Transient coupled heat transfer in multilayer composite with one specular boundary coated

By the ray tracing?node method, the transient coupled radiative and conductive heat transfer in absorbing, scattering multilayer composite is investigated with one surface of the composite being opaque and specular, and the others being semitransparent and specular. The effect of Fresnel’s reflective law and Snell’s refractive law on coupled heat transfer are analyzed. By using ray tracing method in combination with Hottel and Sarofim’s zonal method and spectral band model, the radiative intensity transfer model have been put forward. The difficulty for integration to solve radiative transfer coefficients (RTCs) is overcame by arranging critical angles according to their magnitudes. The RTCs are used to calculated radiative heat source term, and the transient energy equation is discretized by control volume method. The study shows that, for intensive scattering medium, if the refractive indexes are arranged decreasingly from the inner part of the composite to both side directions respectively, then, the total reflection phenomenon in the composite is advantageous for the scattered energy to be absorbed by the layer with the biggest refractive index, so at transient beginning a maximum temperature peak may appear in the layer with the biggest refractive index.     

Improved Finite Volume Method for Three-Dimensional Radiative Heat Transfer in Complex Enclosures Containing Homogenous and Inhomogeneous Participating Media

The paper presents a modified finite volume method for the solution of the radiative transport equation, which implements the FTn angular discretization along with the bounded high-resolution curved line advection method to alleviate ray effect and false scattering, respectively, and consequently improve the accuracy of the final results. Using the blocked-off-region procedure, the present formulation is capable of treating blockage effects caused by inner/outer obstructing bodies. The developed methodology based on the combination of the above methods is evaluated against five three-dimensional test cases considering either homogenous or inhomogeneous participating media. For all cases, the predictions reveal the mitigation of false scattering and ray effects consequently the improvement of accuracy, employing this model for solving radiation heat transfer in industrial applications. In industrial application, the radiative heat transfer problem is solved for a unity boiler furnace where an inhomogeneous medium is assumed. The effects of the scattering albedo, walls emissivity and walls temperature are investigated.     

Chebyshev collocation spectral method for one-dimensional radiative heat transfer in graded index media

Chebyshev spectral collocation method based on discrete ordinates equation is developed to solve radiative transfer problems in a one-dimensional absorbing, emitting and scattering semitransparent slab with spatially variable refractive index. For radiative transfer equation, the angular domain is discretized by discrete ordinates method, and the spatial domain is discretized by Chebyshev collocation spectral method. Due to the exponential convergence of spectral methods, a very high accuracy can be obtained even using few nodes for present problems. Numerical results by the Chebyshev collocation spectral-discrete ordinates method (SP-DOM) are compared with those available data in references. Effects of refractive index gradient on radiative intensity are studied for space dependent scattering media. The results show that SP-DOM has a good accuracy and efficiency for solving radiative heat transfer problems in even spatially varying absorbing, emitting, scattering, and graded index media.     

Meshless local Petrov–Galerkin approach for coupled radiative and conductive heat transfer

A meshless local Petrov–Galerkin approach is employed for solving the coupled radiative and conductive heat transfer in absorbing, emitting and scattering media. The meshless local Petrov–Galerkin approach with upwind scheme for radiative transfer is based on the discrete ordinate equations. The moving least square approximation is used to construct the shape function. Three particular test cases for coupled radiative and conductive heat transfer are examined to verify this new approximate method. The dimensionless temperatures and the dimensionless heat fluxes are obtained. The results are compared with the other benchmark approximate solutions. By comparison, the results show that the meshless local Petrov–Galerkin approach has a good accuracy in solving the coupled radiative and conductive heat transfer in absorbing, emitting and scattering media.     

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.     

Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction-radiation problem

A lattice Boltzmann method (LBM) is used to solve the energy equation in a test problem involving thermal radiation and to thus investigate the suitability of scalar diffusion LBM for a new class of problems. The problem chosen is transient conductive and radiative heat transfer in a 2-D rectangular enclosure filled with an optically absorbing, emitting and scattering medium. The energy equation of the problem is solved alternatively with a previously used finite volume method (FVM) and with the LBM, while the radiative transfer equation is solved in both cases using the collapsed dimension method. In a parametric study on the effects of the conduction-radiation parameter, extinction coefficient, scattering albedo, and enclosure aspect ratio, FVM and LBM are compared in each case. It is found that, for given level of accuracy, LBM converges in fewer iterations to the steady-state solution, independent of the influence of radiation. On the other hand, the computational cost per iteration is higher for LBM than for the FVM for a simple grid. For coupled radiation-diffusion, the LBM is faster than the FVM because the radiative transfer computation is more time-consuming than that of diffusion.     

