Radiative-conductive Heat Transfer Research Articles

Homogenization of a Conductive-Radiative Heat Transfer Problem

This paper focuses on the contribution of the second order corrector in periodic homog- enization applied to a conductive-radiative heat transfer problem. Especially, for a heat conduction problem in a periodically perforated domain with a non-local boundary condition modelling the radia- tive heat transfer, if this model contains an oscillating thermal source and a thermal exchange with the perforations, the second order corrector helps us to model the gradients which appear between the source area and the perforations. Resume. Ce papier est consacremontrer l'influence du correcteur de second ordre en homogeneisation periodique. Dans l'homogeneisation d'un probleme de conduction rayonnement dans un domaine periodiquement perfore par plusieurs trous, on peut voir une contribution non negligeable de ce cor- recteur lors de la presence d'une source thermique oscillante et d'unthermique dans les per- forations. Ce correcteur nous permet de modeliser les gradients qui apparaissent entre la zone de la source thermique et les perforations.

STRICTLY CONVERGENT ALGORITHM FOR AN ELLIPTIC EQUATION WITH NONLOCAL AND NONLINEAR BOUNDARY CONDITIONS

The paper describes a formally strictly convergent algorithm for solving a class of elliptic problems with nonlinear and nonlocal boundary conditions, which arise in modeling of the steady-state conductive-radiative heat transfer processes. The proposed algorithm has two levels of iterations, where inner iterations by means of the damped Newton method solve an appropriate elliptic problem with nonlinear, but local boundary conditions, and outer iterations deal with nonlocal terms in boundary conditions.

3D Inverse Boundary Design Problem of Conduction-radiation Heat Transfer

3D Inverse Boundary Design Problem of Conduction-radiation Heat Transfer

Modeling of the conjugate radiation and conduction problem in a 3D complex multi-burner furnace

Radiation is a major component of heat transfer in the modeling of furnaces. In this study, coupled radiative and conductive heat transfer problems are analyzed in complex geometries with inhomogeneous and anisotropic scattering participating media. A 3-D model is developed using combination of the discrete ordinates method and blocked-off-region procedure. The finite volume method has been adopted to solve the energy equation and the radiative source term in the energy equation is computed from intensities field. The accuracy of radiative conductive model is verified by comparison with benchmark solutions from the literature. As an example of engineering problems, radiative-conductive heat transfer in a furnace model with gray, inhomogeneous, and anisotropic scattering media is numerically studied. The distributions of temperature and heat flux in the furnace are analyzed for different thermoradiative parameters such as conduction-radiation parameter, scattering albedo, and anisotropic scattering coefficient. The numerical algorithm described is found to be fast and reliable for studying combined conductive and radiative heat transfer in 3-D irregular geometries.

Radiative-conductive heat transfer in a semitransparent composite with microspherical particles

A mathematical model for calculating the temperature field in a semitransparent composite material that in- cludes a polymethyl methacrylate matrix and quartz microspheres is suggested. In calculating the optical properties of the composite material, use was made of the optical properties of the matrix and of the inter- acting quartz microspheres at different filling factors which characterize the volume concentration of particles in the matrix. Allowance for the interaction between the composite components is made following the Max- well-Garnett approximation. Data on the complex refractive index of the composite were used for calculating the coefficients of absorption, scattering, and attenuation of packed particles by the Mie theory. The tempera- ture fields in a layer of the material are found from solving the boundary-value problem for the energy equa- tion and a system of radiation transfer equations with the use of these coefficients. perature. Introduction. Semitransparent composites are found in number of promising modern materials. Such materials assume a particular significance in articles in which an important role is played by energy transfer by heat conduction and radiation. Therefore investigations of the parameters of the composite components that influence thermal processes are very pressing. One of the means of increasing the thermoprotective properties is the use of materials involving fine particles that scatter thermal radiation. The composite material considered in the present work consists of hollow and solid quartz microspheres with a characteristic dimension of 3-50 μm introduced into a semitransparent binding matrix; the material is the means of heat shielding under the conditions of radiative-conductive transfer of thermal energy only at a high volume concentration of microspheres. To calculate the thermal fields in such a material, it is necessary to have data on the absorption and scattering coefficients with account for the interaction between particles. The problem of the influence of the proximity of particles on these coefficients remains as yet unsolved. Heat losses from the composite material surface include conductive and radiative components. Account for the indicated losses is possible at the known temperature distribution in a layer of this material. Solution of the problem is performed in the approximation of a continuous medium with effective thermophysical and optical properties. Dur- ing the passage of a radiative energy flux, the interaction between particles appears in the case of a high concentration of particles in the composite. It is known that if the distance between particles greatly exceeds that of their size and of the radiation wavelength, then the interaction between them is absent, and the absorption and scattering coefficients can be calculated by the classical Mie theory with the use of complex refractive indices of the particles and matrix (1). For the majority of optical problems, such an approach turns out to be justifiable. Since the composite material considered in the present work is an effective heat shield only at a high volume concentration of microspheres, the condition of the absence of interaction of particles that scatter and absorb radiation does not hold. Therefore the use of the classical Mie theory can lead in this case to considerable errors in calculating the radiative characteristics of a composite material and, as a consequence, of the temperature fields in it. To determine the attenuating and scattering

