Radiative Heat Transfer Problems Research Articles

Energy performance assessment of a window with a horizontal Venetian blind

This study examines the effects of the presence of a Venetian blind on the thermal performance of a window. The blind is positioned adjacent to the indoor surface of either a single or double glazed window and the coupled convection and radiation heat transfer problem is solved using a two-dimensional finite volume model. The numerical model is validated with published experimental and numerical results in the literature. The results show that the presence of a Venetian blind significantly improves the energy performance of a single and double glazed window. The blind reduces the overall heat transfer rate through the window by reducing the thermal radiation from the indoor glazing. The improved understanding of the benefits of Venetian blinds may lead to better designs of window/shading systems.

Radiative Heat Transfer to Magnetohydrodynamic Couette flow with Variable Wall Temperature

A numerical study of the problem of radiative heat transfer to magneto-hydrodynamic couette flow as affected by the conductance of the wall of the channel is performed in the paper. Numerical solutions are obtained for the temperature using the Runge–Kutta and the Newton–Raphson Shooting algorithm. Results obtained show that the rate of heat transfer increases with decreasing values of the Hartmann number when the wall is non-conducting, but increase with increasing values of the magnetic Reynolds number at a given value of electrical conductance.

Comparison of Radiation Element Method and Discrete Ordinates Interpolation Method Applied to Three-Dimensional Radiative Heat Transfer

We compare and scrutinize the characteristics of radiation element method by ray emission model (REM 2 ) and discrete ordinates interpolation method (DOIM). A three-dimensional radiative heat transfer problem is solved within a rectangular enclosure containing absorbing, emitting, nonscattering medium with temperatures given as a sine function. The calculation results are validated with the zonal results and the analytical solution

Flux limiters in the coupling of radiation and hydrodynamic models

Two numerical approximations to radiative heat transfer problem based on asymptotic and entropy approaches are proposed for hydrodynamics radiation coupling. We compare the radiative fluxes between the two approaches and we show that the coupling based on the entropy approach is flux limited, while the other approach does not preserve this condition. Relaxation schemes are considered for the hydrodynamic part, and an iterative procedure is used for radiation. The new splitting algorithm avoids the use of Riemann solvers and Newton iterations. Numerical examples are carried out on two and three dimensional problems.

Solution of radiative heat transfer problems with the discrete transfer method applied to triangular meshes

The present communication deals with the solution of the radiative transfer equation in a gray absorbing media. The solution is performed on unstructured triangular meshes using the discrete transfer method (DTM). The application of the DTM to triangular meshes is detailed and discussed. The developed code is validated with benchmark cases and applied to pure radiative problem (with and without evaluation of the source term). The approach shows very good performances for the wall heat transfer evaluation. The discrete transfer method also presents a particular ray effect. This effect is clearly brought up with the study of radiative equilibrium between eccentric cylinders: wiggles can appear in the temperature field. To reduce this ray effect, the use of a great amount of rays is required to get a smooth (i.e. wiggle free) solution, in the case of pure radiative problems. The solution of coupled conductive–radiative problems or convective–radiative heat transfer necessitates less rays to obtain a converged solution.

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.

Combined nongray radiative and conductive heat transfer in multiple glazing taking into account specular reflection and absorption

AbstractThe problem of combined nongray radiative and conductive heat transfer in multiple glazing subjected to solar irradiation is analyzed. A spectral solar model proposed by Bird and Riordan is used to calculate direct and diffuse solar irradiance. The radiation element method by ray emission model, REM2, is used to analyze the spectral dependence of radiative heat transfer. Specular reflection at boundary surfaces is taken into account. The spectral dependence of radiation properties of glass such as specular reflectivity, refraction angle, and absorption coefficient is taken into account. The steady‐state temperature and heat flux distributions in the glass layer are obtained and the insulating efficiency of multiple glazing is examined. The overall heat transfer coefficients predicted by the present method are compared with those based on the JIS method. The values obtained by the present method are slightly lower than those obtained by the JIS method. To investigate the spectral variation of radiative heat flux attenuated in the glass layer, the spectral heat flux at the room‐side surface and incident radiation are compared. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(8): 712–726, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10125

Quantum approach to electromagnetic energy transfer between two dielectric bodies

The problem of radiative heat transfer between two dielectric bodies is analyzed from the point of view of elementary quantum electrodynamics. The dielectric properties of the bodies are assumed to be linear, but dispersion and losses are allowed. Quantization of the electromagnetic field in inhomogeneous, dispersive, and lossy dielectrics is performed with the help of the Huttner-Barnett procedure. The electromagnetic energy flux is expressed through the expectation value of the Poynting vector. In order to compute the Poynting vector, two techniques suitable for nonequilibrium processes are employed: the Heisenberg equations of motion and the diagrammatic Keldysh procedure. They are shown to give identical final results. These quantum-mechanical calculations provide a solid basis for the further, mainly numerical, development of the theory of thermal scanning microscopy.

