Radiative Heat Transfer Problems Research Articles

Integration of Monte-Carlo ray tracing with a stochastic optimisation method: application to the design of solar receiver geometry.

A stochastic optimisation method adapted to illumination and radiative heat transfer problems involving Monte-Carlo ray-tracing is presented. A solar receiver shape optimisation case study illustrates the advantages of the method and its potential: efficient receivers are identified using a moderate computational cost.

Different methods for calculating a view factor in radiative applications: Strip to in-plane parallel semi-cylinder

Determining the shape factor is essential for solving radiative heat transfer problems. An important case that has various applications in the heat power plant systems is calculation of the configuration factor between the fins and the in-plane parallel semi-cylinder. In the present work, Monte Carlo method, Cross string method, and analytical solutions were implemented for this problem. Several simulations were performed by varying semi-cylinders radius and different lengths of the fin. Also, the influence of the number of emitting rays and the number of strips was studied. Considering a fin between two tubes, it is found that calculating the view factor between one tube and a fin is sufficient due to axis symmetry. The results show that at the beginning of fin, analytical solution provides the answer, far from reality. Also, the Cross string solution had differences with Monte Carlo solution, especially for large semi-cylinders radius, but these differences were lower in comparison with the differences between Monte Carlo method and analytical solution. Therefore, the analytical solution for this configuration is almost wrong and is not suggested after this research. Monte Carlo solution had a good approximation for shape factor at all locations across the fin, based on the next discussions in the article. Although for smooth answer without any fluctuations Monte Carlo method needs high emitting rays, this solution has a suitable answer for all parts of the fin as the best solution.

Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using Improved Quantum Particle Swarm Optimization

In the present study, the Quantum Particle Swarm Optimization (QPSO) algorithm is applied to solve the inverse problems of radiative heat transfer and phase change in laser heating semitransparent medium. To increase the efficiency and the accuracy of the original QPSO algorithm, an Improved Quantum Particle Swarm Optimization (IQPSO) algorithm is developed based on the original QPSO algorithm. To illustrate the performance of the proposed IQPSO algorithm, the Stefan number or/and conduction to radiation number of the one-dimensional semitransparent phase change medium are retrieved by measuring the transient boundary temperatures. The Finite Volume Method approximation is treated as the forward model and the sensitivity and measurement error are also analyzed. By the IQPSO algorithm presented, the thermophysical parameters can be estimated accurately, even with noisy data. In conclusion, the IQPSO algorithm is demonstrated to be more effective and robust compared with the Basic Particle Swarm Optimization and QPSO algorithms through function estimation and parameter estimation, it is thus has the potential to be implemented in various fields of inverse heat transfer problems.

Parallel algorithm and its convergence of spatial domain decomposition of discrete ordinates method for solving radiation heat transfer problem

To improve the computational efficiency and hold calculation accuracy at the same time, we study the parallel computation for radiation heat transfer. In this paper, the discrete ordinates method (DOM) and the spatial domain decomposition parallelization (DDP) are combined by message passing interface (MPI) language. The DDP–DOM computation of the radiation heat transfer within the rectangular furnace is described. When the result of DDP–DOM along one-dimensional direction is compared with that along multi-dimensional directions, it is found that the result of the latter one has higher precision without considering the medium scattering. Meanwhile, an in-depth study of the convergence of DDP–DOM for radiation heat transfer is made. Analyzing the cause of the weak convergence, we relate the total number of iteration steps when the convergence is obtained to the number of sub-domains. When we decompose the spatial domain along one-, two- and three-dimensional directions, different linear relationships between the number of total iteration steps and the number of sub-domains will be possessed separately, then several equations are developed to show the relationships. Using the equations, some phenomena in DDP–DOM can be made clear easily. At the same time, the correctness of the equations is verified.

