NUMERICAL CALCULATIONS FOR COMBINED CONDUCTION AND RADIATION TRANSIENT HEAT TRANSFER IN A SEMITRANSPARENT MEDIUM

A numerical computer code was developed for calculating the combined conduction and radiation transient heat transfer in cylindrical, semitransparent materials that have temperature-dependent thermal properties. The radiative component is combined with the equation of conduction heat transfer by adding it as a heat source. The finite element method (FEM) was used for calculating the radiative component and for solving the temperature field in the medium. Very good agreement was observed between results obtained by using our code and those that exist in the literature for several steady-state cases. The advantage of the code is due to the fact that it incorporates temperature-dependent properties; thus it leads to more realistic and accurate results. The code was applied to calculate the cooling path of a large cylindrical sapphire boule while using varying, transient, temperature-dependent, combined heat transfer coefficients.     

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。     

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

The 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     

Assessment of the axisymmetric radiative heat transfer in a cylindrical enclosure with the finite volume method

The radiative heat transfer in an axisymmetric enclosure containing an absorbing, emitting, and scattering gray medium is investigated by using the finite volume method (FVM). Especially, formulations with the cylindrical base vectors are introduced and its characteristics is discussed by comparing with other solution methods in the finite volume category. By considering the three-dimensional procedure, the angular redistribution term, which appears in such curvilinear coordinates as axisymmetric and spherically symmetric ones, can be treated efficiently without any artifice usually introduced in the conventional discrete ordinates method (DOM). After a mathematical formulation and corresponding discretization equation for the radiative transfer equation (RTE) are derived, final discretization equation is introduced by using the directional weight, which is the key parameter in the FVM since it represents the inflow or outflow of radiant energy across the control volume faces depending on its sign. The present approach is then validated by comparing the present results with those of previous works. All the results presented in this work show that the present method is accurate and valuable for the analysis of cylindrically axisymmetric radiative heat transfer problems.     

Prediction of radiative heat transfer between two concentric spherical enclosures with the finite volume method

The radiative heat transfer between two concentric spheres separated by an absorbing, emitting, and isotropically scattering gray medium is investigated by using the finite volume method (FVM). Especially, a mapping that simplifies the solution of spherically symmetric radiative heat transfer problems is introduced, thereby, the intensity depending on spatial one-dimension and angular one-dimension is transformed into spatial two-dimensional one. By adopting this mapping process, angular redistribution, which appears in such curvilinear coordinates as cylindrical or spherical ones, is treated efficiently without any artifice usually introduced in the conventional discrete ordinates method (DOM). After a mathematical formulation and corresponding discretization equation for the radiative transfer equation (RTE) are derived, final discretization equation is introduced by using the directional weight, which is the key parameter in the FVM since it represents the inflow or outflow of radiant energy across the control volume faces depending on its sign. The present approach is then validated by comparing the present results with those of previous works by changing such various parameters as temperature ratio between inner and outer spherical enclosure, wall emissivity, and optical thickness of the participating medium. All the results presented in this work show that the present method is accurate and valuable for the analysis of spherically symmetric radiative heat transfer problems between two concentric spheres.     

炉内辐射换热过程的有限体积法

简要分析了含吸收散射性介质的三维空腔内辐射传递方程的有限体积法求解过程,应用该方法对四角切圆炉膛内的辐射换热过程进行模拟计算,得出了炉膛内温度分布,并将计算结果与实测值进行了比较。通过数值计算表明：有限体积法计算速度快,对不规则边界适应性强,具有很高的工程可用性。     

Study of two-dimensional and dynamic heat and mass transfer in a metal–hydrogen reactor

To analyse heat and mass transfer in a metal–hydrogen reactor, the hypothesis that disregards the radiative heat transfer in the reactor, is typically used. In this paper, we take into account the radiative heat transfer and we test the validity of this hypothesis in the case of the LaNi₅ and in the case of the magnesium. A theoretical model is conducted for the two-dimensional system where conduction, convection radiation and chemical reaction take place simultaneously. This model is solved by the finite volume method. The numerical simulation is used to present the time–space evolutions of the temperature and the hydride density in the reactor and to determinate the sensitivity to some parameters (absorption coefficient, scattering coefficient, reactor wall emissivity).     

Inverse estimation of boundary conditions on radiant enclosures by temperature measurement on a solid object

In this paper, we present an inverse analysis to estimate the thermal boundary conditions over a two-dimensional radiant enclosure from the knowledge of the measured temperatures for some points on a solid object within the enclosure. The conduction heat transfer in the solid object and the radiative heat transfer between the surface elements of the enclosure are formulated by the finite volume method and the net radiative method, respectively. The resultant set of nonlinear equations is solved by the Newton's method. The inverse problem for estimation of boundary conditions over the radiant enclosure is solved by the conjugate gradient method.     