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     

Chebyshev collocation spectral domain decomposition method for coupled conductive and radiative heat transfer in a 3D L-shaped enclosure

ABSTRACT

This paper presents a Chebyshev collocation spectral domain decomposition method (CSDDM) to study the coupled conductive and radiative heat transfer in a 3D L-shaped enclosure. The partitioned 3D L-shaped enclosure is subdivided into rectangular subdomains based on the concept of domain decomposition. The radiative transfer equation is angularly discretized by the discrete ordinate method with the SRAP_N quadrature scheme and then solved by the CSDDM using the same grid system as in solving the conduction. The effects of the conduction–radiation parameter, the optical thickness, the scattering albedo, and the aspect ratio on thermal behavior of the system are investigated. The results indicate that the 3D CSDDM has a good accuracy and can be considered as a good alternative approach for the solution of the coupled conduction and radiation problems in 3D partitioned domains.     

Local RBF meshless scheme for coupled radiative and conductive heat transfer

ABSTRACT

A local radial basis function meshless (LRBFM) method is developed to solve coupled radiative and conductive heat transfer problems in multidimensional participating media, in which compact support radial basis functions (RBFs) augmented on a polynomial basis are employed to construct the trial function, and the radiative transfer equation (RTE) and energy conservation equation are discretized directly at nodes by the collocation method. LRBFM belongs to a class of truly meshless methods which require no mesh or grid, and can be readily implemented in a set of uniform or irregular node distributions with no node connectivity. Performances of the LRBFM is compared to numerical results reported in the literature via a variety of coupled radiative and conductive heat transfer problems in 1D and 2D geometries. It is demonstrated that the local radial basis function meshless method provides high accuracy and great efficiency to solve coupled radiative and conductive heat transfer problems in multidimensional participating media with uniform and irregular node distribution, especially for coupled heat transfer problems in irregular geometry with Cartesian coordinates. In addition, it is extremely simple to implement.     

Modeling the 3-D radiation of anisotropically scattering media by two different numerical methods

An original model and code for 3-D radiation of anisotropically scattering gray media is developed where radiative transfer equation (RTE) is solved by finite volume method (FVM) and scattering phase function (SPF) is defined by Mie Equations (ME). To the authors’ best knowledge this methodology was not developed before. Missing the benchmark, another new 3-D model and code, which solve the same problems, based on a combination of zone method (ZM) and Monte Carlo method (MC), as a solution of RTE, is developed. Here SPF is also calculated by Mie Equations. The conception ZM + MC is numerically expensive and is used and recommended only as a benchmark. The 3-D rectangular enclosure and the spherical geometry of particles are considered. The both models are applied: (i) to an isotropic and to four anisotropic scattering cases previously used in literature for 2-D cases and (ii) to solid particles of several various coals and of a fly ash. The agreement between the predictions obtained by these two different numerical methods for coals and ash is very good. The effects of scattering albedo and of wall reflectivity on the radiative heat flux are presented. It was found that the developed 3-D model, where FVM was coupled with ME, is reliable and accurate. The methodology is also suitable for extension towards: (i) mixture of non-gray gases with particles and (ii) incorporation in computational fluid dynamics.     

Two-dimensional transient conduction and radiation heat transfer with temperature dependent thermal conductivity

This paper deals with the effect of the temperature dependent thermal conductivity on transient conduction and radiation heat transfer in a 2-D rectangular enclosure containing an absorbing, emitting and scattering medium. The thermal conductivity of the medium is assumed to vary linearly with temperature. The radiative part of the energy equation was solved using the collapsed dimension method. To facilitate solution of the energy equation, which is a highly nonlinear one, time linearization was done first and then the equation was solved using the alternating direction implicit scheme. Results for the effects of the variable thermal conductivity were found for temperature and heat flux distributions.     

An Iterative Technique for Coupled Conduction–Radiation Heat Transfer in Semitransparent Media

An iterative technique is developed to solve coupled conduction–radiation heat transfer in semitransparent media. Apart from a high convergence rate, the present algorithm preserves the conservation nature of the governing equation far better than other common methods and it is readily combined with other methods in solving radiative transfer. Using the technique described in this study, parametric studies are carried out for coupled heat transfer in a semitransparent slab and the results illustrate the “peak” effects of wall emissivity and scattering albedo on conductive and radiative heat fluxes, which are rarely mentioned in the existing research.     