Numerical simulations of a coupled radiative–conductive heat transfer model using a modified Monte Carlo method

Radiative–conductive heat transfer in a medium bounded by two reflecting and radiating plane surfaces is considered. This process is described by a nonlinear system of two differential equations: an equation of the radiative heat transfer and an equation of the conductive heat exchange. The problem is characterized by anisotropic scattering of the medium and by specularly and diffusely reflecting boundaries. For the computation of solutions of this problem, two approaches based on iterative techniques are considered. First, a recursive algorithm based on some modification of the Monte Carlo method is proposed. Second, the diffusion approximation of the radiative transfer equation is utilized. Numerical comparisons of the approaches proposed are given in the case of isotropic scattering.

Semidiscrete and asymptotic approximations for the nonstationary radiative–conductive heat transfer problem in a periodic system of grey heat shields

We consider semidiscrete and asymptotic approximations to a solution to the nonstationary nonlinear initial-boundary-value problem governing the radiative–conductive heat transfer in a periodic system consisting of n grey parallel plate heat shields of width e = 1/n, separated by vacuum interlayers. We study properties of special semidiscrete and homogenized problems whose solutions approximate the solution to the problem under consideration. We establish the unique solvability of the problem and deduce a priori estimates for the solutions. We obtain error estimates of order $ O\left( {\sqrt {\varepsilon } } \right) $ and O(e) for semidiscrete approximations and error estimates of order $ O\left( {\sqrt {\varepsilon } } \right) $ and O(e 3/4) for asymptotic approximations. Bibliography: 9 titles.

The radiation of alumina melt in the middle IR spectral region at solidification in the course of free cooling

The results are presented of radiation intensity measurements in the middle IR spectral region from 3 to 11 μm at cooling and solidification in ambient air for both “thick” layers several millimeters thick and “thin” layers several tenths of a millimeter thick of a pure aluminum oxide melt. In the former case, the melt was held in a powder bed of the same material; in the latter case, a pool with the melt was created on a ceramic surface. The results on different wavelengths are presented as time dependences of the infrared spectrometer signals, proportional to the intensity of radiation emitted by the melt. In addition, the data on the time dependence of the emissivity for thick melt layers at a solidification plateau are presented. On the basis of the obtained results and the results of previous investigations and radiative-conductive heat transfer calculations at cooling and solidification, it is shown that the intensity of emitted radiation at crystallization is defined not only by optical properties of a melt and a crystal, but depends also on the thickness and the temperature field of the melt before the start of cooling. An almost horizontal section on the solidification plateau is caused by the presence of an isothermal two-phase zone; however, with a melt thickness of several millimeters, such a section of different length is observed only in the range of wavelengths from 5 to 11 μm.

Application of a Particle Swarm Algorithm for Parameter Retrieval in a Transient Conduction-Radiation Problem

This article addresses the application the particle swarm optimization (PSO) algorithm as an optimization tool for retrieval of parameters in a combined mode 1-D transient conduction-radiation heat transfer problem. In the chosen problem, the participating medium is absorbing, emitting, and scattering. The boundaries are taken to be diffuse gray. In both direct and inverse methods, the energy equation is solved using the lattice Boltzmann method (LBM) and the finite volume method (FVM) is used to compute the radiative information. In the inverse method, the objective function is minimized using the PSO algorithm. The objective function considered in the inverse formulation is an error function evaluated with the exact and inverse temperature fields for the simultaneous retrieval of the extinction coefficient and the scattering albedo. The inverse analysis constituted the effect of measurement errors on solution efficacies. In addition, the effect of important PSO parameters such as swarm size, inertia factor and constriction factor on the parameter retrieval is considered. For the chosen problem, it is found that the PSO with 20 discrete particles and 50 iterations is adequate for accurate parameter retrieval. The PSO has been found to provide a better accuracy than the genetic algorithm.

