with gray boundaries

The simultaneous radiation and conduction heat transfer in a semitransparent slab of absorbing-emitting gray medium is solved in this paper. The refractive index of the medium spatially varies in a linear relationship, and the two boundary walls are diffuse and gray. A curved ray tracing technique in combination with a pseudo-source adding method is employed to deduce the radiative intensities on gray walls. Resorting to some of the results presented by Ben Abdallah and Le Dez, an exact expression of the radiative flux in medium is deduced. The influences on the temperature and radiative flux fields are examined, which are caused by the refractive index distribution, absorbing coefficient, thermal conductivity and the boundary wall emissivities. The results display the significant influences of the refractive index distribution and boundary wall emissivities on the radiative flux and temperature in medium.     

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.     

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。     

Analysis of Conduction and Radiation Heat Transfer in a Differentially Heated 2‐D Square Enclosure

Radiative heat transfer with and without conduction in a differentially heated 2‐D square enclosure is analyzed. The enclosure with diffuse gray boundaries contains radiating and/or conducting gray homogeneous medium. Radiatively, the medium is absorbing, emitting and scattering. On the south boundary, four types of discrete heated regions, viz., the full boundary, the left one‐third, left two third and middle one third, are considered. In the absence of conduction, distributions of heat flux along the south boundary are studied for the effect of extinction coefficient. In the presence of conduction, distributions of radiation, conduction and total heat fluxes along the south boundary are analyzed for the effects of extinction coefficient, scattering albedo, conduction–radiation parameter, and south boundary emissivity. Effects of these parameters on centerline temperature distribution are also studied. To assess the performance of three commonly used radiative transfer methods, in all cases, the radiative transfer equation is solved using the discrete ordinate method (DOM), the conventional discrete ordinate method (CDOM) and the finite volume method (FVM). In the combined mode problem, with volumetric radiative information known from one of the three methods, viz., DOM, CDOM, and FVM, the energy equation is solved using the finite difference method (FDM). In all cases, the results from FDM‐DOM, FDM‐CDOM, and FDM‐FVM are in good agreement. Computationally, all three sets of methods are equally efficient.     

Numerical analysis of solidification of a 3-D semitransparent medium in presence of volumetric radiation

Solidification of a 3-D cubical semitransparent absorbing, emitting and scattering semitransparent medium in the presence of volumetric radiation is analyzed. An enthalpy based lattice Boltzmann method is used to analyze the solidification process. Radiative information is computed using the finite volume method. Over a range of temperatures, a distinct liquid-, mushy- and solid-zones are considered. Cases of both Dirichlet and Neumann boundary conditions are taken up. Liquid fraction and temperature distributions in the medium are analyzed for the effects of the extinction coefficient, the scattering albedo, the conduction-radiation parameter and the latent heat.     

Numerical Simulation of Radiative-Conductive Heat Transfer in an Enclosure with an Isotherm Obstacle

In this paper, the lattice Boltzmann method (LBM) and discrete ordinates method (DOM) were applied to investigate the heat transfer in a square radiative-conductive media with heat flux and temperature boundary conditions. Furthermore, an isothermal rectangular obstacle is located in the middle of participating media. The energy equation is solved using the LBM; while the radiative transfer equation is solved using DOM. The effects of various parameters such as the extinction coefficient, scattering albedo, and the conduction–radiation parameter in the presence of an obstacle are studied on temperature and heat flux distributions. It was shown that, decrease in scattering albedo value leads to decrease of the temperature field in participating media. In addition, with increase in scattering albedo value, conductive heat flux increases and radiative heat flux decreases. It was shown that increase in extinction coefficient and decrease in conduction–radiation parameter have some significant effects on increasing the temperature profile, especially in the region with longer distance from obstacle.     