On the Numerical Solution of the Nonlinear Radiation Heat Transfer Problem in a Three-Dimensional Flow

Abstract The steady laminar three-dimensional magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a stretching sheet is investigated. The sheet is linearly stretched in two lateral directions. Heat transfer analysis is performed by utilizing a nonlinear radiative heat flux in Rosseland approximation for thermal radiation. Two different wall conditions, namely (i) constant wall temperature and (ii) prescribed surface temperature are considered. The developed nonlinear boundary value problems (BVPs) are solved numerically through fifth-order Runge-Kutta method using a shooting technique. To ascertain the accuracy of results the solutions are also computed by using built in function bvp4c of MATLAB. The behaviours of interesting parameters are carefully analyzed through graphs for velocity and temperature distributions. The dimensionless expressions of wall shear stress and heat transfer rate at the sheet are evaluated and discussed. It is seen that a point of inflection of the temperature function exists for sufficiently large values of wall to ambient temperature ratio. The solutions are in excellent agreement with the previous studies in a limiting sense. To our knowledge, the novel idea of nonlinear thermal radiation in three-dimensional flow is just introduced here.

Accelerative iteration for coupled conductive–radiative heat transfer computation in semitransparent media

Due to the intensive coupling effect and non-linear characteristic, coupled conductive–radiative heat transfer problem in semitransparent media always consumes an enormous amount of computing time. In present work, an accelerative iteration model is developed to speed up the convergence process of this kind of coupled calculation. It promotes the iterative efficiency by revising the temperature and incident radiation of media during the iteration of energy equation and radiative transfer equation. It can remarkably reduce the computing time of coupled conductive–radiative heat transfer calculation in semitransparent media, even in the cases with complicate boundary conditions. The accuracy of present model is verified by comparing with literature and traditional source iteration method. The influences of conduction–radiation parameter, optical thickness, scattering albedo, emissivity of walls and boundary conditions are investigated as well. The results indicate that the accuracy of present model is reliable and its accelerative effect is more significant for the optically thick and scattering-dominated media with complicate boundary conditions.

Solvability of P1 approximation of a conductive–radiative heat transfer problem

Conductive-radiative heat transfer in a scattering and absorbing medium bounded by two reflecting and radiating plane surfaces is examined. P1 approximation (diffusion model) is used for the simplification of the original problem. The existence and uniqueness of solutions of the diffusion model are proved. The convergence of an iterative procedure for finding solutions is proved. Numerical examples are discussed.

Application of collocation spectral domain decomposition method to solve radiative heat transfer in 2D partitioned domains

A collocation spectral domain decomposition method (CSDDM) based on the influence matrix technique is developed to solve radiative transfer problems within a participating medium of 2D partitioned domains. In this numerical approach, the spatial domains of interest are decomposed into rectangular sub-domains. The radiative transfer equation (RTE) in each sub-domain is angularly discretized by the discrete ordinates method (DOM) with the SRAPN quadrature scheme and then is solved by the CSDDM directly. Three test geometries that include square enclosure and two enclosures with one baffle and one centered obstruction are used to validate the accuracy of the developed method and their numerical results are compared to the data obtained by other researchers. These comparisons indicate that the CSDDM has a good accuracy for all solutions. Therefore this method can be considered as a useful approach for the solution of radiative heat transfer problems in 2D partitioned domains.

Radiation Models and Radiation Transfer in Hypersonics

The paper presents radiation models developed to investigate radiation in entry in Earth, Mars and Jupiter atmospheres. The capacity of ASTEROID computing code to simulate elementary radiative processes, calculate spectral and groups optical properties, and also solve simple radiative heat transfer problems is presented for Earth entry. The large number of radiative processes involved in the radiative flux is put forward. The contributions of the different radiative processes encountered in Mars entry are studied using the HTGR spectroscopic database. The validity of this database with respect to diatomic molecules systems and CO2 infrared radiation is illustrated through experimental validations. The accuracy of statistical narrow-band model to predict radiative flux is illustrated for an afterbody. Finally recent improvements of the model developed for the calculation of radiative properties of high-temperature H2/He mixtures representative of Jupiter atmosphere is presented. The model takes into account the most important radiative processes.

Effective-medium model of wire metamaterials in the problems of radiative heat transfer

In the present work, we check the applicability of the effective medium model (EMM) to the problems of radiative heat transfer (RHT) through so-called wire metamaterials (WMMs)—composites comprising parallel arrays of metal nanowires. It is explained why this problem is so important for the development of prospective thermophotovoltaic (TPV) systems. Previous studies of the applicability of EMM for WMMs were targeted by the imaging applications of WMMs. The analogous study referring to the transfer of radiative heat is a separate problem that deserves extended investigations. We show that WMMs with practically realizable design parameters transmit the radiative heat as effectively homogeneous media. Existing EMM is an adequate tool for qualitative prediction of the magnitude of transferred radiative heat and of its effective frequency band.

