Radiative Heat Transfer Problems Research Articles

Orthogonal function extension to enclosure theory

Enclosure theory is widely used to solve radiative heat transfer problems. This paper proposes a mathematical model to handle radiative heat transfer between spatially inhomogeneous surfaces and volumes by using sets of orthogonal functions to represent the spatial variation of surface and volume radiative intensities and properties. This method facilitates development of finely tuned solvers to exploit the properties of the basis functions while providing an improved pedagogical framework behind Hottel’s zone method. Additionally, this interpretation provides insight into error analysis for these types of computations. A simple case study is performed on a two-dimensional empty box with homogeneous, diffuse-gray emissivity, utilizing indicator functions, Fourier series, and Legendre polynomials as sample function bases. An additional proof-of-concept study with participating media was performed with the orthogonal functions using a ray tracing solver in a Monte Carlo wrapper. The studies show that this orthogonal function method can be practically used to mitigate truncation error without any increase in the amount of run-time calculations compared to standard zonal methods.

Real-time retrieval of transient heat flux on the surface of participating medium by using the EKF-RLSE technique

A hybrid algorithm of extended Kalman filtering and recursive least-square estimator (EKF-RLSE) is developed to solve the nonlinear inverse heat conduction-radiation problems in participating medium. By measuring the time-resolved temperature signals from a thermocouple installed on the other boundary of the participating medium, the proposed EKF-RLSE algorithm can realize real-time retrieval of the time-varying heat flux on the medium surface. The influence factors of the sampling interval, measurement and process covariance, forgetting factor, and medium thickness on the reconstruction accuracy and stability of the EKF-RLSE are investigated by numerical experiments. All the estimated results show that the present algorithm is robust and accurate in real-time estimating transient heat flux. If the nonlinear coupled conduction and radiation heat transfer problems is regard as the linear problems, the unknown time-dependent heat flux predicted by the KF-RLSE are also illustrated in this work.

Transient radiative-conductive heat transfer modeling in constructional semitransparent silica ceramics

The article deals with transient radiative – conductive heat transfer investigation in constructional silica ceramics with 10% of total porosity in 2D slab geometry. An empirical model, the so-called effective thermal conductivity (ETC) approximation, and rigorous radiative heat transfer (RCHT) problem solution are compared. Effective thermal conductivity coefficients were determined by both quasi-stationary and non-stationary sample heating and corresponding conductive heat transfer inverse problem solution. Rigorous RCHT calculations were based on radiative transfer equation solution. Spectral directional-hemispherical reflectances were used for scattering and absorption coefficients determination by an identification technique. Identification was based on direct problem solution by invariant embedding technique and parametric optimization. Mie theory and independent scattering approximation with regard to scatterers (pores) size distribution were used for mean scattering cosine estimation. It was shown that in the case of non-stationary temperature regime with rapid heating and cooling stages ETC models fail to predict through the thickness temperature distribution with absolute error less than 502013100 K. The absolute value of this error is strongly affected by the heating schedule. Moreover, calculations revealed several features of the heat flux through the unheated boundary that could not be taken into considerations by effective thermal conductivity approaches.

Investigation of transient conduction–radiation heat transfer in a square cavity using combination of LBM and FVM

In this paper, the effect of surface radiation in a square cavity containing an absorbing, emitting and scattering medium with four heated boundaries is investigated, numerically. Lattice Boltzmann method (LBM) is used to solve the energy equation of a transient conduction–radiation heat transfer problem and the radiative heat transfer equation is solved using finite-volume method (FVM). In this work, two different heat flux boundary conditions are considered for the east wall: a uniform and a sinusoidally varying heat flux profile. The results show that as the value of conduction–radiation decreases, the dimensionless temperature in the medium increases. Also, it is clarified that, for an arbitrary value of the conduction–radiation parameter, the temperature decreases with decreasing scattering albedo. It is observed that when the boundaries reflect more, a higher temperature is achieved in the medium and on boundaries.