A novel case study for thermal radiation through a nanofluid as a semitransparent medium via discrete ordinates method to consider the absorption and scattering of nanoparticles along the radiation beams coupled with natural convection

Natural convection in a volumetric radiant enclosure filled by a nanofluid is studied numerically for the first time by using discrete ordinates (DO) method to consider the absorption and scattering coefficients of nanoparticles on the radiation beams through the nanofluid as a semitransparent medium. Present nanofluid is a mixture of Al₂O₃ nanoparticles suspended in water as the base fluid. The volume concentration percentages of nanoparticles are almost small to make a semitransparent medium which means the achieved results can be used in the flat plate solar collectors. Moreover the SIMPLE algorithm of finite volume method for Navier-Stokes continuity, momentum and energy equations are solved and coupled with DO to simulate the total radiation and natural convection in a shallow inclined rectangular 2-D enclosure. This shape of enclosure is chosen due to it might represent the usual configuration of a solar collector. The enclosure inner walls are the gray diffuse emitters and reflectors. The effects of various amounts of Rayleigh number and volume concentration at different values of wavelength are investigated. The positive effect of wave length on radiation heat flux and consequently total heat flux of radiation and natural convection is observed.     

Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm

A stochastic particle swarm optimizer (SPSO) algorithm, which can guarantee the convergence of the global optimization solution with probability one, is adopted to estimate the parameters of radiation system. To illustrate the performance of this algorithm, three cases are investigated, in which the source term, the extinction coefficient, the scattering coefficient, and the non-uniform absorption coefficients in a one-dimensional slab are retrieved. The directional radiative intensity, reflectance and transmittance, radiative flux simulated by discrete ordinate method (DOM) are served as input for the inverse analysis, respectively. By SPSO algorithm presented, all these radiative parameters could be estimated accurately, even with noisy data. In conclusion, the SPSO algorithm is proved to be fast and robust, which has the potential to be implemented in various fields of inverse radiation problem.     

Internal radiation effects in semitransparent high‐temperature coatings

Internal thermal radiation in semitransparent coatings should be considered in the calculation of temperature and heat flux distribution in metal wall with a thermal barrier coating. In this paper, a ray tracing/node analysis method is used in the numerical simulation of a coupled transient radiative and conductive heat transfer in an absorbing‐scattering non‐gray coating. The present results show that the operating temperature is higher than the design temperature when the radiation is not considered. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(5): 271–278, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20021     

Integral equation solutions based on exact ray paths for radiative transfer in a participating medium with formulated refractive index

The exact analytical path length of radiation traveling in a slab with formulated variable refractive index is derived. Based on the analytical path lengths, the integral equations in terms of intensity moments for radiative transfer in a participating slab with one of the family of spatially varying refractive indices are developed. We solve the integral equations for radiative transfer in a slab at radiative equilibrium or for radiative transfer in an isothermal slab. The boundaries are assumed to be black for the slab at radiative equilibrium and the index jumps at both boundaries for the isothermal slab are considered. For comparison purpose, we also solve the radiative equilibrium problems by the discrete ordinates method (DOM). The nondimensional emissive power and nondimensional radiative heat flux obtained by solving integral equations show an excellent agreement with those obtained by the DOM. For the slab at radiative equilibrium and with positive gradient of refractive index, the jump of the emissive power at bottom boundary decreases with the increase of optical thickness for the cases with slightly varying refractive index, but the trend may not hold for the cases with significantly varying refractive index. For the non-scattering slab with positive gradient of refractive index and fixed refractive indices at the boundaries, the directional emittances at both boundaries for the case with linear refractive index are smaller than those for the case with a refractive index of slope-increasing profile. Effects of the scattering albedo and the scattering phase function coefficient are investigated too.     

Internal distribution of radiation absorption in one-dimensional semitransparent medium

The internal distribution of spectral radiation absorption in one-dimensional semitransparent slab, sphere and cylinder irradiated uniformly and isotropically is determined by the ray tracing method, and the detailed theory for computation are deduced. The computed results show that the internal distribution of spectral radiation absorption in slab differs from that in spherical and cylindrical particles. The peak of internal volumetric spectral radiation absorption may locate at interior shell of the semitransparent sphere and cylinder. The dimensionless volumetric spectral radiation absorption is higher near the center for weakly absorbing or small size parameter, but is higher near the surface for strongly absorbing or large spheres and cylinders. Refraction focuses the rays close to the sphere and cylinder center. With the increases of the refractive index, the dimensionless volumetric spectral radiation absorption increases near the sphere and cylinder centers and decreases near the sphere and cylinder surfaces.     

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.     