Analysis of Conduction-Radiation Heat Transfer in a 2D Enclosure Using the Lattice Boltzmann Method

Application of the lattice Boltzmann method (LBM) recently extended by Pietro et al. [P. Asinari, S. C. Mishra, and R. Borchiellini, A Lattice Boltzmann Formulation to the Analysis of Radiative Heat Transfer Problems in a Participating Medium, Numer. Heat Transfer B, 57(2), 126–146, 2010] for calculation of volumetric radiative information is extended for the analysis of a combined mode transient conduction and radiation heat transfer in a 2D rectangular enclosure containing an absorbing, emitting and scattering medium. Unlike all previous studies, with volumetric radiative information computed using the proposed LBM, the energy equation is formulated and solved using the LBM. In the combined mode conduction–radiation problem, to assess the computational advantage of computing the radiative information too using the LBM, the same problem is also solved using the LBM–finite volume method (FVM) formulation. In this LBM–FVM formulation, the FVM is used to calculate the volumetric radiative information needed for the energy equation, and the energy equation is solved using the LBM. Comparisons are made for the effects of the extinction coefficient, the scattering albedo and the conduction–radiation parameter on the temperature distributions in the medium. Although the number of iterations for the converged solution in LBM–LBM is much more than that of the LBM–FVM, computationally, the LBM–LBM is faster than the LBM–FVM.

Radiation heat transfer model using Monte Carlo ray tracing method on hierarchical ortho-Cartesian meshes and non-uniform rational basis spline surfaces for description of boundaries

Abstract The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD). The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS) surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.

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.

A New Simplified Zonal Method for Furnace Thermal Radiation Calculation Based on Imaginary Planes

When solving the complex radiative heat transfer problems in reheating furnaces, there are a number of difficulties with the traditional zonal methods. To circumvent these difficulties, a new simplified method was proposed, which employed imaginary planes, referred to as the imaginary plane model. With the new model, crown wall reduction process was simplified. Therefore, every model zone could be treated as a closed square cavity. It could also solve the problem of radiative blocking in industrial furnaces more effectively. Besides, the new imaginary plane based model may lead to a problem that the denominator was zero. This problem was solved by transforming the expressions of reflex heat flux in the model. The model was capable of dealing with the systems that included black surfaces. The model was validated by considering the heat transfer in a reheating furnace where the temperature fields in the furnace chamber (including the steel, wall and gas) were obtained. A detailed comparison was made between the simulation and the black box experiment. The results show that the new model developed was valid and accurate.

Second-order two-scale computations for conductive—radiative heat transfer problem in periodic porous materials

In this paper, a kind of second-order two-scale (SOTS) computation is developed for conductive—radiative heat transfer problem in periodic porous materials. First of all, by the asymptotic expansion of the temperature field, the cell problem, homogenization problem, and second-order correctors are obtained successively. Then, the corresponding finite element algorithms are proposed. Finally, some numerical results are presented and compared with theoretical results. The numerical results of the proposed algorithm conform with those of the FE algorithm well, demonstrating the accuracy of the present method and its potential applications in thermal engineering of porous materials.

An insight into the science of unstructured meshes in computer numerical simulation

Computer numerical simulation is a beneficial tool for studying various domains of knowledge. Among the steps in the whole process of numerical simulation is the generation of unstructured meshes. Since the unstructured meshes are usually generated using automatic software, the fundamental knowledge of the unstructured meshes is often neglected. This paper highlighted some useful insights into the unstructured meshes in numerical simulation for several application domains, such as the radiative heat transfer problem, ocean modelling and biomedical engineering. It also reviewed some fundamental concepts and frameworks for element generation in producing unstructured meshes, particularly the Delaunay triangulation and advancing front techniques.