Thermoelastic study of a functionally graded annular fin with variable thermal parameters using semiexact solution

Abstract

In this paper, the thermoelastic behavior of a functionally graded material (FGM) annular fin is investigated. The material properties of the annular fin are assumed to vary radially. The heat transfer coefficient and internal heat generation are considered to be functions of temperature. A closed form solution of nonlinear heat transfer equation for the FGM fin is obtained using the homotopy perturbation method (HPM) which leads to nonuniform temperature distributions within the fin. The temperature field is then coupled with the classical theory of elasticity and the associated thermal stresses are derived analytically. For the correctness of the present closed form solution for the stress field, the results are compared with the ANSYS-based finite element method (FEM) solution. The present HPM-based closed form solution of the stress field exhibits a good agreement with the FEM results. The effect of various thermal parameters such as the thermogeometric parameter, conduction-radiation parameter, internal heat generation parameter, coefficient of variation of thermal conductivity, and the coefficient of thermal expansion on the thermal stresses are discussed. The results are presented in both nondimensional and dimensional form. The dimensional stress analysis discloses the suitability of FGM as the fin material in practical applications.     

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.     

Coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes

The coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes is investigated numerically. The medium flows in a laminar and fully developed state with a Poiseuille velocity distribution, but the thermal status is developing. By the discrete ordinate method, the nonlinear integrodifferential radiative transfer equation in a cylindrical coordinate form is solved to give the radiative source term in the energy equation of coupled heat transfer. The energy equation is solved by the control volume method. The local Nusselt number and wall heat flux of convection as well as the total wall heat flux are employed to evaluate the influence of radiation heat transfer on convection. The analysis shows that the radiation heat transfer weakens the convection effect, promotes the temperature development, and significantly shortens the tube length with obvious heated/cooled effect. There is an obvious difference between the coupled heat transfer in a heated tube and that in a cooled tube, even though the medium properties are kept constant. The wall emissivity, the medium thermal conductivity and scattering albedo have significant influences on the coupled heat transfer, but the effect of medium scattering phase function is small. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 64–72, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10137     

Numerical investigation of heat and mass transfer during the desorption process of an Mg2Ni–H2 reactor

In this paper, a numerical study of coupled heat and mass transfer during the desorption process of metal–hydrogen reactor (Mg₂Ni–H₂), is presented. Analytical expressions describing, the reaction kinetic and the equilibrium pressure of the Mg₂Ni-H₂ system have been determined and integrated into a theoretical model that describes the dynamic behavior of the reactor. This model, which takes into account radiative heat transfer, is solved by the control volume finite element method (CVFEM). The numerical simulation is used to present the time–space evolutions of the temperature and the hydride density within the reactor and to evaluate the effect of radiative heat transfer and the governing operating parameters (outlet pressure, temperature of heating fluid, heat exchange coefficient) on the dynamic behavior of the reactor. In addition, a new geometric configuration of the reactor is proposed and simulated.     

The Combined Radiative Integral Equations and Finite-Element Method for Radiation in Anisotropic Scattering Media

A combined procedure of the radiative integral equation and finite-element method (IEFEM) is proposed for handling radiative heat transfer in linearly anisotropic scattering media. The IEFEM can eliminate the angular discretization and easily handle irregular geometries. The present work provides a solution of radiative transfer in rectangular and irregular quadrilateral enclosures containing participating media. The influences of emissivities, albedos, and anisotropy on the boundary fluxes or incident intensity have been analyzed. Compared with the results in published references, the present IEFEM has no limitation to geometry and can predict the radiative heat transfer in linearly anisotropic scattering media accurately.     

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     

Numerical simulation of coupled radiation‐convection heat transfer of high‐temperature developing flow in tube

By combining the discrete ordinate method with the control volume method, the coupled radiation‐convection heat transfer of high‐temperature developing laminar flow in a tube is investigated numerically. The radiative transfer is solved by the discrete ordinate method and its contribution to thermal balance is dealt with as a source term in the energy equation, which is solved, as well as the momentum equation, by the control volume method. The effects of medium optical thickness and tube wall temperature on the temperature distribution in medium as well as the heat flux and local Nusselt number on wall are analyzed. The results show that the radiation heat transfer of high‐temperature medium influences the temperature distribution and convection heat transfer greatly, and plays an important role in the heat transfer of developing laminar flow in a tube. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 53–63, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10135     

Combined heat transfer of radiation and natural convection in a square cavity containing participating gases

This article deals with analyzing the effect of radiative heat transfer on natural convection heat transfer in a square cavity under normal room conditions. The governing equations of natural convection and radiative transfer are solved simultaneously to obtain the temperature, velocity and heat flux distributions inside the participating medium. The finite volume method has been adopted to solve the governing equations and the discrete ordinates method (DOM) is used to model the radiative transfer in absorbing-emitting media. The radiative–convective model is validated by comparison with test cases solutions from the literature. Then, the effects of Rayleigh number from 10² to 10⁶ and optical thickness in a broad range from 0 to 100 on temperature and velocity distributions and Nusselt numbers are investigated. The results show that even under normal room conditions with a low temperature difference, the radiation plays a significant role on temperature distribution and flow pattern in the cavity. Also, several interesting effects of radiation are observed such as a sweep behavior on the isotherms, streamlines and velocity distributions of the cavity along the optical thickness and a reverse behavior on maximum stream function and convective Nusselt number at different Rayleigh numbers.     

