Radiative-conductive Heat Transfer Research Articles

Effect of deformation of diamond anvil and sample in diamond anvil cell on the thermal conductivity measurement* *Project supported by the National Key Research and Development Program of China (Grant No. 2018YFA0702700) and the National Natural Science Foundation of China (Grant Nos. 11674404 and 11774126).

Studies show that the sample thickness is an important parameter in investigating the thermal transport properties of materials under high-temperature and high-pressure (HTHP) in the diamond anvil cell (DAC) device. However, it is an enormous challenge to measure the sample thickness accurately in the DAC under severe working conditions. In conventional methods, the influence of diamond anvil deformation on the measuring accuracy is ignored. For a high-temperature anvil, the mechanical state of the diamond anvil becomes complex and is different from that under the static condition. At high temperature, the deformation of anvil and sample would be aggravated. In the present study, the finite volume method is applied to simulate the heat transfer mechanism of stable heating DAC through coupling three radiative-conductive heat transfer mechanisms in a high-pressure environment. When the temperature field of the main components is known in DAC, the thermal stress field can be analyzed numerically by the finite element method. The obtained results show that the deformation of anvil will lead to the obvious radial gradient distribution of the sample thickness. If the top and bottom surfaces of the sample are approximated to be flat, it will be fatal to the study of the heat transport properties of the material. Therefore, we study the temperature distribution and thermal conductivity of the sample in the DAC by thermal-solid coupling method under high pressure and stable heating condition.

Evaluation of Radiant Heat Transfer Influence on the Temperature Field of Fuel Element Microcell of Pressurized Water-Cooled Nuclear Reactor

Optimization of the core composition of the pressurized water reactors is associated with the calculation of the temperature fields of heat exchange microcells containing separate fuel elements. Taking into account the radiation-conductive heat transfer inside the fuel element is based on the statement that the helium gap between the column of fuel pellets and the wall of the fuel element has the properties of a black body. This is not true as helium is a monatomic gas, it neither absorbs nor emits, i.e. transparent to heat radiation. The article substantiates the physical and mathematical model of a microcell of a fuel element of a pressurized water-cooled nuclear reactor, taking into account radiation heat transfer. The model takes into account that helium is transparent to thermal radiation, and the fuel element is cooled by a flow-through system of the coolant. The implementation of the model is carried out analytically using the Karman-Pohlhausen integral relations method. The temperature fields of the column of fuel pellets and the coolant channel are calculated, the temperatures of the side surfaces of the cell are determined, and the effect of radiation heat transfer on the temperature distribution in the cell is estimated.

A Multiscale Method for Coupled Steady-State Heat Conduction and Radiative Transfer Equations in Composite Materials

Abstract Predictions of coupled conduction-radiation heat transfer processes in periodic composite materials are important for applications of the materials in high-temperature environments. The homogenization method is widely used for the heat conduction equation, but the coupled radiative transfer equation is seldom studied. In this work, the homogenization method is extended to the coupled conduction-radiation heat transfer in composite materials with periodic microscopic structures, in which both the heat conduction equation and the radiative transfer equation are analyzed. Homogenized equations are obtained for the macroscopic heat transfer. Unit cell problems are also derived, which provide the effective coefficients for the homogenized equations and the local temperature and radiation corrections. A second-order asymptotic expansion of the temperature field and a first-order asymptotic expansion of the radiative intensity field are established. A multiscale numerical algorithm is proposed to simulate the coupled conduction-radiation heat transfer in composite materials. According to the numerical examples in this work, compared with the fully resolved simulations, the relative errors of the multiscale model are less than 13% for the temperature and less than 8% for the radiation. The computational time can be reduced from more than 300 h to less than 30 min. Therefore, the proposed multiscale method maintains the accuracy of the simulation and significantly improves the computational efficiency. It can provide both the average temperature and radiation fields for engineering applications and the local information in microstructures of composite materials.

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.

Inverse estimation of temperature-dependent refractive index profile in conductive-radiative media

The aim of this paper is to retrieve the temperature-dependent refractive index distribution in parallel-plane semi-transparent media with combined conduction-radiation heat transfer, by the measurement of exit intensities over the boundaries. The finite volume method in combination with the discrete ordinates method is used to solve the energy equation. The results of the direct solution for both linear-spatially and linear-temperature-dependent refractive index distributions are compared and the effects of the main parameters are examined. The results confirm a remarkable difference between the results for spatially and temperature-dependent refractive index profiles. Finally, the refractive index profile is estimated using the conjugate gradient method in an inverse manner. The coefficients of the linear profile are estimated for three cases with different levels of measurement errors; 1%, 3% and 5%. The results show that the temperature-dependent refractive index distribution can be retrieved in a good range of errors for noisy data.

