Radiative-conductive Heat Transfer Research Articles

Radiative-conductive heat transfer dynamics in dissipative dispersive anisotropic media

Abstract We develop a self-consistent theoretical formalism to model the dynamics of heat transfer in dissipative, dispersive, anisotropic nanoscale media, such as metamaterials. We employ our envelope dyadic Green’s function method to solve Maxwell’s macroscopic equations for the propagation of fluctuating electromagnetic fields in these media. We assume that the photonic radiative heat transfer mechanism in these media is complemented by dynamic phononic mechanisms of heat storage and conduction, accounting for effects of local heat generation. By employing the Poynting theorem and the fluctuation-dissipation theorem, we derive novel closed-form expressions for the radiative heat flux and the coupling term of photonic and phononic subsystems, which contains the heating rate and the radiative heat power contributions. We apply our formalism to the paraxial heat transfer in uniaxial media and present relevant closed-form expressions. By considering a Gaussian transverse temperature profile, we also obtain and solve a system of integro-differential heat diffusion equations to model the paraxial heat transfer in uniaxial reciprocal media. By applying the developed analytical model to radiative-conductive heat tranfer in nanolayered media constructed by layers of silica and germanium, we compute the temperature profiles for the three first orders of expansion and the total temperature profile as well. The results of this research can be of interest in areas of science and technology related to thermophotovoltaics, energy harvesting, radiative cooling, and thermal management at micro- and nanoscale.

Estimation of Multiple Parameters in Semitransparent Mediums Based on an Improved Grey Wolf Optimization Algorithm

This work investigates the inverse coupled radiation–conduction problem for estimating thermophysical parameters and source terms by an improved grey wolf optimization (GWO). The transient coupled radiation–conduction heat transfer problem in participating slab media is solved by the finite volume method. The radiative intensities on both boundaries are adopted as known measurement information in the inverse model. To overcome the disadvantages of the original GWO algorithm, an improved grey wolf algorithm (IGWO) is developed by introducing the weight strategy and nonlinear factors. Three benchmark functions are adopted to prove that the IGWO has a faster convergence speed and higher estimation accuracy than the original one. The IGWO is applied to inverse the thermophysical parameters and source terms based on the coupled radiation–conduction model; the results indicate that the IGWO is accurate and effective for estimating refractive index, absorption coefficient, and source terms.

Decision support system based on a hybrid genetic algorithm–Kohonen map for combined mode conduction–radiation heat transfer in a porous medium: A comparative assessment of three variations of the Kohonen map

AbstractA hybrid genetic algorithm (GA)–Kohonen map, with its three variants, is explored for the first time for the decision‐making system in a porous ceramic matrix (PCM)‐based burner through determination of the regime of operation. Four different attributes of PCMs such as convective coupling (P2), extinction coefficient (β), downstream porosity (ϕ2), and scattering albedo (ω) are selected for determining the regime of operation of a PCM‐based burner. Changes in any of these attributes of a PCM lead to significant changes in the temperature profiles of the gas and solid phases. Temperature profiles of the gas and solid phases are computed by developing a numerical model. Various samples corresponding to different regimes are generated and used in a hybrid GA–Kohonen map. The best architectural details such as the neuron number and training epochs are obtained from GA as output. The best Kohonen map is trained with the input data, and regimes of operation for new temperature profiles are predicted. A supervised Kohonen map is able to provide the highest average class prediction of more than 40%. All the variants are assessed under two different types of neuron grids: hexagonal and rectangular. Comparative assessments of the three different variants of Kohonen maps, in terms of CPU time and average class prediction, are carried out.

