Inverse Thermal Conductivity Research Articles

Improved Bayesian Optimization Framework for Inverse Thermal Conductivity Based on Transient Plane Source Method

In order to reduce the errors caused by the idealization of the conventional analytical model in the transient planar source (TPS) method, a finite element model that more closely represents the actual heat transfer process was constructed. The average error of the established model was controlled at below 1%, which was a significantly better result than for the analytical model, which had an average error of about 5%. Based on probabilistic optimization and heuristic optimization algorithms, an optimization model of the inverse heat transfer problem with partial thermal conductivity differential equation constraints was constructed. A Bayesian optimization algorithm with an adaptive initial population (BOAAIP) was proposed by analyzing the influencing factors of the Bayesian optimization algorithm upon inversion. The improved Bayesian optimization algorithm is not affected by the range and individuals of the initial population, and thus has better adaptability and stability. To further verify its superiority, the Bayesian optimization algorithm was compared with the genetic algorithm. The results show that the inversion accuracy of the two algorithms is around 3% when the thermal conductivity of the material is below 100 Wm-1K-1, and the calculation speed of the improved Bayesian optimization algorithm is three to four times faster than that of the genetic algorithm.

New Method for Solving the Inverse Thermal Conduction Problem (θ-Scheme Combined with CG Method under Strong Wolfe Line Search)

Most thermal researchers have solved thermal conduction problems (inverse or direct) using several different methods. These include the usual discretization methods, conventional and special estimation methods, in addition to simple synchronous gradient methods such as finite elements, including finite and special quantitative methods. Quantities found through the finite difference methods, i.e., explicit, implicit or Crank–Nicolson scheme method, have also been adopted. These methods offer many disadvantages, depending on the different cases; when the solutions converge, limited range stability conditions. Accordingly, in this paper, a new general outline of the thermal conduction phenomenon, called (θ-scheme), as well as a gradient conjugate method that includes strong Wolfe conditions has been used. This approach is the most useful, both because of its accuracy (16 decimal points of importance) and the speed of its solutions and convergence; by addressing unfavorable adverse problems and stability conditions, it can also have wide applications. In this paper, we applied two approaches for the control of the boundary conditions: constant and variable. The θ-scheme method has rarely been used in the thermal field, though it is unconditionally more stable for θ∈ [0.5, 1]. The simulation was carried out using Matlab software.

Toward the Solution of Inverse Thermal Conductivity and Thermal Elasticity Problems

Toward the Solution of Inverse Thermal Conductivity and Thermal Elasticity Problems

The Solving of the Inverse Thermal Conductivity Problem for Study the Short Linear Heat Pipes

The results of studies by solving the inverse thermal conductivity problem of the heat capacity of evaporator of the short linear heat pipes (HP’s) with a Laval nozzle-liked vapour channel and intended for cooling spacecraft and satellites with strict take-off mass regulation are presented. Mathematical formulation of the inverse problem for the HP’s thermal conductivity in one-dimensional coordinate system is accompanied by the measurement results using the monotonic heating method in a vacuum adiabatic calorimeter the HP’s surface temperatures along the longitudinal axis over the entire temperature load range, thermal resistance, and arrays of thermal power data on the evaporator Qev and vortex flow calorimeter Qcond for the condensation surface allow us to estimate the average value of the evaporator heat capacity Cev by solving the inverse thermal conductivity problem in the HP’s evaporator region. Since at the beginning of working fluid boiling for a certain time interval, the temperature of the capillary-porous evaporator remains close to constant, and with the continuation of heating and by solving the inverse thermal conductivity problem, it becomes possible to calculate the heat capacity of the working evaporator and the evaporation specific heat of the boiling working fluid and compare it with the table values.