SLA (Second-law analysis) of transient radiative transfer processes

This paper concerns a SLA (second-law analysis) of transient radiative heat transfer in an absorbing, emitting and scattering medium. Based on Planck’s definition of radiative entropy, transient radiative entropy transfer equation and local radiative entropy generation in semitransparent media with uniform refractive index are derived. Transient radiative exergy transfer equation and local radiative exergy destruction are also derived based on Candau’s definition of radiative exergy. The analytical results are consistent with the Gouy–Stodola theorem of classical thermodynamics. As an application concerning transient radiative transfer, exergy destruction of diffuse pulse radiation in a semitransparent slab is studied. The transient radiative transfer equation is solved using the discontinuous finite element based discrete ordinates equation. Transient radiative exergy destruction is calculated by a post-processing procedure.     

Thermal analysis of a 2-D heat recovery system using porous media including lattice Boltzmann simulation of fluid flow

The present work deals with the fluid flow simulation and thermal analysis of a two-dimensional heat recovery system using porous media. A basic high-temperature flow system is considered in which a high-temperature non-radiating gas flows through a random porous matrix. The porous medium, in addition to its convective heat exchange with the gas, may absorb, emit and scatter thermal radiation. It is desirable to have large amount of radiative heat flux from the porous segment in the upstream direction (towards the thermal system). The lattice Boltzmann method (LBM) is used to simulate fluid flow in the porous medium. The gas and solid phases are considered in non-local thermal equilibrium, and separate energy equations are applied to these phases. Convection, conduction and radiation heat transfers take place simultaneously in solid phase, but in the gas flow, heat transfer occurs by conduction and convection. In order to analyze the thermal characteristics of the heat recovery system, volume-averaged velocities through the porous matrix obtained by LBM are used in the gas energy equation and then the coupled energy equations for gas and porous medium are numerically solved using finite difference method. For computing of radiative heat flux in the porous medium, discrete ordinates method is used to solve the radiative transfer equation. Finally the effect of various parameters on the performance of porous heat recovery system is studied.     

Development and comparison of the DTM,the DOM and the FVM formulations for the short-pulse laser transport through a participating medium

The present article deals with the analysis of transient radiative transfer caused by a short-pulse laser irradiation on a participating medium. A general formulation of the governing transient radiative transfer equation applicable to a 3-D Cartesian enclosure has been presented. To solve the transient radiative transfer equation, formulations have been presented for the three commonly used methods in the study of radiative heat transfer, viz., the discrete transfer method, the discrete ordinate method and the finite volume method. To show the uniformity in the formulations in the three methods, the intensity directions and the angular quadrature schemes for computing the incident radiation and heat flux have been taken the same. To validate the formulations and to compare the performance of the three methods, effect of a square short-pulse laser having pulse-width of the order of a femtosecond on transmittance and reflectance signals in case of an absorbing and scattering planar layer has been studied. Effects of the medium properties such as the extinction coefficient, the scattering albedo and the anisotropy factor and the laser properties such as the pulse-width and the angle of incidence on the transmittance and the reflectance signals have been compared. In all the cases, results of the three methods were found to compare very well with each other. Computationally, the discrete ordinate method was found to be the most efficient.     

Enhancement of heat transfer: Combined convection and radiation in the entrance region of circular ducts with porous inserts

Using porous ceramic inserts in high temperature equipment has been proven to be an effective means to enhance combined convective–radiative heat transfer. The porous ceramic insert was referred to as a convection-to-radiation converter (CRC) by previous investigators. We consider a novel application of CRC cores in a partial by pass flow system for heat transfer enhancement. Both hydrodynamically and thermally developing laminar flow is considered in the entrance region of a circular pipe with a porous insert located at the center. The momentum and Darcy–Brinkman equations are applied to the flow field in the annular gas layer and central porous layer respectively. The energy equation is coupled with the radiative transfer equation by the radiation source term. The radiative transfer is simulated by the newly developed integral equations [X.L. Chen, W. Sutton, Radiative transfer in finite cylindrical media using transformed integral equations, J. Quant. Spectrosc. Radiat. Transfer 77 (3) (2003) 233–271; W. Sutton, X.L. Chen, A general integration method for radiative transfer in 3-D non-homogeneous cylindrical media with anisotropic scattering, J. Quant. Spectrosc. Radiat. Transfer 84 (2004) 65–103] to avoid singularity problem and give high accuracy. The working fluid and porous medium are both considered as participating media. Finally, this highly non-linear system of equations is solved by a mixed iteration method. The results are compared between the cases with and without the porous insert. The porous insert enhances both convective and radiative transfer by about 35% and 105% respectively at the most. The effects of important parameters on this enhancement are discussed in detail.