Problem Of Radiative-conductive Heat Transfer Research Articles

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 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.

Heat Transfer Study in Cylindrical Cavity with Heat Absorption or Generation

Lattice Boltzmann mesoscopic (LBM) is applied to solve energy equation of a transient conduction radiation heat transfer problem in a two-dimensional cylindrical participating (absorbing, emitting and scattering) medium in the presence of heat generation/absorption coefficient. Control volume finite element method (CVFEM) formulation is used to obtain the radiative information. To study the effectiveness of the LBM-CVFEM combination on unsteady conduction-radiation problems in cylindrical media, the energy equation of the problem is also solved using the finite difference method (FDM) in which the CVFEM is used to compute radiative information. The effects of heat generation/absorption coefficient on temperature distributions in the medium are studied. Results of the present work are benchmarked against those available in the literature. The hybrid numerical model’s results are also compared with those obtained by the FDM-CVFEM combination. All the results presented in this work show that the present method is accurate and valuable for the analysis of cylindrically axisymmetric radiative heat transfer problems .

On a Nonlinear Initial—Boundary Value Problem with Venttsel Type Boundary Conditions Arizing in Homogenization of Complex Heat Transfer Problems

We consider a non-standard nonlinear singularly perturbed 2D initial-boundary value problem with Venttsel type boundary conditions, arising in homogenization of radiative-conductive heat transfer problems. We establish existence, uniqueness and regularity of a weak solution v. We obtained estimates for the derivatives Dtv, D12v, D22v, D1D2v with a qualified order in the small parameter ε.

Volume Penalization Method for Solving Coupled Radiative-Conductive Heat Transfer Problems in Complex Geometries

Volume Penalization Method for Solving Coupled Radiative-Conductive Heat Transfer Problems in Complex Geometries

Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions

The paper is devoted to a nonstationary initial–boundary value problem governing complex heat exchange in a convex semitransparent body containing several absolutely black inclusions. The existence and uniqueness of a weak solution to this problem are proven herein. In addition, the stability of solutions with respect to data, a comparison theorem and the results of improving the properties of solutions with an increase in the summability of the data were established. All results are global in terms of time and data.

Unique Solvability of the Stationary Complex Heat Transfer Problem in a System of Grey Bodies with Semitransparent Inclusions

We establish the unique solvability of a radiative-conductive heat transfer problem in a system of grey bodies with semitransparent inclusions and prove the comparison theorem. We show that higher summability of the data improves the properties (exponential summability and boundedness) of the solution.

Unique solvability of a stationary radiative–conductive heat transfer problem in a semitransparent body with absolutely black inclusions

We consider a stationary boundary value problem describing a radiative–conductive heat transfer in a semitransparent body with absolutely black 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. Besides, we proved the comparison theorems and established the results on improving the properties of solutions with increasing exponents of data summability.

Error Estimate for Discrete Approximation of the Radiative-Conductive Heat Transfer Problem in a System of Absolutely Black Rods

We prove an error estimate of order $$ O\left(\sqrt{\varepsilon }/\uplambda \right) $$ for a discrete approximation of the radiative-conductive heat transfer problem in a system of absolutely black rods bundled in a square box; here, e is the rod diameter and λ is the heat transfer coefficient.

Simultaneous reconstruction of nonlinear temperature-dependent properties in a 1D radiation-conduction medium

In this paper, a set of new data is proposed for the simultaneous reconstruction of thermal radiation and conduction properties in a radiation-conduction medium into the one-dimensional layer. The radiation problem is modeled by the modified discrete ordinates method, and the conduction-radiation heat transfer problem is solved via the finite volume approach. The inverse problem is solved using the particle swarm optimization algorithm. Various cases are solved in this paper. In the first section, the constant absorption coefficient and radiation-conduction parameters are reconstructed by measuring the exit radiation intensities. To increase the accuracy of results, a two-stage hybrid optimization algorithm is used in this section. In the first stage, the absorption coefficient is calculated, and in the second stage, the radiation-conduction parameter is obtained. In the second section, the ability of the proposed algorithm and the measured data for reconstruction of the temperature-dependent radiation-conduction parameter is tested. To improve the results' accuracy in this section, a set of new data is used. Consequently, the proposed algorithm with a modified objective function that uses new data is presented to decrease the Planck number's sensitivity to the measurement errors.

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.

