Radiative Heat Transfer Problems Research Articles

Generalized source term multiflux method coupled with Runge-Kutta ray tracing technique for arbitrary radiative intensity of graded-index media.

The generalized source term multiflux method (GSMFM) combined with Runge-Kutta ray tracing technique is developed to calculate arbitrary directional radiative intensity of graded-index media. In this method, the finite volume method is employed to solve source terms along the curved ray path determined by the Fermat principle. Runge-Kutta ray tracing technique is adopted to obtain the ray trajectory numerical solution in graded-index media. And the GSMFM is used to solve radiative intensity to be expected. One-dimensional and two-dimensional radiative heat transfer problems are investigated to verify the performance of this method. The numerical results show that the accuracy of the GSMFM is close to that of backward Monte Carlo (BMC) method, while the efficiency of GSMFM is much higher than that of the BMC. Therefore, the GSMFM developed can be considered as a promising method to solve arbitrary radiative intensity in graded-index media.

Improved Monte Carlo Method for Total Radiant Exchange Areas in Cylindrical Enclosure

An improved Monte Carlo method (IMCM) is developed to solve radiative heat transfer in participating media in this work. Monte Carlo method (MCM) as a high-precision method has good applicability for the calculation of radiative heat transfer in a complex-shape medium. However, it is highly time-consuming for a large number of energy beams tracing, which limits its application in practical engineering. To overcome this problem of the MCM, there are two improvements proposed: 1) the location of the zone emission points and the number of emission energy beams are subdivided; and 2) the energy of reflection and scattering part is solved by proportional iteration accumulation. In the IMCM, the reflection and scattering processing only needs to be calculated once, which significantly reduces the computing time of a large number of energy beams tracing. A series of radiative heat transfer problems in a two-dimensional cylindrical enclosure with different absorption coefficients, wall emissivity, and scattering albedo are studied, and results show that the IMCM is a high-precision and high-efficiency method for radiative heat transfer.

Study of Various Approximations Used in Modeling Radiative Heat Transfer Problems

Study of Various Approximations Used in Modeling Radiative Heat Transfer Problems

Discontinuous finite element method applied to transient pure and coupled radiative heat transfer

The discontinuous finite element method (DFEM) is applied to transient pure and coupled radiative heat transfer problems in participating media. The DFEM discretization is presented for the time-dependent governing equations that take the full time-dependent term into account. Transient pure radiative transfer problems in a slab medium illuminated by a collimated Gaussian pulse and in a vacuum gapped medium subjected to diffuse irradiation is solved via the DFEM. The DFEM is further extended to transient radiation-conduction problems in two-dimensional media. The DFEM solutions of time-dependent radiation-intensity-based quantities are verified to be highly accurate and they are presented in the form of tabulated numbers with four decimal digits.

Application of the immersed boundary method in solution of radiative heat transfer problems

The immersed boundary method (IBM) was developed for the first time in the present study to simulate the radiative heat transfer problems in complex geometries. The pseudo time stepping technique was applied to solve the radiative transfer equation (RTE) using the finite volume method (FVM). Also, the direct forcing-sharp interface was used in IBM. This method was validated with some benchmark problems in two states of pure radiative and combined radiative-conductive heat transfer. Then, the effects of the conduction-radiation parameter and absorption coefficient on heat flux distribution and isotherms were investigated in an enclosure with inner complex bodies. The results indicated that this method acts well in solving the radiative heat transfer problems in complex geometries. Also, due to using unique Eulerian and Lagrangian grids for solving the energy and radiative transfer equations, production of a separate grid is not required in solving combined heat transfer problems. This is one of the most significant features of the presented method.

Spectral radiate characteristics of gas phase combustion product of energetic fules

The results of long-term experimental studies of the spectral radiation characteristics of the gas phase of the combustion products, performed on measuring complexes of medium and high spectral resolution in the temperature range 200-2800 K, are carried out. The spectral transmission functions are parametrized by the two-parameter equivalent mass method, which makes it possible to solve radiation heat transfer problems in structurally inhomogeneous high - temperature multicomponent gas environments of the products of combustion of energy fuels of the combustion chambers of energy units to generate thermal and electrical energy. The results of modeling radiation heat transfer in combustion chambers and heat exchangers of multi - chamber furnaces with hearth multi-row burner devices and bottom feeding of solid fuel combustion products into a radiation heat exchanger from cyclone furnaces are discussed.