Numerical and experimental characterization of high-temperature heat transfer in a ceramic foam with dual-scale porosity

In this paper, we compare numerical predictions and measurements of the high-temperature apparent thermal conductivity of an insulating alumina foam with dual-scale porosity: the foam contains ▪-sized cells and also ▪-sized pores in the highly scattering foam skeleton. Simulations of the apparent thermal conductivity are performed on tomography-reconstructed foams, with a three-part multi-scale approach to account for the dual-scale porosity. The effective phonon thermal conductivity of the foam is first computed using a finite element homogenization technique. The spectral and temperature-dependent effective radiative properties of the foam are next computed through an improved Monte Carlo ray-tracing approach, with foam skeleton scattering modeled using a physical-optics-based approach. The apparent thermal conductivity of the foam is then simulated by resolving the coupled conductive-radiative heat transfer through a semi-infinite homogeneous slab. The simulated high-temperature apparent thermal conductivity is found to be in good agreement with experimental data up to ▪, obtained by parallel hot wire measurements coupled with an improved quadrupolar model for low-density insulating materials. The large influence of scattering at the cell-skeleton interface is shown through a numerical parametric study. It is also shown that the Rosseland conductivity calculated directly from the simulated spectral radiative properties provides a good estimation of radiative heat transfer for optical thicknesses exceeding 30.

Conduction-radiation heat transfer in a gray semi-transparent medium: combining integral transforms and discrete ordinate method

This work presents a novel approach to solve the unsteady one-dimensional coupled heat conduction-radiation problem for a gray semi-transparent, absorbing, emitting, and diffusing medium, non-linearly anisotropic, bounded by two gray parallel-plane surfaces that are diffuse in emission, and diffuse and specular in reflection. A combination of the Discrete Ordinate Method (DOM), to discretize the angular coordinate of the Radiative Transfer Equation (RTE), and the Generalized Integral Transform Technique (GITT), to solve the energy equation, is proposed as solution methodology. Results are presented in terms of the temperature field, incident radiation, hemispherical reflectance, and conductive, radiative and total heat fluxes. The versatility and the accuracy of the methodology are verified/ validated with solutions of the literature for different phase functions, conduction-radiation coupling parameters, and albedo, emphasizing the effects of these parameters, as well as, the characteristics of the present methodology for different kinds of quadrature rules. The results show that the combination DOM/GITT proved to be adequate as a tool for solving the governing equations of the coupled conduction-radiation problem.

Fuzzy Levenberg-Marquardt damping factor update strategy and Tikhonov regularization applied to a coupled conduction-radiation inverse heat transfer problem

The recently proposed Fuzzy Levenberg-Marquardt Damping Factor Updating Strategy (FLM) is used along with Tikhonov Regularization (TR) in order to solve a coupled conduction-radiation function estimation inverse problem. FLM consists of updating the Levenberg-Marquardt (LM) damping factor with the assist of Fuzzy Logic. To test the FLM algorithm combined with TR, a conduction-radiation problem is addressed, and it serves as test bed to the numerical experiments, where the objective is to obtain estimatives of parameters, such as the spatially variable scattering albedo, the thermal conductivity and the optical thickness, simultaneously, which is often performed separately. Two main test cases are presented, one considering only the radiation problem, used as benchmark, in order to investigate noise levels and hyperparameters. The second main test case deals with the coupled conduction-radiation heat transfer problem for different functional forms of the spatially variable scattering albedo. For all presented numerical experiments, good estimates were achieved for the sought functions and parameters. These results demonstrate that the methodology presented in this work, through the combination of the Fuzzy LM dampting factor updating strategy and the Tikhonov regularization scheme, may provide valuable tools for inverse heat transfer problems.

Investigation of the lattice Boltzmann method to resolve combined radiation-conduction heat transfer in participating media with curved boundaries

PurposePresent study aims to extend the lattice Boltzmann method (LBM) to simulate radiation in geometries with curved boundaries, as the first step to simulate radiation in complex porous media. In recent years, researchers have increasingly explored the use of porous media to improve the heat transfer processes. The lattice Boltzmann method (LBM) is one of the most effective techniques for simulating heat transfer in such media. However, the application of the LBM to study radiation in complex geometries that contain curved boundaries, as found in many porous media, has been limited.Design/methodology/approachThe numerical evaluation of the effect of the radiation-conduction parameter and extinction coefficient on temperature and incident radiation distributions demonstrates that the proposed LBM algorithm provides highly accurate results across all cases, compared to those found in the literature or those obtained using the finite volume method (FVM) with the discrete ordinates method (DOM) for radiative information.FindingsFor the case with a conduction-radiation parameter equal to 0.01, the maximum relative error is 1.9% in predicting temperature along vertical central line. The accuracy improves with an increase in the conduction-radiation parameter. Furthermore, the comparison between computational performances of two approaches reveals that the LBM-LBM approach performs significantly faster than the FVM-DOM solver.Originality/valueThe difficulty of radiative modeling in combined problems involving irregular boundaries has led to alternative approaches that generally increase the computational expense to obtain necessary radiative details. To address the limitations of existing methods, this study presents a new approach involving a coupled lattice Boltzmann and first-order blocked-off technique to efficiently model conductive-radiative heat transfer in complex geometries with participating media. This algorithm has been developed using the parallel lattice Boltzmann solver.