A non-linear transform approach for conduction-radiation heat transfer in the extended thermal discrete element method

Conduction-radiation heat transfer widely exists in nuclear pebble beds, packed beds and powder materials under moderate or high temperatures. Because of the considerable computational cost, it is unrealistic to trace all possible obstructed view factors between spheres in transient particle-scale simulations. With a non-linear transform approach, an extended thermal discrete element method (TDEM) with almost the same computational cost as that required for conduction alone is proposed here. Particle-particle conduction in the contact area, particle-fluid-particle conduction near the contact point and the Knudsen effect under low gas pressures are considered in the determination of the contact thermal resistance (CTR). A particle conduction-radiation scalar is applied in the particle energy balance equation, which is a function of the particle temperature, CTR and radiation exchange factor. The numerical results of the pebble bed are in good agreement with the continuum model and measured results under high temperatures. The temperature transport process in conduction-radiation heat transfer involves anomalous diffusion by discrete and continuum methods. The proposed extended TDEM is proven to be efficient for conduction-radiation heat transfer and feasible to be applied in large-scale computational fluid dynamics (CFD)-DEM simulations.

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.

Theoretical prediction and experimental characterization of radiative properties and thermal conductivities of fibrous aramid fabrics

Nonwoven aramid fabric is widely used as thermal barrier of fireproofing clothing due to its inherent flame retardancy and light weight. In fire or high temperature scenario, radiative heat transfer becomes the predominant heat transfer mode inside firefighters’ clothing. In this work, Fourier transform infrared spectroscopy (FTIR) was adopted to measure the spectral transmittance and spectral extinction coefficients of four aramid fabrics with different porosity in infrared wavelength range between 2.5 and 25 μm. It was found that the radiative properties of fibrous aramid fabric are strongly dependent on its bulk density or porosity. The spectral extinction coefficient decreases with increasing porosity or decreasing bulk density. The infrared optical properties combined with infrared imaging measurements demonstrate that aramid fabric may be used as infrared semi-transparent textile. A predicted model, combined the effects of conduction-radiation heat transfer, has been developed to calculate the effective thermal conductivity of aramid fiber materials. The model implemented the Rosseland diffusion approximation to evaluate radiative thermal conductivity, and the Parallel-Series structural model to evaluate tortuosity-weighted phonic thermal conductivity. The predicted results were also compared with experimental data obtained from TPS method. This work provides useful information for future studies of heat transfer mathematical modeling of firefighters’ clothing.

On the null-controllability of a radiative heat transfer system

This paper studies the null controllability for radiative conductive convective heat transfer system in a grey, semi-transparent, scattering and bounded domain with control acting locally in a subset. The well-posedness of PDE is proved by the Banach fixed point theorem. Moreover, the null controllability proof is based on a fixed point argument and Carleman estimates in the presence of source terms, and it avoids tackling the linearized problems. Finally, a numerical experiment is included to validate the theoretical results.

Simultaneous reconstruction of thermal boundary condition and physical properties of participating medium

A hybrid optimization technique, which combines decentralized fuzzy inference method (DFIM) and sequential quadratic programming (SQP) algorithm, is developed to reconstruct the thermal boundary condition and physical properties of participating medium simultaneously. The coupled radiation-conduction heat transfer in the medium is solved by finite volume method in combination with discrete ordinate method. The reconstruction task is formulated as an inverse problem which is solved by the hybrid DFIM-SQP technique from the knowledge of surface temperature and exit radiative intensity. Retrieval results demonstrate that the time-dependent heat flux, absorption coefficient, scattering coefficient and thermal conductivity of participating medium can be accurately retrieved by the present methodology. The proposed DFIM-SQP technique is more accurate and efficient in solving the simultaneous reconstruction problem than DFIM, conjugate gradient method, SQP, particle swarm optimization and krill herd algorithms.

Transient thermal characteristics of infrared window coupled radiative transfer subjected to high heat flux

<abstract> <p>In infrared detection system on aircrafts, the infrared window, as an essential part, always faces heating condition generated by aerodynamic effects. The accurate thermal analysis can ensure the safety and reliability of internal detection system. In this work, the transient thermal characteristics of infrared window-based encapsulation structure are investigated under a high heat flux loading. The physical model of coupled radiative-conductive heat transfer in the window is established while the spectral selectivity of the window to thermal radiation is considered. The transient temperature response is used to evaluate the thermal characteristics. The effect of the radiative heat transfer is firstly analyzed and compared with the pure heat conduction model. There is a temperature deviation (74.1 K) when the radiative heat transfer is ignored. Subsequently, the transient temperature response is simulated under three different kinds of heat flux respectively. It is found that the effect of external heat flux loading is significant. The highest temperature difference reaches 32.9% (299 K) when the heat flux is reduced by 0.5 times and achieves 86.3% (794 K) when the heat flux is increased by 2.5 times. Moreover, the geometric dimensions of window (shape of a truncated cone) generate an effect on its heat transfer characteristics. The temperature decreases significantly (37.8%) when the thickness rises from 10 mm to 20 mm (<italic>r</italic> = 25 mm) while the temperature decreases relatively small (8.1%) when the radius increases from 15 mm to 45 mm (<italic>d</italic> = 15 mm). The results reveal that the radiative heat transfer in the window should be carefully considered, especially under the high heat flux loading. Additionally, reducing heat flux or thickening window can improve insulation effectiveness so as to ensure the stable working of the internal equipment.</p> </abstract>

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.