Thermal analysis of advanced plate structures based on ceramic coating on carbon/carbon substrates for aerospace Re-Entry Re-Useable systems

The development of reusable launch vehicles (RLV) must include a significant reduction of the payload transportation costs. One of the most expensive components of a RLV is the thermal protection system (TPS), which preserves the spacecraft from the high thermal loads during re-entry. Reusability and on-orbit environment are key parameters in TPS design, mainly as far as the adopted materials are concerned. Aim of the work is to analyze a novel TPS concept, proposing an hybrid multiscale ceramic coating - i.e., alumina-based varnish enriched by silica nanoparticles - to be applied on Carbon/Carbon (C/C) plates. The treatment is aimed at preserving the thermo-mechanical properties of the ceramic substrate from the detrimental space environment conditions, such as LEO thermal cycles, outgassing due to ultra-high vacuum, as well as Atomic Oxygen/UV irradiation. Experimental measurements of the coefficient of thermal expansion (CTE) are performed in order to evaluate the thermal stress and performance of both substrate and coating layer. Particular emphasis is devoted to evaluate the effect of coating/substrate adhesion, which may result in anomalous mechanical behavior. By the use of a robust numerical technique, known as the inverse method, heat capacity and thermal conductivity are analyzed; such approach is particularly suited to address these kind of problems, as a number of physical parameters concur for a reliable determination of material properties. The special test equipment and the regularizing algorithm for solving the heat conduction problem are described. After thermal conditioning, the integrity of coating and substrate is investigated by full morphological analysis using SEM/EDX techniques.

ОЦІНЮВАННЯ ВОГНЕСТІЙКОСТІ ВОГНЕЗАХИЩЕНИХ СТАЛЕВИХ КОНСТРУКЦІЙ

Purpose. Evaluation of fire resistance of fire-resistant steel structures using the developed calculation and experimental method. Methods. Finite difference method, landfill fire test method, mathematical and computer modeling of non-stationary heat exchange processes, determination of thermophysical characteristics of fire-retardant coatings based on solving direct and inverse thermal conductivity problems. Results. Geometric, physical, computer models have been developed, with the help of which the fire resistance of fire-resistant steel structures has been evaluated by the calculation-experimental method. The adequacy of the developed method for assessing the fire resistance of fire-resistant steel structures in assessing the fire resistance of fire-resistant I-beam steel column has been checked. The analysis of tests on fire resistance of fire-resistant steel columns exposed to fire at the standard temperature of the fire without the load applied to them has been carried out. A computer model of the “steel column – reactive flame retardant coating” system has been built for numerical simulation of non-stationary heating of such a system. The fire resistance of fire-resistant steel columns of I-beam section without load applied to them has been evaluated using the calculation-experimental method. Verification of results of experimental research with results of numerical modeling has been carried out. Scientific novelty. The convergence of the results of experimental data on the duration of fire exposure at the standard temperature of the fire to reach the critical temperature of steel with the results of numerical simulations has been determined. Based on the comparison of the experimental results and numerical modeling, the adequacy of the developed model to the real processes that occur when heating fire-retardant steel columns without applying a load under fire conditions at a standard fire temperature has been confirmed. The efficiency of the proposed calculation and experimental method for assessing the fire resistance of fire-resistant steel structures has been confirmed. Practical significance. It consists in the implementation of the results on objects of different purposes in assessing the fire resistance of fire-resistant steel structures by evaluating the effectiveness of fire-retardant coatings of steel building structures.

A Method for Quantitative Interpretation of Stationary Thermal Fields for Layered Media

A new method to solve thermal conjugacy problems is presented for layered models with a thermal conductivity jump at their boundaries. The purpose of this method is to approximate the inverse thermal conductivity coefficient, which has breaks, by using a combination of step functions. A generalized continuous operator is constructed in a continuous space of piecewise–homogeneous media. We obtained an analytical solution for the stationary problem of heat conjugacy in the layered model with finite thickness and with Dirichlet–Neumann conditions at the external boundaries. An algorithm was constructed for downward continuation of the heat flux to depths that correspond to the top of the mantle layer. The advantages of this method are illustrated by testing the crustal seismic, gravity and geothermal data of a study area in the Urals and neighboring regions of Russia. We examined statistical relations between density and thermal parameters and determined heat flux components for the crust and the mantle. The method enables a downward continuation of the heat flux to the base of the upper mantle and allows us to determine the thermal effects of the lateral and vertical features of deep tectonic structures.