Итерационный алгоритм решения начально-краевой задачи для квазилинейной модели сложного теплообмена

An initial-boundary value problem for a system of quasilinear equations of radiative-conductive heat transfer, simulating the process of endovenous laser ablation, is considered. An algorithm for finding its solution is proposed and its convergence is proved. The efficiency of the algorithm is illustrated by numerical experiments.

Lattice Boltzmann method for coupled radiation-conduction heat transfer in participating medium with graded-index

Graded-index materials are effective to control thermo-optical systems, due to its special physical characteristics. And quantitatively calculation for energy transfer process is valuable for the research of graded-index materials. Thus, reliable numerical method is required. Lattice Boltzmann method (LBM) is a mesoscopic numerical method with unique advantages on coupling muti-physical field. Here, we provide a LBM to couple radiation and conduction within graded-index medium under a unified framework. Through several 1-D cases, the great consistence between present LBM and references indicates that LBM has excellent availability and accuracy. Furthermore, LBM is expanded to coupled 2-D problem. The present LBM is expected to simulate coupled radiation-conduction heat transfer in participating medium with graded-index effectively.

Experimental characterization of Al2O3 foam based on high temperature thermal response experiments

Alumina foam has potential application value in aerospace, solar energy, and other fields. This study proposes a combined radiative-conductive heat transfer model, in which the thermal conductivity and extinction coefficient are temperature-dependent, and the radiation transfer equation is solved by the Monte Carlo method. A self-designed setup is used to measure the high temperature thermal response experiments of alumina foams in 10PPI, 20PPI, and 40PPI. Combined with the genetic algorithm, the thermal conductivity, extinction coefficient, albedo and asymmetry factor of scattering are solved. According to the inversion results, the extinction coefficient of materials with a high pore density is more sensitive to temperature than those with a lower pore density. The thermal conductivity of high pore density materials is greater than that of low pore density materials. The thermal conductivity and extinction coefficient slightly remain basically unchanged as atmospheric pressure increases.

A reconstructed approach for online prediction of transient heat flux and interior temperature distribution in thermal protect system

Thermal protect system (TPS) is a crucial part of spacecraft to shield them from the aerodynamic heating during the atmospheric entry/re-entry. In this paper, the aerodynamic heating on the surface of a reusable launch vehicle is predicted to achieve rational design of the TPS. The conduction-radiation heat transfer in the TPS that was regard as a kind of index graded medium, was computed using finite volume method and discrete ordinate method. The extended Kalman filtering coupled with Rauch-Tung-Striebel smoother is introduced for calculating the inverse problem to obtain the time-variant heat flux and interior temperature fields in TPS. The impact of the structure parameters and future measurement temperature information on the lag and stability of retrieval results is investigated. The actual heat flux generated at NASA Langley Research Center for the Reusable Launch Vehicle is employed for examining the effectiveness and dependability of the proposed approach. The numerical results demonstrate the present approach can realize precise and on-line prediction of the time-variant heat flux and interior temperature fields in TPS.

A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media

We propose a new mixed finite element formulation for solving radiation–conduction heat transfer in optically thick anisotropic media. At this optical regime, the integro-differential equations for radiative transfer can be replaced by the simplified PN approximations using an asymptotic analysis. The conductivity is assumed to be nonlinear depending on the temperature along with anisotropic absorption and scattering depending on both the direction and location variables. The simplified PN approximations are enhanced by considering a diffusion tensor capable of describing anisotropic radiative heat transfer. In the present study, we investigate the performance of the unified and mixed formulations combining cubic P3, quadratic P2, and linear P1 finite elements to approximate the temperature in the simplified P3 model. To demonstrate the performance of the proposed methodology, three-dimensional examples of nonlinear radiation–conduction equations in optically thick anisotropic media are presented. The obtained numerical results demonstrate the accuracy and efficiency of the proposed mixed finite element formulation over the conventional unified finite element formulation to accurately solve the simplified P3 equations in anisotropic media.