Анализ комбинированного радиационно-кондуктивного теплообмена при деструкции пористого углерод-керамического композиционного материала тепловой защиты

Carbon-ceramic composites are considered promising materials to be used in thermal protection shields of innovative descent vehicles that are currently being designed. The development of thermal shield material requires modelling its thermal-phase state under operational conditions. In this paper, physical and mathematical models are proposed for analysis of the destruction and radiation-conductive heat transfer in a porous carbon-ceramic composite material consisting of carbon fibres covered by silicon carbide. The models take into account all main physical and chemical processes of heating up and thermo-chemical destruction. A software package DMA based on the finite element method was developed, and modelling of heating up and destruction of the material was conducted. It was established that when the temperature was above 800 °С, the contribution of the radiation heat exchange became considerable. A comparison of the surface microstructures obtained through modelling and gas-dynamic testing in a plasmatron facility showed their qualitative agreement, while the mass loss did not exceed 16%.

Contribution of radiant component to thermal conductivity of the medium

Radiation-conductive heat transfer in a semi-transparent medium has been studied. Two methods for measuring thermal conductivity components are described. Thermal resistance of a remote reflecting surface, the thickness of radiation-conductive relaxation, the depth of penetration of thermal radiation, as well as radiant and conductive components of thermal conductivity of foamed polyethylene were measured using an aluminum foil radiation screen. The dependences of the total thermal conductivity of simple and aluminum-metalized polyester bulk non-woven canvases on the thickness to which it is compressed were measured. Radiant and conductive components of the thermal conductivity of non-woven material are calculated. It is shown how metal nanocoating of fibers reduces radiant thermal conductivity of the material.

Study of instability of sapphire tubes growth by Stepanov method

The paper considers the experimentally observed instability of capillary shaping during the growth of thick-walled sapphire tubes by the Stepanov method. The explanation of this phenomenon is based on the theoretical model of radiative-conductive heat transfer in a crystal. An algorithm is developed for the asymptotic expansion of the problem based on the presence of two small parameters. It is shown that the spatial density of the radiation is inhomogeneous along the cross section of the tube and is maximum near its inner walls. This leads to their overheating and the meniscus separation from the inner edges of the shaper.

Inverse extremum problem for a model of endovenous laser ablation

Abstract An inverse extremum problem (optimal control problem) for a quasi-linear radiative-conductive heat transfer model of endovenous laser ablation is considered. The problem is to find the powers of the source spending on heating the fiber tip and on radiation. As a result, it provides a given temperature distribution in some part of the model domain. The unique solvability of the initial-boundary value problem is proved, on the basis of which the solvability of the optimal control problem is shown. An iterative algorithm for solving the optimal control problem is proposed. Its efficiency is illustrated by a numerical example.

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.

Design of thermal insulation based on Open-Cell carbon materials for spacecraft

High-temperature open-cell carbon materials with a porosity between 60 and 95% are the object of study. The aim of this work is to find ways to reduce the weight of spacecraft thermal insulation due to the rational choice of porosity level and characteristic pore size of high-temperature carbon materials. This aim is achieved by building geometric models of representative volume elements of open-cell carbon materials based on Voronoi diagrams, modeling radiation-conductive heat transfer in representative volume elements of materials, theoretical calculation of thermophysical properties, and performing thermal design of the solar probe heat shield using materials of the optimized structure.

Improved teaching-learning-based optimization for estimation of temperature-dependent radiative properties of semitransparent media

Inverse estimation of temperature-dependent refractive index and absorption coefficient of semitransparent media is studied in this work. The forward transient coupled radiation-conduction heat transfer in semitransparent media is simulated by the finite volume method. The time-varying radiative response signals at the boundary (not the laser irradiation boundary) is adopted as measurement information in the inverse model. An improved teaching-learning-based optimization (ITLBO) algorithm is developed to retrieve the temperature-dependent refractive index and absorption coefficient simultaneously. Effects of model parameters (i.e. the laser heating time and measurement errors) and thermophysical parameters (i.e. the thermal conductivity and heat capacity) on the estimated results are analyzed thoroughly. All the retrieval results show that the inverse model and inverse algorithm is accurate and effective for predicting the temperature-dependent radiative properties of semitransparent media.