Application of the lattice Boltzmann method to transient conduction and radiation heat transfer in cylindrical media

In this paper, the lattice Boltzmann method (LBM) is applied to solve the energy equation of a transient conduction–radiation heat transfer problem in a two-dimensional cylindrical enclosure filled with an emitting, absorbing and scattering media. The control volume finite element method (CVFEM) is used to obtain the radiative information. To demonstrate the workability of the LBM in conjunction with the CVFEM to conduction–radiation problems in cylindrical media, the energy equation of the same problem is also solved using the finite difference method (FDM). The effects of different parameters, such as the grid size, the scattering albedo, the extinction coefficient and the conduction–radiation parameter on temperature distribution within the medium are studied. Results of the present work are compared with those available in the literature. LBM-CVFEM results are also compared with those given by the FDM-CVFEM. In all cases, good agreement has been obtained.

Influence of the air gap between protective clothing and skin on clothing performance during flash fire exposure

A finite volume model was developed to simulate transient heat transfer in protective clothing during flash fire exposure. The model accounts for the combined conduction-radiation heat transfer in the air gap between the fabric and skin. The variation in the fabric and air gap properties with temperature and the thermochemical reactions in the fabric are also considered. This study investigates the influence of the air gap in protective clothing on the energy transfer through the clothing and hence on its performance. Different parameters that affect the conduction-radiation heat transfer through the air gap such as the air gap absorption coefficient and the air gap width were studied. Finally, the paper demonstrates that an innovative and potentially significant way to improve protective clothing performance is to reduce the emissivity on the backside of the fabric.

Analysis of two-dimensional transient conduction–radiation problems in an anisotropically scattering participating enclosure using the lattice Boltzmann method and the control volume finite element method

This study deals with the performance evaluation of the lattice Boltzmann method (LBM) and the control volume finite element method (CVFEM) in terms of their abilities to provide accurate results in solving combined transient conduction and radiation mode problems in a two-dimensional rectangular enclosure containing an absorbing, emitting and anisotropically scattering medium. Coupling problems for mixed kind thermal boundary are worked out for reflective interfaces. Effects of various parameters are studied on the distributions of temperature, radiative and conductive heat fluxes. The results of the LBM in conjunction with the CVFEM have been found to compare very well with available results in the literature. So, the numerical approach is extended to deal with a practical combination of mixed boundary conditions in a transient multi-dimensional combined conductive radiative heat transfer problems in an emitting, absorbing, anisotropically scattering enclosure.

BEM for coupling radiation-conduction heat transfer

A boundary element method is presented for solving radiation-conduction coupling heat transfer problems. Two heat transfer processes are coupled by using radiation sources. Firstly, equations of radiative heat transfer, radiative heat source and heat conduction are discretized using BEM, respectively. Secondly, the radiative heat flux in radiative heat source equation is eliminated using radiative heat transfer equation. Then, a set of nonlinear equations is obtained according to the Stefan-Boltzmann law. All domain integrals appearing in integral equations are converted into equivalent boundary integrals using the radial integration method (RIM), which results in a pure BEM algorithm only needing boundary discretization even for participating media. Finally, The Newton-Raphson iteration method is adopted to solve the non-linear system of equations. Numerical examples are given to illustrate the accuracy and effectiveness of the developed technique.

Parametric study of simultaneous transient conduction and radiation in a two-dimensional participating medium

The lattice Boltzmann method (LBM) has been used to solve the energy equation of a transient conduction–radiation heat transfer problem in a two dimensional Cartesian enclosure filled with an emitting, absorbing and scattering media. The control volume finite element method (CVFEM) is used to obtain the radiative information. Based on this new nonlinear hybrid algorithm, the effects of various influencing parameters on the transient thermal response such as the scattering albedo, the conduction–radiation parameter, and the wall emissivity are studied on the distributions of temperature, radiative heat fluxes. Numerical results are presented as compared with other published works and they are found to be in satisfactory agreement. The advantages of the proposed numerical approach include, among others, simple implementation on a computer, accurate CPU time and capability of stable simulation. Therfore, the method can capture fundamental behaviours in thermal flows of engineering interest, in addition it will have computaional advantages when the geometry is more complex.