McrtFOAM: A mesh-agglomeration Monte Carlo ray-tracing solver for radiative transfer in gray semitransparent solids

Monte Carlo ray-tracing method has become a promising technique for solving radiative transfer. However, large memory footprint or long CPU time hampers its further utilization. In this work, a Monte Carlo ray-tracing method radiation solver called mcrtFOAM is developed in the framework of open source CFD toolbox OpenFOAM. The radiative source term is calculated based on the radiation distribution factor to avoid repeated ray tracing. In addition, a mesh-agglomeration technique is used to overcome the problem of memory catastrophe for storing a huge radiation distribution factor matrix caused by a large number of mesh elements. The key principle is to agglomerate the refined mesh elements to the coarse ones, and the calculation of radiation distribution factor as well as radiative source term is carried out in the coarse mesh, while the procedure of ray tracing as well as solving the heat conduction is performed in the refined mesh. After validation of the algorithm code within a cubic enclosure, a coupled conductive–radiative heat transfer problem within a cylindrical enclosure filled with gray semitransparent solids is also tested. To test the present solver in realistic industrial systems, a coupled conductive–radiative heat transfer within a tomographic porous structure with gray surfaces is further investigated. All results are compared with previous studies and the solutions by the Finite Volume Discrete Ordinate Method (FVDOM) in OpenFOAM, and they all show great satisfaction. When the mcrtFOAM solver is used for solving the radiative transfer equation, it is found that the CPU time and the memory footprint consumed by the present mcrtFOAM solver with mesh-agglomeration technique are far less than that without this technique. Convincing first implementation exercises indicate that both significant memory and CPU benefits can be expected for configurations of industrial interest These findings will contribute greatly to achieve the calculation of coupled heat transfer involving radiation within large number of mesh elements.

Temperature Distribution in Porous Fins, Subjected to Convection and Radiation, Obtained from the Minimization of a Convex Functional

This work proposes a convex functional endowed with a minimum, which occurs for the solution of the thermal radiation and natural convection heat transfer problem in a rectangular profile porous fin with a fluid flowing through it. The minimum principle ensures the (mathematically demonstrated) uniqueness of the solution and allows the problem simulation by employing a minimization procedure. Darcy’s law with the Oberbeck–Boussinesq approximation simplifies the momentum equation. The energy equation assumes thermal equilibrium between the porous matrix and fluid, allowing comparisons with previous authors’ models, which accounts for the effects of a porosity parameter, a radiation parameter, and a temperature ratio on the temperature. Results for very long fin and finite-length fin with insulated tip were successfully compared with previous works. Closed-form exact solutions for two limiting cases (no convection and no thermal radiation) are also presented.

A reliable treatment to solve nonlinear Fredholm integral equations with non-separable kernel

This work is devoted to solve integral equations formulated in terms of the kernel functions and Nemytskii operators. This type of equations appear in different applied problems such as electrostatics and radiative heat transfer problems. We deal with both cases separable and non-separable kernels by setting the theoretical semilocal convergence results for an adequate iterative scheme that can be useful for approximating the solution of the infinite dimensional problem. We pay special attention to non-separable kernels avoiding the solution given in previous works where the original nonlinear integral equation has been approximated by means of an equation with separable kernel. However, in this case, we introduce an approximation of the derivative operator that it is needed for applying the iterative scheme considered. Moreover, we study the localization and separation of possible solutions of nonlinear integral equation by means of a result of semilocal convergence for the iterative scheme considered. The theoretical results obtained have been tested with some applied problems showing competitive results.

An efficient inverse approach for reconstructing time- and space-dependent heat flux of participating medium* *Project supported by the Natural Science Foundation of Chongqing (CSTC, Grant No. 2019JCYJ-MSXMX0441).

The decentralized fuzzy inference method (DFIM) is employed as an optimization technique to reconstruct time- and space-dependent heat flux of two-dimensional (2D) participating medium. The forward coupled radiative and conductive heat transfer problem is solved by a combination of finite volume method and discrete ordinate method. The reconstruction task is formulated as an inverse problem, and the DFIM is used to reconstruct the unknown heat flux. No prior information on the heat flux distribution is required for the inverse analysis. All retrieval results illustrate that the time- and space-dependent heat flux of participating medium can be exactly recovered by the DFIM. The present method is proved to be more efficient and accurate than other optimization techniques. The effects of heat flux form, initial guess, medium property, and measurement error on reconstruction results are investigated. Simulated results indicate that the DFIM is robust to reconstruct different kinds of heat fluxes even with noisy data.