Investigation of Radiative-Conductive Heat Transfer by Noncontact Measurements. 2. Approval of the Computational-Experimental Method

Investigation of Radiative-Conductive Heat Transfer by Noncontact Measurements. 2. Approval of the Computational-Experimental Method

MATHEMATICAL MODELING AND NUMERICAL STUDY OF BIOMASS FIXED CARBON GASIFICATION IN A DENSE BED AT ATMOSPHERIC PRESSURE. PART 2. ANALYSIS OF NUMERICAL RESULTS

Using the constructed two-dimensional model of aerodynamics, heat-mass transfer and chemical reaction of coke-ash residue in a steam-air mixture at a pressure of 1 atm, taking into account interphase convective heat transfer, radiative-conductive heat transfer of the solid phase, radiative and conductive heat transfer of the bed with the reactor wall, gravitational forces and aerodynamic resistance, the unsteady process of lignin gasification in a fixed bed was theoretically investigated. It is shown that: 1) the maximum value of biomass temperature of 887 °С is reached in the oxidation zone, where exothermic reactions prevail over endothermic reactions; 2) the specified temperature turns out to be lower than the temperature of the beginning of ash deformation of 1050 °С, which indicates the slag-free operation of the gas generator; 3) the largest yield of gasification products occurs in the redox reaction zone, where heat absorption dominates over heat release; 4) a slag pad is formed near the grate, protecting the grate from overheating; 5) the largest changes in discrete phase movement speeds are observed in the oxidizing and reducing zones of the gas generator from –5.791.10−5 m/s до –1.86.10−5 m/s due to the change in particle diameter from 10 mm to 6.83 mm (ash). Bibl. 12, Fig. 6.

Unified discontinuous Galerkin finite-element framework for transient conjugated radiation-conduction heat transfer.

Research on conjugated radiation-conduction (CRC) heat transfer in participating media is of vital scientific and engineering significance due to its extensive applications. Appropriate and practical numerical methods are essential to forecast the temperature distributions during the CRC heat-transfer processes. Here, we established a unified discontinuous Galerkin finite-element (DGFE) framework for solving transient CRC heat-transfer problems in participating media. To overcome the mismatch between the second-order derivative in the energy balance equation (EBE) and the DGFE solution domain, we rewrite the second-order EBE as two first-order equations and then solve both the radiative transfer equation (RTE) and the EBE in the same solution domain, resulting in the unified framework. Comparisons between the DGFE solutions with published data confirm the accuracy of the present framework for transient CRC heat transfer in one- and two-dimensional media. The proposed framework is further extended to CRC heat transfer in two-dimensional anisotropic scattering media. Results indicate that the present DGFE can precisely capture the temperature distribution at high computational efficiency, paving the way for a benchmark numerical tool for CRC heat-transfer problems.

Thermodynamics second-law analysis in an unsteady conduction and radiation heat transfer system with internal heat source

This paper presents an improved thermodynamic analysis method used to evaluate the irreversibility and efficiency of a coupled conductive-radiative heat transfer process. The exergy analysis of the conductive-radiative process is developed based on the exergy balance equation. In the method, the local entropy generation rates due to the radiative heat transfer and heat conduction processes are calculated. Based on the entropy generation analysis, an exergy analysis is performed, the stored exergy of the system and the exergetic efficiency are determined, and the thermodynamic efficiency of the system is further evaluated. The results are verified by the principle of exergy balance and the exergy generation rate calculated by the method does not deviate from the theoretical value by more than 0.1%. Four heat source distributions are specified in the numerical analysis, which include completely uniform, partially uniform, and non-uniform heat source distributions in the numerical analysis. The effects of heat source distribution, conductive-radiative coefficient and total heat generation rate of medium on entropy generation and stored exergy of system are investigated. The numerical results show that the average temperatures and exergy storage rate of the systems with partially uniform heat source distribution are 5.1–79.7 K and 6.8–49.8% higher than the other distributions, and uniform and centralized heat generation in the internal region of the system is proposed. The total stored exergy of the systems has a tendency to first increase and then decrease, reaching its maximum at N = 1 as the conduction and radiation coefficients increase, and increasing as the total heat generation rate increases.