Simultaneous estimation of internal temperature field and boundary time-dependent heat flux in absorbing and scattering media using the unscented Kalman smoothing technique

Based on the future measured temperature, the Rauch-Tung-Striebel smoothing technique coupled with unscented Kalman filter is introduced to resolve the nonlinear inverse radiation-conduction heat transfer problem, which is nonlinear because of specific heat and thermal conductivity with temperature and existence of the radiative heat transfer. For the direct process, the finite volume method is applied to calculate the energy equation and radiative transfer equation is computed by the discrete ordinate method. Based on the measurement temperature signals of the right surface, the left surface time-dependent heat flux and interior temperature in absorbing and scattering medium are retrieved in near real time by using the proposed method. The different number of the future measured temperature, measurement noise, and process noise covariance are applied to examine the feasibility and reliability of the present algorithm. All retrieval results show that the Rauch-Tung-Striebel smoothing technique coupled with unscented Kalman filter is accurate and stable. Compared to the unscented Kalman filter, the accuracy of the retrieval temperature distribution is improved significantly, the deviation and oscillation of the retrieval time-dependent heat flux are also decreased substantially.

Discrete and asymptotic approximations for one stationary radiative–conductive heat transfer problem

AbstractSpecial discrete and asymptotic approximations are proposed for the boundary value problem describing a stationary radiative–conductive heat transfer in a system of absolutely black heat-conducting rods of circular cross-section. Results of numerical experiments are presented to confirm the efficiency of proposed approximations.

On a Nonstandard Boundary Value Problem Arising in Homogenization of Complex Heat Transfer Problems

We consider a nonstandard boundary value problem appearing in homogenization of some radiative-conductive heat transfer problems. We establish the existence, uniqueness, and regularity of a weak solution u. We obtain estimates for the derivatives $$ {D}_1^2u,{D}_2^2u,\kern0.33em {D}_1{D}_2u\kern0.33em in\kern0.33em {L}^2\left({\varOmega}_{\upvarepsilon}\right)\kern0.33em and\kern0.33em {D}_s^2u\kern0.33em in\kern0.33em {L}^2\left({\varGamma}_{\varepsilon}\right) $$ with qualified order with respect to e, where Ωe is the square (e/2, 1 − e/2) × (e/2, 1 − e/2) with boundary Γe.

Efficient and robust prediction of internal temperature distribution and boundary heat flux in participating media by using the Kalman smoothing technique

The Kalman smoothing (KS) technique, which is consisted of the Kalman filtering and Rauch-Tung-Striebel smoothing technique, is introduced to resolve the inverse radiation-conduction heat transfer problem by using the future temperature measurement information. For the forward problem, the discrete ordinate method is employed to solve the radiative transfer equation and the energy equation is resolved by using the finite volume method. The boundary time-dependent heat flux and internal temperature filed in participating media are retrieved in near real time from measurement temperature on the right surface. Different forms of time-dependent heat flux are imposed on the left surface to examine the performance of the proposed algorithm. All the reconstruction results indicate that the KS technique is effective and robust for resolving the retrieval of the boundary time-dependent heat flux and internal temperature fields in near real time. The effect of different parameters on the accuracy and stability of the reconstruction results, including the future temperature information, sampling interval, measurement noise covariance, initial state error, and initial state error covariance, are analyzed in detail. Compared with the KF technique, the reconstruction accuracy of KS technique can be improved obviously. Meanwhile, the time delay and oscillation of reconstructed heat flux are reduced significantly and the deviation of the retrieval temperature is also decreased greatly.

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.

Real-time reconstruction of the time-dependent heat flux and temperature distribution in participating media by using the Kalman filtering technique

The Kalman filtering (KF) algorithm is introduced to solve the inverse coupled radiation-conduction heat transfer problem in the participating medium for the first time. The time-dependent surface heat flux and internal temperature distribution of the participating medium is reconstructed simultaneously from the (non-intrusive transient temperature) measurements made on the other surface. The governing energy equation and radiative transfer equation are calculated by using the finite volume method (FVM). Different forms of transient heat flux are employed to test the performance of the KF method. The influence of initial state, initial state error covariance, measurement noise, process noise, measurement noise covariance, process noise covariance, sampling step, refractive index, medium thickness, and absorption coefficient on the accuracy and stability are discussed thoroughly. All the retrieval results show that the surface heat flux and internal temperature distribution can be reconstructed simultaneously in real time. Compared with the hybrid algorithm of KF and recursive least-square estimator (RLSE), the KF algorithm can obtain better reconstruction results and a noticeable decrease of the sensitivity to measurement noise, initial temperature distribution, and absorption coefficient is observed from the retrieval results.