Thermal Conductivity of Defective Graphene Oxide: A Molecular Dynamic Study.

In this paper, the thermal properties of graphene oxide (GO) with vacancy defects were studied using a non-equilibrium molecular dynamics method. The results showed that the thermal conductivity of GO increases with the model length. A linear relationship of the inverse length and inverse thermal conductivity was observed. The thermal conductivity of GO decreased monotonically with an increase in the degree of oxidation. When the degree of oxidation was 10%, the thermal conductivity of GO decreased by ~90% and this was almost independent of chiral direction. The effect of vacancy defect on the thermal conductivity of GO was also considered. The size effect of thermal conductivity gradually decreases with increasing defect concentration. When the vacancy defect ratio was beyond 2%, the thermal conductivity did not show significant change with the degree of oxidation. The effect of vacancy defect on thermal conductivity is greater than that of oxide group concentration. Our results can provide effective guidance for the designed GO microstructures in thermal management and thermoelectric applications.

Heat flow map and geothermal resources in Mexico

Heat flow maps are a powerful tool for regional exploration of geothermal resources. Mexico is one of the main producers ofgeothermal energy and the search for undiscovered resources at a regional level should be based on heat flow values. Here, we
 present a heat flow map at 1:4,000,000 scale, produced with heat flow data compiled from open data bases and previously unpub-lished data. The compiled heat flow data includes bottom hole temperature, temperature logs, transient temperature measurements
 and measured temperature logs. The new data were calculated from temperature gradient information and estimating a mean con-ductivity value characteristic for the type of rock present in the stratigraphic column or assigning the mean conductivity value for
 the crust. Geothermal gradient and the thermal resistivity (inverse thermal conductivity) were plotted and heat flow was calculatedusing the Bullard method. The map covers the whole continental territory of Mexico and shows that most of the country has valueshigher than the world average. The highest heat flow values are concentrated in two provinces: the Gulf of California extensionalprovince and the Trans-Mexican Volcanic Belt.

Filler free technology for enhanced thermally conductive optically transparent polymeric materials using low thermally conductive organic linkers

This work presents for the first time a non-conventional technology for higher thermally conductive optically transparent polymeric material by employing lower thermally conductive organic molecules. In last couple of decades, practically all work on thermally conductive polymer based materials has been mainly confined to conventional polymer-filler composites which comes with various challenges like high loading, expensive fillers, etc., in addition to pronounced phonon scattering at filler-polymer interface. In this work, we have thrown light on alternating yet promising strategy for thermally conductive polymer based materials without incorporating any traditional metallic, ceramic or carbon fillers. One of the fascinating fact is the achievement of effective higher thermal conductivity in spite of using constituent components with lower thermal conductivity. This was achieved by rationally designed polymer-organic molecules system where thermal conduction was induced by engineering intermolecular interaction within the polymer chain. Additionally, these materials were optically transparent. Apart from presenting these new classes of materials, this study generates some of the prominent fundamental understanding on the heat transport of polymers. Short chains of diethylene glycol (DEG) were incorporated into base polymer matrix of polyvinyl alcohol (PVA) which lead to remarkable thermal conductivity enhancement of 260% and 175% than DEG and neat PVA respectively. Phonon transport was driven by the “thermal bridges” designed through intermolecular hydrogen bonding between PVA and DEG. A further impact of the length of “thermal bridges” and its functional groups (hydroxyl, carboxyl, carbonyl) at terminal position were investigated. It was found that shorter organic molecules are more efficient in driving thermal conduction owing to less inter-chain resistance. Interestingly, these materials were found to have inverse thermal conductivity–crystallinity relationship which is usually an opposite trend to the present belief. Overall, it was found that size, molecular geometry, terminal functional group of the thermal bridging chain in host polymer are very crucial factors in determining thermal conductance. Overall, this work demonstrates an intriguing tale of engineering intermolecular interaction in polymer based material for the development of thermally conductive and optically transparent materials for thermal management applications.