Inverse radiation problem of temperature field in three-dimensional rectangular furnaces

The discrete ordinates method is used to developed a solution to an inverse radiation problem of temperature field in rectangular furnaces. It is assumed that, with the exception of the inhomogeneous temperature field, all aspects of the radiation transport problem are known. A method is developed to determine the inhomogeneous temperature field from specified incident radiation heat fluxes at the centers of boundary walls. The inverse problem is solved using conjugate gradient method that minimize the error between the incident radiation heat fluxes calculated and the experimental data. The results of temperature estimation show that the temperature field can be estimated accurately, even with noisy data.     

Inverse radiation–conduction design problem in a participating concentric cylindrical medium

Inverse conduction–radiation problem for design analysis in a two-dimensional concentric cylindrical absorbing, emitting and isotropically scattering medium has been solved, when the desired boundary conditions are available on the design surface. The finite-volume method was adopted to deal with energy conservation equation including conduction and radiation. The radiative transfer equation was also taken into consideration in direct problem, whereas the Levenberg–Marquardt method was used to solve a set of equations in inverse problem, which are expressed by errors between estimated and desired total heat fluxes on the design surface. The automatic differentiation as well as the Broyden combined update was utilized to reduce computational time in calculating the sensitivity matrix. The results have shown that the desired total heat flux distribution on design surface could be successfully estimated with less computational time using the present inverse procedure developed here.     

Transient coupled radiative and conductive heat transfer in a composite of semitransparent media

INTRODUCTIONIhsemitransparentmaterial(STM),energyisusuallytransferredbyradiationinaddihontoheatconduchon.WhenthesemitransparentmaterialisexPOsedtohightemperatUresurroundingsorwhenanintensiveincidentradiationexists,theeffectoftheradiationonthetransienttempef~fieldsismoreimpobotthanthat'oftheconduchon.msfeatUreplaysanimpoftalltroleinmanufactUreandengineeringaPPlicationsofalotofsemitransparentnderialsll],suchasglassindustry,ceramicandfiber~rials,mulh-layersemiconductors,moltensaltmedia,se…     

Analysis of Radiative Transport in a 2-D Cylindrical Participating Medium Subjected to Collimated Radiation

This article deals with the numerical analysis of radiative transport in a 2-D axisymmetric cylindrical enclosure containing absorbing, emitting, and scattering medium. The participating medium receives collimated radiation from the top boundary of the enclosure. Attenuation of the collimated radiation in the medium gives rise to the diffuse radiation. Thus, the governing radiative transfer equation accounts for both collimated and diffuse radiation. The radiative transfer equation is solved using the modified discrete ordinate method. Effects of extinction coefficient, scattering albedo, and aspect ratio on radial and axial distributions of heat flux and incident radiation are studied. In all cases, results are validated against those available in the literature. Modified discrete ordinate method has been found to provide accurate results.     

Numerical study of transient heat transfer in semitransparent porous medium

Transient solutions were obtained for heat transfer through a semitransparent porous medium placed in a flow passage and submitted to incident radiation. The one-dimensional physical model takes into account, conduction, convection and radiation simultaneously. The porous medium is assumed to be homogenous continuum, which absorbs, emits and scatters thermal radiation. A fully implicit time-marching algorithm was used to solve the nonlinear coupled energy equations for gas and porous medium numerically. The present study utilizes the differential–discrete–ordinate (DDO) method to account for the radiation contribution. The effects of the Reynolds number, optical depth, anisotropic scattering, conduction–radiation parameter and scattering albedo on temperatures and fluxes profiles are investigated.     

Transient radiative transfer in a scattering slab with variable refractive index and diffuse substrate

In this work, we applied the discrete ordinates method (DOM) with a first-order spatial scheme and adapted a modified DOM (MDOM) to solve transient radiative transfer in a refractive, absorbing and scattering slab suddenly exposed to a diffuse strong irradiation at one of its boundaries. The other boundary is diffusely reflecting. From the comparison of the results obtained by the first-order DOM, the MDOM and the Monte Carlo method, it can be seen that the results obtained by the three methods are in excellent agreement as the time is long enough. Besides, the solutions of optically thin and moderate cases obtained by the first-order DOM include some early transmitted radiation due to numerical diffusion and those obtained by the MDOM do not show numerical diffusion in the beginning of a transient process. The reason is that the MDOM solves exactly the reduced incident intensity which dominates radiative transfer in the beginning of a transient process. The time-resolved hemispherical reflectance and transmittance of the slab are obtained for various linearly varying refractive indices, optical thicknesses, scattering albedos and substrate reflectivities. Effects of those parameters are investigated.