Coupled optical and thermal analyses of a new type of solar water heaters using parabolic trough reflectors

A new type of solar water heating system using an array of parabolic trough collectors (PTCs) was investigated. A coupled simulation technique was used to solve the complex radiation, convection, and conduction heat transfer problem inside the system. The realistic non-uniform heat flux at the walls of the receiver pipe was obtained by optical analysis and was used simultaneously in thermal modeling. A comprehensive model by considering thermal losses under the non-uniformity of heat flux was proposed and verified with experimental data. In the experiments, the water with different inlet temperatures and flow rates was tested. The obtained results demonstrate that the location of the receiver pipe relative to the PTCs significantly affects the system's thermal efficiency. For the system under study, the best position of the absorber pipe was found at the d/f ratio of 0.8. At the optimal position of absorber pipe, the average daily system's thermal efficiency is about 70%, and for an absorber pipe located at the focal line of the collectors, it is less than 60%. It can be concluded that the thermal efficiency of the current system is higher than that of conventional systems under the same conditions.

An improved model to calculate radiative heat transfer in hot combustion gases

Radiative heat transfer plays an important role in the chemical reactions in the combustor. The widely used WSGG model proposed by Smith is established for normal pressure, which shows inevitable computational errors when dealing with radiative heat transfer problems at reduced or elevated pressures. In this paper, an improved global model is established to calculate the radiant energy exchanges between combustion gases and combustor chamber walls. Compared with the Smith model, the new model shows better performance in a wide range of pressure regions. The model accuracy is examined by computing the emissivity, radiative heat flux as well as the radiative source of H2O–CO2 gas mixtures at different pressure values. Finally, the radiative heat transfer inside a 3D TBCC(turbine-based combined cycle) engine exhaust system where strong gradients of pressure and temperature exist, is also addressed. The computational results show that the developed model provides approximate results at much less computational costs than the high-precision MSMGFSK-c8 model, which makes it competitive in complicated combustion systems.

Analysis of the Quasi-Transfer Approximation in Problems with Analytical Solution

The quasi-transfer approximation reduces the numerical solution of the kinetic equation to solving the diffusion equation through introducing correction factors. The transition to the diffusion equation simplifies the numerical solution of the kinetic equation and makes it possible to use monotonic schemes of the second order of accuracy in solving problems of radiative heat transfer. In this case, it is very important to know the behavior of the correction coefficients, because, for the correctness of the diffusion equation, it is necessary that the diffusion coefficient be positive. This can be verified most easily in problems having analytical solutions. The aim of this work is to study the quasi-transfer approximation in problems with an analytical solution and the behavior of correction coefficients in optically dense and transparent media.

Improving thermo-optic properties of smart windows via coupling to radiative coolers.

In this work we first solve the radiative heat transfer problem in one dimension to perform a comparative analysis of the time-averaged performance of the partially transparent radiative windows and radiative coolers. In doing so, we clearly distinguish the design goals for the partially transparent windows and radiative coolers and provide optimal choice for the material parameters to realize these goals. Thus, radiative coolers are normally non-transparent in the visible, and the main goal is to design a cooler with the temperature of its dark side as low as possible relative to that of the atmosphere. For the radiative windows, however, their surfaces are necessarily partially transparent in the visible. In the cooling mode, the main question is rather about the maximal visible light transmission through the window at which the temperature on the window somber side does not exceed that of the atmosphere. We then demonstrate that transmission of the visible light through smart windows can be significantly increased (by as much as a factor of 2) without additional heating of the windows. This is accomplished via coupling the windows to the radiative coolers using transparent cooling liquid that flows inside of the window and radiative cooler structures. We also demonstrate that efficient heat exchange between radiative coolers and smart windows can be realized using small coolant velocities (sub-1 mm/s for ${\sim}{1}\;{\rm m}$∼1m large windows) or even using a purely passive gravitationally driven coolant flows between a hot smart window and a cold radiative cooler mounted on top of the window with only a minimal temperature differential (sub-1K) between the two. We believe that our simple models complemented with an in-depth comparative analysis of the standalone and coupled smart windows and radiative coolers can be of interest to a broad scientific community pursuing research in these disciplines.

Discrete unified gas kinetic scheme for multiscale anisotropic radiative heat transfer

In this work, a discrete unified gas kinetic scheme (DUGKS) is developed for radiative transfer in anisotropic scattering media. The method is an extension of a previous one for isotropic radiation problems [1]. The present scheme is a finite-volume discretization of the anisotropic gray radiation equation, where the anisotropic scattering phase function is approximated by the Legendre polynomial expansion. With the coupling of free transport and scattering processes in the reconstruction of the flux at cell interfaces, the present DUGKS has the nice unified preserving properties such that the cell size is not limited by the photon mean free path even in the optical thick regime. Several one- and two-dimensional numerical tests are conducted to validate the performance of the present DUGKS, and the numerical results demonstrate that the scheme is a reliable method for anisotropic radiative heat transfer problems.