A hybrid strategy of lattice Boltzmann method and finite volume method for combined conduction and radiation in irregular geometry

Lattice Boltzmann method (LBM) has been a trendy tool for fluid flow and heat transfer problems. Recently it has been applied to combined heat transfer problems with radiation, while most of the work consider a square enclosure. To extend the LBM to combined heat transfer problems with radiation in irregular geometries, it is coupled with the finite volume method (FVM) to solve the energy equation and radiative transfer equation (RTE), respectively. Blocked-off method is used in the FVM to approximate the curved boundary for radiation modeling. By using the half-way bounce back boundary method in the LBM, it can be perfectly coupled with the blocked-off FVM. Treatments of complex boundaries of these two methods are validated, and then the hybrid method is used to solve combined conduction and radiation heat transfer in enclosures with inclined and curved walls. Effects of the conduction-radiation number, optical thickness, scattering albedo and wall emissivity on the temperature distribution and wall heat flux are analyzed. Results show that this hybrid method can solve combined conduction and radiation heat transfer problems in irregular geometries.

Multiscale analysis and computation for coupled conduction, convection and radiation heat transfer problem in porous materials

This paper discusses the multiscale analysis and numerical algorithms for coupled conduction, convection and radiation heat transfer problem in periodic porous materials. First, the multiscale asymptotic expansion of the solution for the coupled problem is presented, and high-order correctors are constructed. Then, error estimates and their proofs will be given on some regularity hypothesis. Finally, the corresponding finite element algorithms based on multiscale method are introduced and some numerical results are given in detail. The numerical tests demonstrate that the developed method is feasible and valid for predicting the heat transfer performance of periodic porous materials, and support the approximate convergence results proposed in this paper.

Chebyshev collocation spectral method for radiative transfer in participating media with variable physical properties

Chebyshev collocation spectral method based on discrete ordinates equation is employed to solve radiative heat transfer problems in participating media with variable physical prosperities (including space-dependent or temperature-dependent refractive index, absorption coefficient and scattering coefficient). Discrete ordinates method is employed to discretize the solid angle domain. Chebyshev polynomial and collocation spectral method are adopted to express and discretize space domain, respectively. Numerical results obtained by the Chebyshev collocation spectral-discrete ordinates method (CCS-DOM) are presented in this paper and the results show the CCS-DOM has a good accuracy and efficiency for radiative heat transfer problems in participating media. At last, the effects of variable physical properties on radiative heat transfer are analyzed and it can be found that the distributions of refractive index, absorption coefficient and scattering coefficient have a significant effect on radiative transfer and energy distribution.

Radiative heat transfer in fractal structures

The radiative properties of most structures are intimately connected to the way in which their constituents are ordered on the nano-scale. We have proposed a new representation for radiative heat transfer formalism in many-body systems. In this representation, we explain why collective effects depend on the morphology of structures, and how the arrangement of nanoparticles and their material affects the thermal properties in many-body systems. We investigated the radiative heat transfer problem in fractal (i.e., scale invariant) structures. In order to show the effect of the structure morphology on the collective properties, the radiative heat transfer and radiative cooling are studied and the results are compared for fractal and non-fractal structures. It is shown that fractal arranged nanoparticles display complex radiative behavior related to their scaling properties. we showed that, in contrast to non-fractal structures, heat flux in fractals is not of large-range character. By using the fractal dimension as a means to describe the structure morphology, we present a universal scaling behavior that quantitatively links the structure radiative cooling to the structure gyration radius.

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

ABSTRACTThe 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.

Analysis of radiative heat transfer in two-dimensional semitransparent medium with piece-wise constant refractive index

In this work, radiative heat transfer in a medium with piece-wise constant refractive index is considered. The interfaces between two different materials are smooth, thus can be treated as Fresnel surfaces. Based on the Fresnel's equations and Snell's law, the interfacial intensity formulas for the whole solid angle space considering Fresnel reflection and refraction phenomena are introduced. To solve the radiative transfer equation, the angular space is discretized by the discrete-ordinates approach, and the spatial discretization is conducted by natural element method. Radiative heat transfer problems in rectangular medium with a circle or rectangular inclusion are studied. The results show that, due to the existence of the Fresnel interface, the radiative heat transfer with piece-wise constant refractive index is much more complicate than the case with uniform refractive index, and obvious discontinuous characteristics are observed on the interface. The refractive index distributions and optical parameters greatly influence the radiative heat transfer. Several interesting phenomenon is observed and analyzed.