Investigation of coupled radiation-conduction heat transfer in cylindrical systems by discontinuous spectral element method

Nowadays, in order to achieve higher efficiency in aero-engines, the increase of turbine inlet temperature in aero-engine is in urgent need. At present, the turbine inlet temperature is around 2,000 K, which means the radiation and coupled radiation-conduction heat transfer play more and more important roles in hot section of aero-engines. As we all konw, considering the cylindrical symmetry of aero-engines. It is convenient to adopt the cylindrical coordinate to simplify the description of these systems, such as annular combustor, exhaust nozzle, etc. In this paper, Discontinuous Spectral Element Method (DSEM) is extended to solve the radiation and coupled radiation-coduction heat transfer in cylindrical coordinate system. Both the spatial and angular computational domains of radiative transfer equation (RTE) are discretized and solved by DSEM. For coupled radiation-conduction heat transfer problem, Discontinuous Spectral Element Method-Spectral Element Method (DSEM-SEM) scheme is used to avoid using two sets of grid which would cause the increase of computational cost and the decrease of accuracy. Then, the effects of various geometric and thermal physical parameters are comprehensively investigated. Finally, these methods are further extended to 2D cylindrical system.

Nonstationary radiative–conductive heat transfer problem in an absolutely black body with semitransparent inclusions

We consider a nonstationary initial‐boundary value problem governing a radiative–conductive heat transfer in an absolutely black body with semitransparent inclusions. To describe the radiative transfer, the integro‐differential radiative transfer equation is used. We do not take into account the dependence of the radiation intensity and the properties of semitransparent materials on the radiation frequency. We proved at the first time the unique solvability of this problem. In addition, we proved the stability of solutions with respect to data, established a comparison theorem and results on improving the properties of solutions with an increasing on the summability of the data.

A unified lattice Boltzmann framework for combined radiation-conduction heat transfer

As the wider application of combined radiation-conduction heat transfer, effective numerical framework is required to precisely predict the heat transfer process. In this paper, a unified lattice Boltzmann framework is proposed for combined radiation-conduction heat transfer problem. As a complete form of lattice Boltzmann framework, the radiative transfer equation (RTE) and energy equation are both solved under the versatile, consistent D1Q3, D2Q9 and D3Q15 lattice model to construct a combined LB framework. Through several numerical cases from 1-D to 3-D problems for both steady and transient problems, we validated the applicability and accuracy of our framework. Besides, taking account of various parameters, we discuss the effects of different medium properties and anisotropic scattering condition. Our unified LB framework for radiation-conduction transfer is tested to be available for muti-dimensional problems through 1-D to 3-D cases. Furthermore, the anisotropic scattering condition is considered as an extension of our framework. The present work is expected to provide an effective numerical tool for various of combined radiation-conduction heat transfer questions.

Volume penalization method for solving coupled radiative-conductive heat transfer problems in complex geometries

A novel immersed boundary method for simulating coupled radiative-conductive heat transfer based on a volume penalization method is proposed and verified. A smooth source/sink term is introduced to the governing equations for radiative and conductive heat transfer in order to take into account the absorption, reflection and emission at a solid surface. The proposed algorithm is successfully implemented into an open-source CFD solver, OpenFOAM with adaptive mesh refinement to guarantee sufficiently fine grid resolution near solid surfaces. Benchmark problems of pure radiation and combined conduction-radiation are considered for verifying the proposed method. The present simulation results under various absorption and emission conditions show good agreement with analytical solutions as well as existing literature data within around 5% errors. In addition to its superior performance in terms of accuracy, the present approach does not require special treatments around the solid surface with arbitrary complex geometry to impose boundary conditions for radiative heat transfer, and thereby wide applicability in scientific and engineering problems.