Stationary Problem of Radiative Heat Transfer with Cauchy Boundary Conditions

A stationary problem of radiative-conductive heat transfer in a three-dimensional domain is studied in the $${{P}_{1}}$$ -approximation of the radiative transfer equation. A formulation is considered in which the boundary conditions for the radiation intensity are not specified but an additional boundary condition for the temperature field is imposed. Nonlocal solvability of the problem is established, and it is shown that the solution set is homeomorphic to a finite-dimensional compact. A condition for the uniqueness of the solution is presented.

Geometric Inverse Problem of Radiative Heat Transfer as Applied to the Development of Alternate Spacecraft Orientation Systems

At present, the angular position of small spacecraft is determined using solar sensors, magnetometers, and angular-velocity pickups as a rule, whereas star trackers are used for complicated problems requiring high accuracy. Each individual system has its advantages and disadvantages. Therefore, combined systems are used to avoid them. Also, to improve the reliability of a craft, recourse to redundancy of the sensors must be had. All these subtleties result in the increased materials intensity and in the complicated mutual synchronization of the systems. In the present work, the authors analyze the possibilities of creating and using the main or alternative orientation system for small spacecraft with radiative-heat-flux sensors on the basis of the methodology of inverse heat-transfer problems. This system will allow checking and correcting the craft's angular position.

Reverse Monte Carlo coupled with Runge-Kutta ray tracing method for radiative heat transfer in graded-index media

The Reverse Monte Carlo coupled with Runge-Kutta ray tracing (RMCRKRT) method is developed to solve the radiative heat transfer problems in semitransparent media with graded index. Due to the fact the curved ray trajectory determined by Fermat principle almost can’t be expressed as the simple explicit functions except for a few special refractive index distributions. In RMCRKRT, the Runge-Kutta ray tracing technique is employed to obtain the ray trajectory numerical solution of graded index medium, and the Reverse Monte Carlo method is employed to solve the radiative heat transfer problems. The correctness and accuracy of RMCRKRT is validated by comparing with the benchmark numerical solutions. The diffuse, specular and bidirectional reflectance distribution function (BRDF) surfaces are considered, and the effects of diffuse, specular and BRDF surfaces on radiative heat transfer are investigated by using the RMCRKRT developed in this work. Calculation results show that significant differences exist in the radiative intensity under different boundary conditions. Therefore, BRDF should be used instead of diffuse reflection and mirror reflection in practical application.

A numerical simulation of MHD ow and radiation heat transfer of nano uids through a porous medium with variable surface heat ux and chemical reaction

In this paper, the problem of MHD ow and radiation heat transfer of nanouids against a at plate in porous medium with the eects of variable surface heat ux and rst-order chemicalreaction is investigated numerically. Three dierent types of nanoparticles, namely Cu, Al2O3 andAg are considered by using water as a base uid with Prandtl number Pr = 6:2. The governingpartial dierential equations can be written as a system of nonlinear ordinary dierential equationsover a semi-innite interval using a similarity transformation. A new eective collocation methodis proposed based on exponential Bernstein functions to simulate the solution of the resultingdierential systems. The advantage of this method is that it does not require truncating ortransforming the semi-innite domain of the problem to a nite domain. In addition, this methodreduces the solution of the problem to the solution of a system of algebraic equations. Graphicaland tabular results are presented to investigate the inuence of the solid volume fraction, types ofnanoparticles, radiation and suction/blowing, magnetic eld, permeability, Schmidt number andchemical reaction, on velocity, temperature and concentration proles. The obtained results ofthe current study are in excellent agreement with previous works.

Fine structural spectrometry and spectroradiometry of combustion products of energy fuels

The results of experimental studies of the fine structure of the spectra of molecular absorption and emission of combustion products of energetic fuels and their application in solving problems of radiative heat transfer in structurally inhomogeneous multicomponent media are considered. The methods of determining the parameters of the spectral absorption lines from the experimental emission spectra of the flame in the combustion products of gas fuel the identification of optically active ingredients in the combustion products and anthropogenic emissions into the atmosphere are analyzed. Attention is drawn to the fact that the emission of gas components is selective and the methods for calculating the radiative heat exchange in the combustion chambers of power units must take into account the acute selection of the molecular absorption spectra of radiation.