Study on solar photo‐thermal conversion efficiency of a solar parabolic dish system

The solar parabolic dish system is an effective means to concentrate and convert solar energy into usable forms. Systematical investigation on the photo‐thermal conversion efficiency is important to improve the cost effectiveness of the system. In this article, Monte‐Carlo ray‐tracing method is used to calculate the radiation flux distribution of the receiver, and then Fluent with User Defined Functions is used for radiation and convection heat transfer problems; lastly the energy efficiency of the system has been investigated by experimental method. During the period of the simulation and experiment, various direct normal irradiations were considered in this article. Model of the energy efficiency of the system has been established based on the first law of thermodynamics. The results show that outlet water temperature and energy input linearly increase with increasing direct normal irradiations, but energy output non‐linearly increases with increasing direct normal irradiation. The results also show that the maximum energy efficiency is 52.12% when the direct normal irradiation is 80 W/m2, whereas it has a minimum of 40.51% when the direct normal irradiation is 570 W/m2. © 2013 American Institute of Chemical Engineers Environ Prog, 33: 1438–1444, 2014

The effect of BRDF surface on radiative heat transfer within a one-dimensional graded index medium

The traditional diffuse or specular surface assumption, which is simple but provides limited information, is insufficient to fully characterize a real surface. The BRDF (Bidirectional Reflectance Distribution Function) surface, which is closer to the real surface, is introduced into the radiative heat transfer problem for the first time. A Minnaert model for the BRDF surface is applied and the genetic algorithm is used to obtain the parameters of the proposed model. The DRESOR (Distribution of Ratios of Energy Scattered by medium Or Reflected by surface) method and the RMC (Reverse Monte Carlo) method are extended to solve the radiative heat transfer within a 1-D absorbing, emitting and scattering graded index medium with BRDF surfaces. The temperature and radiative flux distributions under radiative equilibrium are analyzed under different kinds of graded indexes, optical thicknesses and scattering albedos. The results obtained by the DRESOR method and the RMC method coincide well with each other, which indicates the accuracy of the calculation. Compared with the corresponding diffuse surface, though the relative temperature difference of the BRDF surface is slightly within ±2%, the radiative flux increases significantly by 3.5–12%. And this influence is enhanced by the shortening of the optical thickness while varies little with the changes of graded index and scattering albedo.

Analysis of non-Fourier conduction and volumetric radiation in a concentric spherical shell using lattice Boltzmann method and finite volume method

Application of the lattice Boltzmann method (LBM) has been extended to formulate and solve the energy equation of a non-Fourier conduction and radiation heat transfer problem in a concentric spherical shell. The enclosed conducting-radiating medium is absorbing, emitting and scattering. The non-Fourier conduction effect is induced by thermally perturbing one of the boundaries and incorporating the finite propagation speed of the thermal wave front in Fourier’s law of heat conduction. The volumetric radiative information needed in the energy equation has been computed using the finite volume method (FVM). To establish the accuracy of the LBM approach, with volumetric radiative information obtained from the FVM, the energy equation is also solved using the FVM. Effects of extinction coefficient, scattering albedo, conduction–radiation parameter, emissivity, radius ratio and the magnitude of thermal perturbations are studied on transient temperature distributions. Effects of the aforesaid parameters on the steady-state conduction, radiation and total energy flow rates are also studied. Steady-state LBM and FVM results are compared. In all the cases, the LBM results compare exceedingly well with the FVM results, and LBM has a faster convergence than the FVM.

Natural element method analysis for coupled radiative and conductive heat transfer in semitransparent medium with irregular geometries

This paper analyzes the radiative heat transfer problem coupled with conduction in an absorbing, emitting and isotropically scattering medium with the irregular geometries using the natural element method (NEM). Two kinds of optical boundary conditions are considered: semitransparent boundary with diffuse reflection and transmission of radiation and opaque gray boundary. The boundary is kept at constant temperature or subjected to the convective heating (cooling) and irradiation of black surroundings. The NEM as a meshless method is a relative new numerical scheme in the field of computational mechanics. It has been employed to solve the radiative heat transfer recently. In this paper, we first validate the natural element solutions in dealing with the coupled heat transfer problem with the semitransparent surface considering mixed boundary conditions by comparison with those reported in the literature. Afterward, we study the steady state and transient heat transfer problems coupled with radiation and conduction in the semicircular enclosure with an inner circle. For the steady state coupled heat transfer, only one surface with convective heating and irradiation of black environment is considered semitransparent, while other surfaces are opaque and subjected to constant wall temperature. For transient coupled heat transfer, the conditions of convective heating and environment irradiation are set on two surfaces that are semitransparent and opaque, respectively. Effects of various parameters such as the conduction–radiation parameter, refractive index of the medium, extinction coefficient, scattering albedo, convective heat transfer coefficient and the temperature of the black surrounding are analyzed on the temperature distributions in the medium.