ANALYSIS OF RADIATIVE HEAT TRANSFER IN A PARTITIONED IDEALIZED FURNACE

In this article, the finite-volume method is applied, in conjunction with the blocked-off-region procedure, to solve the radiative heat transfer problem in a three-dimensional partitioned rectangular enclosure containing absorbing-emitting and isotropic scattering medium in the presence of heat generation. Three-dimensional test cases were chosen to benchmark this model against other methods, namely, the discrete transfer method, the discrete ordinates method, and the zone method. For all cases, excellent agreement is obtained using reasonable spatial and angular discretizations. Then the radiative heat transfer problem is solved for an idealized furnace with a finite-thickness opaque partition. The shadowing partition effect is discussed for different optical medium properties and partition surface emissivities.

A general integration method for radiative transfer in 3-D non-homogeneous cylindrical media with anisotropic scattering

A general set of integral equations is presented to solve 3-D radiative heat transfer problems in emitting, absorbing and linear anisotropic scattering finite hollow or solid cylinders with non-homogeneous media. By tracing a ray to compute the intensity,it is much easier to handle the spatial change properties including extinction coefficient. Both the continuous change property and step-change property are dealt with without difficulties. The solid angle integration in getting the incident radiation and heat fluxes is represented by the bounding surface integration. In order to avoid the singularity problem near the bounding surface, the surface integrations are transformed to new modified integral equations by mathematical methods. By doing so, we get more flexible general integral equations applicable to all cases (3-D solid cylinders, 3-D hollow cylinders, finite cylinders or infinite cylinders). This scheme has been verified by comparing the results with published data in the literature. It is believed that this method will be useful in combined radiation and convection heat transfer problems.

Use of the Approximation of Optically Thin Pulsations in the Problems of Radiative Heat Transfer in Turbulent Media

Use of the Approximation of Optically Thin Pulsations in the Problems of Radiative Heat Transfer in Turbulent Media

Thermal radiation modelling of DC smelting furnace freeboards

The problem of radiation heat transfer in a system of large numbers of surface elements was considered. A numerical-mathematical model detailing the radiative exchange between surfaces in a generalised multiple-surface shape model was constructed, developed, and tested to a satisfactory degree of complexity, at which point it was incorporated into a general-purpose computer program. Predictions by the model were compared to selected results from pilot-scale DC arc furnace tests run at Mintek, to evaluate the significance of radiation heat transfer to the overall energy loss from the freeboard regions of such furnaces. Finally, the model was used to examine a range of process and design variables, and scale-up issues. Several interesting aspects and phenomena come out of the exhaustive modelling work, to hopefully aid the designer of DC arc furnace freeboards in the future on both the pilot and full industrial scale.

AN UNSTEADY CONDUCTION AND TWO-PHASE RADIATION IN A 2-D RECTANGULAR ENCLOSURE WITH GAS AND PARTICLES

A problem of combined conductive and two-phase radiative heat transfer in a two-dimensional rectangular enclosure with two-phase (gas-particles) media is analyzed. A two-phase radiative transfer equation (RTE) considering radiation by both gas and particles is studied. Its nonlinear integrodifferential RTE is solved using the discrete ordinates method (DOM, or so-called S N method). To validate the program, we compare the solution in a two-dimensional rectangular black enclosure with others. The DOM is then applied to the unsteady thermal development in two-phase media contained in a rectangular enclosure. A parametric study is performed by changing the gas and particle absorption coefficients, particle number density, particle emissivity, wall emissivity, and aspect ratio of the enclosure. The results confirm a significant effect of the two-phase radiation on the thermal development in the geometry. However, it is found that the conduction is predominant near the hot wall.

NUMERICAL METHODS AND OPTIMAL CONTROL FOR GLASS COOLING PROCESSES

ABSTRACT In this paper, we discuss numerical and analytical approximations of radiative heat transfer equations used to model cooling processes of molten glass. Simplified diffusion type approximations are discussed and investigated numerically. These approximations are also used to develop acceleration methods for the iterative solution of the full radiative heat transfer problem. Moreover, applications of the above diffusion type approximations to optimal control problems for glass cooling processes are discussed.

F134 ナトリウム燃焼で発生したエアロゾル雰囲気中での 3 次元透過解析

A method to estimate optical properties of sodium oxide aerosol is developed. They are used to solve the radiative heat transfer problems in a system with aerosol generated by sodium fire. For the purpose, three-dimensional radiative transfer in an absorbing-scattering media is solved by the Monte Carlo method. The Mie's scattering theory is used to handle particle scattering during the analysis. By comparing the experimental results of the intensity and the angular distribution of the transmitted energy with the analyzed results obtained by assuming the complex index of refraction, it is shown that the value if the complex refractive index can be estimated.

USE OF GCG METHODS FOR THE EFFICIENT SOLUTION OF MATRIX PROBLEMS ARISING FROM THE FVM FORMULATION OF RADIATIVE TRANSFER

Preconditioned generalized conjugate gradient (GCG) iterative methods are applied to the solution of large, sparse, and unsymmetric linear algebraic equations resulting from the application of the finite-volume method to the problem of radiative heat transfer in an absorbing, emitting, and scattering gray medium, with the boundary surfaces reflecting radiation in both diffuse and specular regimes. The governing radiative transfer equation, which is a complicated integro-differential equation, has been discretized using the S N finite-volume method (FVM). Different variants of GCG methods have been tested on a problem of 2-D radiation in a cylinder, and efficiencies of the methods have been compared. Numerical results indicate that preconditioning suggested in the article dramatically improves the performance of the GCG methods. Results on test problems based on S 8 FVM agree well with exact results reported in the literature.