Performance analysis of near-field thermophotovoltaic system with 2D grating tungsten radiator

The effect of hyperbolic modes on near-field thermophotovoltaic (TPV) system performance is investigated by implementing a hyperbolic metamaterial (HMM) radiator. Specifically, the near-field TPV system consists of a 2D grating tungsten radiator and a gallium antimonide (GaSb) cell separated by a gap thickness varying between 100nm and 500nm. The temperatures of the radiator and the TPV cell are fixed at 2000K and 300K, respectively. The effective medium theory (EMT) is proposed to solve the near-field radiative heat transfer problem with a uniaxial anisotropic radiator. Near-field TPV performance is evaluated via maximum power output and conversion efficiency. Enhanced radiative heat transfer is observed within the spectral band where hyperbolic modes are supported by the radiator. As a result, the radiative heat flux absorbed by the cell is enhanced from broadband tunneling of evanescent waves. Furthermore, near-field TPV maximum power output and conversion efficiency are improved. The highest maximum power output and conversion efficiency are 4.28×105Wm−2 and 35%, respectively. When the gap thickness is smaller than 300nm, the effect of hyperbolic modes is strong, and radiative losses affect the conversion efficiency as radiative flux is enhanced both below and above the cell bandgap. For gap thicknesses larger than 300nm, the effect of hyperbolic modes is weak and the conversion efficiency is mostly affected by the spatial distribution of radiative flux absorbed in the cell. In this study, radiative heat flux enhancement and the improvement of near-field TPV performance are attributed to hyperbolic modes supported by the radiator. These findings will further contribute to the design of near-field TPV experimental systems outperforming their far-field counterparts.

Comparison of the blocked-off and embedded boundary methods in radiative heat transfer problems in 2D complex enclosures at radiative equilibrium

Radiative heat transfer in participating media at radiative equilibrium in two-dimensional complex geometries will be investigated using two Cartesian boundary treatments, i.e. the blocked-off method and the embedded boundary method. The main advantages of Cartesian formulation are to simplify grid generation and using efficient Cartesian solvers for complicated problems. Angular and spatial discretization of the radiative transfer equation are performed using the discrete ordinates method and the finite volume method, respectively. The accuracy of both methods in solution of radiative heat transfer problems in irregular geometries are verified by comparison with benchmark solutions from literatures. Then, in order to investigate all features of the blocked-off and embedded boundary methods, two radiative problems with complex enclosures that contain gray absorbing and emitting medium at radiative equilibrium are examined. The results obtained from the two methods are compared with each other as well as with results obtained by body-fitted grid system. It has been shown that for a medium at radiative equilibrium with Cartesian formulation, the embedded boundary method is the method of choice, especially for calculations near the complex boundaries. It should be noted that for optically thick media, both blocked-off and embedded boundary methods show poor performance.

A lattice Boltzmann method to simulate combined radiation–force convection heat transfer mode

Lattice Boltzmann method is extended to solve a combined mode of radiation and force convection heat transfer problem in a channel. Effects of different parameters such as radiation parameters, Peclet number, and emissivity on temperature distribution are investigated. To benchmark the accuracy of the LBM model, the results are compared by the published results of the same geometry modeled by the finite volume method. It is observed that there are good agreements between the LBM and FVM results for all cases. Moreover, the shares of advection, radiation and conduction terms in energy equation are 0.0024, 0.9974, and 0.0002, respectively, for the last one-third piece of the channel.

Incident energy transfer equation and its solution by collocation spectral method for one-dimensional radiative heat transfer

The ray-effect is a major discretization error in the approximate solution method for the radiative transfer equation (RTE). To overcome this problem, the incident energy transfer equation (IETE) is proposed. The incident energy, instead of radiation intensity, is obtained by directly solving this new equation. Good numerical properties are found for the incident energy transfer equation. To show the properties of numerical solution, the collocation spectral method (CSM) is employed to solve the incident energy transfer equation. Three test cases are taken into account to verify the performance of the incident energy transfer equation. The result shows that the radiative heat flux obtained based on IETE is much more accurate than that based on RTE, which means that the IETE is very effective in eliminating the impacts of ray-effect on the heat flux. However, on the contrary, the radiative intensity obtained based on IETE is less accurate than that based on RTE due to the ray-effect. So, this equation is more suitable for those radiative heat transfer problems, in which the radiation heat flux and incident energy are needed rather than the radiation intensity.