Temperature-dependent anisotropic bodies thermal conductivity tensor components identification method

This paper describes a new method of solving of inverse coefficient thermal conductivity problems in anisotropic bodies directed on the identification of temperature dependences of thermal conductivity tensor components. This method includes the following: quadratic residue construction between testing and theoretical temperature values, minimized gradient descent implicit method, parametric identification method, construction and numerical solution of conjugate problems relating to anisotropic thermal conduction, regularizing functional development based on prior assumptions on smoothness of temperature functions of thermal conduction components of anisotropic bodies, permitting to increase the whole method stability. Basing on this method many results were found relating to the identification of thermal conduction tensor components depending on temperature in the form of practically arbitrary functions: monotonous functions, having minimum and maximum points, flex points, etc.

Numerical simulation of laser-supported combustion wave induced by millisecond-pulsed laser on aluminum alloy

In this paper, the energy transmission of a laser-supported combustion wave (LSCW) is numerically studied, which includes inverse bremsstrahlung, thermal conduction and convection. A physical model is established to simulate an LSCW induced by millisecond-pulsed laser on aluminum alloy. This physical model is a 2D axis-symmetric numerical model of radiation gas dynamics. Moreover, the simulation focuses on the interaction process in different laser conditions such as various pulse widths and peak energies. As a result, the speed of the LSCW increases by increasing the laser energy while keeping the laser pulse constant, whereas the speed is reduced by increasing the laser pulse width while keeping the laser energy constant. After a comparison of the theoretical, numerical and experimental results, analyses are performed while the experimental results are explained reasonably. Furthermore, the consistency between the numerical and experimental results implies that the numerical calculation model used in this paper can describe the motion of the LSCW of the millisecond-pulsed laser on aluminum alloy very well.

Unsteady heat transfer during subcooled film boiling

Cooling of high-temperature bodies in subcooled liquid is of importance for quenching technologies and also for understanding the processes initiating vapor explosion. An analysis of the available experimental information shows that the mechanisms governing heat transfer in these processes are interpreted ambiguously; a more clear-cut definition of the Leidenfrost temperature notion is required. The results of experimental observations (Hewitt, Kenning, and previous investigations performed by the authors of this article) allow us to draw a conclusion that there exists a special mode of intense heat transfer during film boil- ing of highly subcooled liquid. For revealing regularities and mechanisms governing intense transfer of energy in this process, specialists of Moscow Power Engineering Institute’s (MPEI) Department of Engineering Thermal Physics conduct systematic works aimed at investigating the cooling of high-temperature balls made of different metals in water with a temperature ranging from 20 to 100°C. It has been determined that the field of temperatures that takes place in balls with a diameter of more than 30 mm in intense cooling modes loses its spherical symmetry. An approximate procedure for solving the inverse thermal conductivity problem for calculating the heat flux density on the ball surface is developed. During film boiling, in which the ball surface temperature is well above the critical level for water, and in which liquid cannot come in direct contact with the wall, the calculated heat fluxes reach 3–7 MW/m2.

Cuboids of Infrared Images Reduction

The main idea of this scientific article is tomography usage. Projections of multidimensional signal carrying the information about the spatial structure of objects' thermal physic properties are represented by thermal tomograms obtained in active mode of test material surface heating by infrared radiation. Processing of a thermal tomogram is produced by solving the inverse thermal conductivity problem. This solution applies to cuboids of infrared images reduction class of problems. Because of reduction, we get the distribution image of thermal conductivity identified values on isotropic material surface (thermal tomogram) allowing revealing foreign inclusions in the heterogeneous object structure based on the contrast over thermal conductivity. Implementation of this idea is associated with certain difficulties due to the necessity of mathematical modeling of nonlinear thermal transients. The paper presents quartz sand thermal tomograms with temperature conductivity of 9 10-7 m2 s and thermal conductivity of -1 0.9 W m-1 K-1 which structure contains thermal insulation material - expanded foam, and thermally conductive material - aluminum.