Numerical Study of Convective and Radiative Heat Transfer from a Window Glazing with a Venetian Blind

A two-dimensional numerical solution has been obtained of the effect of a venetian blind on the conjugate heat transfer at an indoor window glazing. A solution has been obtained to the coupled laminar free convection and radiation heat transfer problem, including conduction along the blind slats. The local convective Nusselt number distributions were found to compare well with published experimental data for an aluminum blind. Also, there was good qualitative agreement with temperature and flow field visualization photographs. The results show that, over a wide range of Rayleigh numbers, an aluminum venetian blind can have a strong effect on the heat transfer rate from the indoor window glazing. Depending upon the specific conditions, the average convective heat transfer rate can either increase or decrease. However, for all cases studied, the blind was found to substantially reduce the radiative heat transfer rate from the window, even when the slats were fully open.

A quasi diffusive reflective method for the calculation of radiative heat transfer in semitransparent media between parallel planes with angle dependent reflection behaviour

The problem of radiation heat transfer in a semitransparent infinite plane parallel layer with purely diffusive reflection, emission and transmission behaviour (referred to as optical boundary conditions), in which the temperature depends only on the coordinate perpendicular to the boundaries, can be solved exactly by using exponential integrals of different orders. On the other hand the attenuation for the reflected, emitted and transmitted heat currents in the case of specular reflecting, emitting and transmitting boundaries has to be described by more complicate functions or the problem has to be treated by different methods as the discrete ordinates method (DOM). Within this work, a new method to describe radiation heat transfer for this geometry especially in the case of strongly angle dependent optical boundary conditions, including total reflection as described by Fresnel's equations, is developed. This method uses discrete angle ranges with averaged optical properties of the boundaries as well as the exponential integral formalism and is therefore referred to as quasi-diffusive reflective method (QDR-method). Exact solutions and solutions by means of the QDR-method including heat transfer by conduction are compared. The results of the QDR-method are sufficiently accurate in the most practical cases and allow calculations with a temperature dependent absorption coefficient in a much easier way.

Modified Collapsed Dimension Method for Radiative Heat Transfer Problems

Introduction C OLLAPSED dimensionmethod (CDM) is one of the ray tracing methods used for the solution of radiative transfer problems. Development of this method is partly based on the works of Shih and Chen1 and Shih and Ren2 on the discretized intensity method. Some light on the method was thrown by Blank. Subsequent developmentof the method was made by Blank andMishra.4 Detailed description of this method is available in Ref. 5. In CDM, three-dimensionalradiative information is mapped into a two-dimensionalsolutionplane in terms of effective intensity (EI) andoptical thicknesscoefŽ cient (OTC). Thus, unlikeothermethods, analysis and computations in this method are performed in a twodimensional solution plane instead of three-dimensionalspace. CDMhas beenused for the solutionof radiativetransferproblems with highaccuracy.4;5 Thismethodhasbeenfoundtowork for awide rangeof optical thickness (very low to high optical thickness). Furthermore, CDM has also been found to work well for the conjugate mode heat transfer problems. In CDM, for determinationof heat  ux and temperature information, at each point of interest EIs have to be integrated over planar angle in the solutionplane.Theseangularintegrationsareperformed by dividing the planar angle into intervals of equal sizes. In each subinterval, EI is assumed isotropic. Hence, for higher accuracy, CDM requiresmore EIs and, thus, higher computational time. In the presentwork,with the objectiveofmakingCDMmore economical, the method is modiŽ ed. In the modiŽ ed CDM (MCDM), angular integrations of the EIs are performed differently. The discretizationand integrationsperformed in thismethod originatefrom the concept of the discrete ordinate method (DOM). Here, the planar angle is divided into a Ž nite number of subintervals according to the number of Gaussian quadraturepoints considered.Hence, in MCDM, angular subintervals are unequal and instead of considering average values of interval, the weighted mean corresponding to the Gauss points is considered. With this, the method becomes more realistic, and it derives computational efŽ ciency with a more realistic representationof the radiative transfer process. In the present work, improvements in MCDM over CDM are tested by solving radiative transfer problems in oneand twodimensional Cartesian enclosures with gray and homogeneous, absorbing, emitting, and anisotropically scattering medium. Both radiative and nonradiative equilibrium situations are considered. MCDM and CDM results are compared with results from the exact method and DOM.

Using Unsteadiness of the Processes in Diagnostics of Burning Objects

A technique for studying burning processes based on their unsteadiness is proposed. The temperature and spectral dependences of emitting and absorbing characteristics of MgO particles and their mixtures with gases at high temperatures are studied. The rates obtained allow one to solve problems of radiative heat transfer. The problem of existence of equilibrium between the gaseous and condensed magnesium oxide in the combustion zone is discussed.