Implementation of SLW model in the radiative heat transfer problems with particles and high temperature gradients

PurposeThe paper aims to test the spectral line-based weighted sum of gray gases (SLW) method in axisymmetric geometries with particles and high temperature gradients.Design/methodology/approachAn SLW model is coupled with Trivic’s mean wavelength approach to estimate the radiative heat fluxes at the wall of an enclosure and to the base wall of the rocket exhaust, thereby subsequently studying the effect of concentration variation of the gases and particles in these cases. Radiative transfer equation is solved using modified discrete ordinates method. Anisotropic scattering is modeled using transport approximation.FindingsTwo cases considered show the importance of particle emission and scattering in the rocket plume base heating problems. In cases involving only gases, the concentration of H2O tends to have more impact on the flux values than any other gas.Originality/valueA full model of gases with particles in an axially varying temperature field is reported. Such cases are very common in practical applications. The present methodology gives more insight and a firm handle on the problem vis-a-vis other traditional techniques.

Assessment of different radiative transfer equation solvers for combined natural convection and radiation heat transfer problems

This work investigates the performance of the DOM, FVM, P1, SP3 and P3 methods for 2D combined natural convection and radiation heat transfer for an absorbing, emitting medium. The Monte Carlo method is used to solve the RTE coupled with the energy equation, and its results are used as benchmark solutions. Effects of the Rayleigh number, Planck number and optical thickness are considered, all covering several orders of magnitude. Temperature distributions, heat transfer rate and computational performance in terms of accuracy and computing time are presented and analyzed.

Immersed Boundary Method for Radiative Heat Transfer Problems in Nongray Media With Complex Internal and External Boundaries

The immersed boundary method (IBM) is gaining attention in the computational fluid dynamics but its applications in the field of a conjugated radiative–conductive or radiative–convective heat transfer seem limited. Therefore, the paper presents extension of this method to heat transfer problems dominated by thermal radiation in a nongray medium. The present model enables simulation of heat and fluid flows in a domain with complex stationary or moving internal and external boundaries on a fixed Cartesian grid (FCG) by applying the finite volume method. The special attention is paid to modeling thermal radiation and optical phenomena at highly curved, opaque, or transparent boundaries which confine the computational domain or separate zones of different thermophysical and optical properties, e.g., different values of a refractive index. The model is limited to a 2D planar or axisymmetric spaces. Detailed verification procedure proves accuracy and correctness of the developed model and shows its potential application field. The model may be used for simulations of a conjugated radiative–conductive or radiative–convective heat transfer in a nongray medium in a complex domain with opaque or transparent curved internal or external boundaries without unstructured or body fitted mesh generation.

Evaluation of three different radiative transfer equation solvers for combined conduction and radiation heat transfer

This work investigates the performance of P1 method, FVM and SP3 method for 2D combined conduction and radiation heat transfer problem. Results based on the Monte Carlo method coupled with the energy equation are used as the benchmark solutions. Effects of the conduction-radiation parameter and optical thickness are considered. Performance analyses in term of the accuracy of heat flux and temperature predictions and of computing time are presented and analyzed.

Direct numerical simulation of the turbulent premixed flame propagation with radiation effects

This paper investigates the effects of turbulence on radiative heat transfer in premixed flame propagation using a combination of direct numerical simulation (DNS) and the discrete ordinates method (DOM). The DNS code has been validated and established in previous research, and the newly written DOM code is validated by solving a sample radiative heat transfer problem. The DOM code is explicitly combined with the DNS code using the 3rd-order Runge–Kutta scheme. In the numerical experiments, an initially flat laminar premixed flame interacts with imposed turbulent fluctuations and evolves over time. A remarkable increase in the temperature self-correlation factor <T4>/<T>4 is observed in the middle of the reaction. Higher u′ conditions induced faster and more intensive flame wrinkle evolution. However, flow turbulence reduces the radiative heat loss in planar premixed flame due to the flame curvature effects.

Local RBF meshless scheme for coupled radiative and conductive heat transfer

ABSTRACTA 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.