On inverse boundary thermal conductivity problem of recovery of heat fluxes to the boundaries of anisotropic bodies

A method for solution of the inverse boundary thermal conductivity problem of recovery of the heat fluxes to the structural components of aircraft fabricated of anisotropic materials is proposed. The method is based on a previously obtained analytical solution of a 2D nonstationary thermal conductivity problem in an anisotropic fin under boundary heat transfer. The method consists in parametric identification and finite-element approximation of the dependence of the heat flux on the spatial variable. A regularizing algorithm is developed that permits identification of heat fluxes with large, up to 10%, errors in the experimental temperature values. The results obtained in numerical experiments are analyzed.

Comparative studies of the thermal conductivity of spinel oxides with orbital degrees of freedom

We studied the thermal conductivity of various transition-metal oxides with the spinel structure $({\mathrm{MnV}}_{2}{\mathrm{O}}_{4}$, ${\mathrm{FeV}}_{2}{\mathrm{O}}_{4}$, ${\mathrm{CoV}}_{2}{\mathrm{O}}_{4}$, and ${\mathrm{Mn}}_{3}{\mathrm{O}}_{4})$ upon varying the temperature and magnetic field. We found that for the spinel oxides having ${\mathrm{V}}^{3+}$ ions (two electrons in the ${t}_{2g}$ states) at the octahedral site, the orbital ordering suppresses the thermal resistivity (inverse thermal conductivity) in contrast to purely magnetic ordering, indicating that the orbital fluctuation of the V ${t}_{2g}$ states is the main factor affecting the thermal conductivity. On the other hand, for ${\mathrm{Mn}}_{3}{\mathrm{O}}_{4}$, which has ${\mathrm{Mn}}^{3+}$ ions (one electron in the ${e}_{g}$ states) at the octahedral site, the thermal resistivity is suppressed in association with the successive magnetic phase transitions with decreasing temperature and increasing magnetic field. This can be explained by the frustration of ${\mathrm{Mn}}^{3+}$ spins and the fluctuation of ${\mathrm{Mn}}^{3+}$ ${e}_{g}$ orbitals.

A methodology for solving inverse coefficient problems of determining nonlinear thermophysical characteristics of anisotropic bodies

A methodology is proposed for solving inverse coefficient thermal-conductivity problems of defining the thermal-conductivity tensor components that depend on the temperature by introducing a quadratic residual functional, its linearization, a minimization iteration algorithm, and a method of parametric identification considering errors in determining the experimental temperature values. The existence and uniqueness of the solution to inverse coefficient problems of nonlinear thermal conductivity in anisotropic bodies at moderate constraints on the descent parameters and the sensitivity matrix norms are proven. The results obtained for carbon-carbon composites support the entire methodology for numerical solution to inverse coefficient problems with an allowable error of the experimental temperature values. The proposed methodology can be applied to define both linear and nonlinear characteristics of anisotropic heat-protection materials used in aircraft and space engineering.

Energy transport of laser-driven moving optical discharge in air

The processes of energy transport in a laser-driven moving optical discharge (LMOD), which include inverse bremsstrahlung, thermal conduction and convection, are numerically studied. And their roles in the maintenance of plasma and the motion of LMOD are discussed. A two-dimensional axis-symmetric numerical model of radiation gas dynamics is introduced to simulate the LMOD. The results indicate that the energy exchanges caused by thermal radiation and inverse bremsstrahlung are the dominant factors in the maintenance of plasma, and that the dominant factor governing the motion of LMOD is the reabsorption of vacuum ultraviolet radiation from plasma core ahead of the front of LMOD.

Numerical solution of some inverse nonstationary thermal conduction problems using pseudoinverses

Systems of linear algebraic equations that allow solving inverse linear diffusion problems in a finite number of arithmetic operations are derived. They can be solved by using pseudoinversion.

1064 赤外線サーモグラフィによる温度場計測に基づく塑性域同定(J09 逆問題解新手法の開発と最新応用,ジョイントセッション,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

Plastic zone identification was conducted by 2f lock-in technique, in which temperature change due to plastic heat generation was separately identified from thermoelastic temperature change under variable loading. Accuracy improvement was performed using motion compensation based on modified digital image correlation, inverse thermal conduction analysis and noise reduction based on mollification method.