Meshless method for radiation heat transfer in graded index medium

Because ray goes along a curved path determined by the Fermat principle, curved ray tracing is very difficult and complex in graded index media. To avoid the difficult and complex computation of curved ray trajectories, a meshless local Petrov–Galerkin approach based on discrete-ordinate equations is developed to solve the radiative transfer problem in multi-dimensional absorbing–emitting–scattering semitransparent graded index media. A moving least square approximation is used to construct the shape function. Two particular test problems in radiative transfer are taken as examples to verify this meshless approach. The predicted temperature distributions and the dimensionless radiative heat fluxes are determined by the proposed method and compared with the other benchmark approximate solutions. The results show that the meshless local Petrov–Galerkin approach based on discrete-ordinate equations has a good accuracy in solving the radiative transfer problems in absorbing–emitting–scattering semitransparent graded index media.     

New aspects of the diffusion approximation for radiative transfer

The diffusion approximation is generalized to arbitrary locally isotropic participating media. It proves to be an approximate special solution of the full equation of radiative transfer accounting for absorption, scattering, and emission. This special solution must be completed with a solution of the radiative transfer equation without emission term in order to match the boundary conditions for the radiative field. Applied to combined heat and radiative transfer this scheme offers distinct computational advantages and broad applicability. Following these ideas a simple and robust method for one-dimensional radiation–conduction computations is constructed and verified.     

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.     

Meshless Method for Solving Transient Radiative and Conductive Heat Transfer in Two-Dimensional Complex Geometries

A diffuse approximation meshless method (DAM) is employed to solve the transient radiative and conductive heat transfer problem in a semitransparent medium enclosed in 2-D complex geometries. The computational spatial domain is discretized by a set of nodes scattered in the domain and boundary without information on the relationship between them. The meshless method for radiative transfer equation is based on the even-parity formulation of the discrete ordinates method without any form of upwinding. Results of dimensionless temperature distribution at different dimensionless times are obtained and validated with other benchmark approximate solutions in order to illustrate the performance of the proposed method.     

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.     

Radiative heat transfer in a participating medium with specular–diffuse surfaces

The results obtained by ray-tracing method can be regarded as benchmarks for its good accuracy. However, up to now, this method can be only used to solve radiative transfer within medium confined between two specular surfaces or two diffuse surfaces. This article proposes a hybrid ray-tracing method to solve the radiative transfer inside a plane-parallel absorbing–emitting–scattering medium with one specular surface and another diffuse surface (S–D surfaces). By the hybrid ray-tracing method, radiative transfer coefficients (RTCs) for S–D surfaces are deduced. Both surfaces of the medium under consideration are considered to be semitransparent or opaque. This paper examines the effects of scattering albedo, opaque surface emissivity and anisotropically scattering on steady-state heat flux and transient temperature fields. From the results it is found that the effects of anisotropic scattering is more for a bigger optical thickness medium; and keeping other optical parameters unchanged, anisotropic scattering affects transient temperature distributions so much in a small refractive index medium.     

Assessment of different spatial/angular agglomeration multigrid schemes for the acceleration of FVM radiative heat transfer computations

ABSTRACT

The development and comparison of different parallel spatial/angular agglomeration multigrid schemes to accelerate the finite volume method, for the prediction of radiative heat transfer, are reported in this study. The proposed multigrid methodologies are based on the solution of radiative transfer equation with the full approximation scheme coupled with the full multigrid method, considering different types of sequentially coarser spatial and angular resolutions as well as different V-cycle types. The encountered numerical tests, involving highly scattering media and reflecting boundaries, reveal the superiority of the nested scheme along with the V(2,0)-cycle-type strategy, while they highlight the significant contribution of the angular extension of the multigrid technique.     

Transient modeling of combined conduction and radiation in wood fibre insulation and comparison with experimental data

This is an innovative study of wood wool used for building insulation and the reported results could be important for improving the cooling and the heating efficiency of buildings. Wood fibre boards are non-grey, absorbing and scattering media. The radiative properties of the wood wool (albedo, optical thickness and phase function coefficients) were identified using an inverse method based on infrared experimental measurements of reflection and transmission. The radiative part was then found negligible with respect to the phonic part in steady state for the material tested. Transient one-dimensional coupled radiative and conductive heat transfer was solved in a wood wool material. The transient numerical results were validated by comparing them with fluxmeter measurements when temperatures were fixed at the boundaries. The temperatures and the heat capacity had strong influence on the transient numerical results. Finally, our computations showed that a purely conductive model gives the same fluxes at the boundary as the coupled radiative-conductive model.