A new hybrid algorithm for solving transient combined conduction radiation heat transfer problems

A new algorithm based on the lattice Boltzmann method (LBM) and the Control Volume Finite Element Method (CVFEM) is proposed as an hybrid solver for two dimensional transient conduction and radiation heat transfer problems in an optically emitting, absorbing and scattering medium. The LBM was used to solve the energy equation and the CVFEM was used to compute the radiative information. The advantages of the proposed methodology is to avoid problems that confronted when previous techniques are used to predict radiative heat transfer, essentially, in complex geometries and when there is scattering and/or non-black boundaries surfaces. This method combination, which is applied for the first time to solve this unsteady combined mode of heat transfer, has been found to accurately predict the effects of various thermo-physical parameters such as the scattering albedo, the conduction-radiation parameter and the extinction coefficient on temperature distribution. The results of the LBM-CVFEM combination were found to be in excellent agreement with the LBM-CDM (Collapsed Dimension Method)this proposed numerical approach include, among others, simple implementation on a computer, accurate CPU time, and capability of stable simulation.

Analysis of Non-Fourier Conduction-Radiation Heat Transfer in a Cylindrical Enclosure

This article deals with the analysis of non-Fourier conduction and radiation heat transfer in a participating medium contained between 1-D concentric cylinders. The conducting-radiating medium is radiatively absorbing, emitting, and scattering. The non-Fourier effect is analyzed by suddenly perturbing the temperatures of the concentric cylinders. With radiative information computed using the finite volume method, the finite difference method is used to solve the hyperbolic energy equation. Effects of various parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the emissivity and the radius ratio are studied on the temporal evolution of temperature field in the medium. These parameters have been found to significantly influence the temporal temperature field, and non-Fourier effects are captured well. For non-Fourier conduction and Fourier conduction–radiation cases, results have been benchmarked against those available in the literature. A good comparison has been observed. In case of non-Fourier conduction-radiation, for some sample cases, the steady-state temperature distributions have been compared against those available in the literature. Results have been found to agree well.

Numerical Simulation of Transient Heat Transfer in a Protective Clothing System during a Flash Fire Exposure

A finite volume model was developed to simulate the transient heat transfer in a protective clothing system. The model domain consists of a fire-resistant fabric, the human skin, and the air gap between the fabric and the skin. The model uses a more sophisticated treatment of the air gap compared to previous models: it accounts for transient combined conduction-radiation heat transfer within the air gap and includes the variation in the air gap properties with temperature. Predictions were obtained for the temperature and heat flux distributions in the fabric, skin, and air gap as a function of time, as well as the time to receive skin burn injuries. The numerical model was used to explore the physics of heat transfer in protective clothing, which could potentially be used to improve the performance of this clothing. This study illustrates the dependence of the temporal behavior of the heat fluxes on the specific model assumptions, as well as the associated sensitivity of skin burn predictions to these assumptions.

Spectral Collocation Method for Transient Conduction-Radiation Heat Transfer

A spectral collocation method is developed to solve transient coupled conduction and radiation heat transfer problems. For both the radiative transfer equation and the energy equation, the spatial domain is discretized by the spectral collocation method. The angular domain is discretized by the discrete-ordinates method for radiative transfer equation. The formulations and implementation of the spectral collocation with discrete-ordinates method reveal its high efficiency. Because of the exponential convergence of spectral methods in space, a very high accuracy can be obtained, even though a small number of nodes are used for the present problems. Numerical results in onedimensional planar and two-dimensional rectangular geometries by the spectral collocation with discrete-ordinates methodarecomparedwithavailableresultsintheliterature.Thesecomparisonsindicatethatthespectralcollocation with discrete-ordinates method for transient conduction–radiation heat transfer is accurate and efficient. Effects of variousparameters,suchasthescatteringalbedo,theconduction–radiationparameter,andtheopticalthicknessare studied for absorbing, emitting, and isotropically scattering media.

The effect of thermal radiation on the propagation of temperature waves in a semitransparent medium

The propagation of temperature waves arising as a result of periodic external thermal stimulation is investigated in a plane layer of semitransparent absorbing and radiating medium without scattering. The classification of temperature waves on the basis of two dimensionless parameters is suggested. It is rigorously demonstrated that not more than two temperature waves may simultaneously exist in a gray semi-infinite medium. The relative contribution of radiation to complex heat transfer is estimated. The system of equations of radiative-conductive heat transfer is reduced to a single integral equation on the boundary. The effect of reflection on the boundary is discussed.

Nonstationary radiative—conductive heat transfer problem in a periodic system of grey heat shields

We consider a nonstationary nonlinear initial-boundary value problem governing radiative-conductive heat transfer in a periodic system of grey heat shields. The existence and uniqueness of a weak solution and a regular weak solution are established. Estimates for the solutions in terms of the data of the problem are obtained. Bibliography: 36 titles.