Inverse Heat Conduction Problem Research Articles

Estimation of the local instantaneous heat flux inside a pulsating heat pipe for space applications

Pulsating Heat Pipes (PHP) are promising and effective passive two-phase heat transfer devices in terms of high heat transfer capability, efficient thermal control, adaptability and low cost and therefore they have been extensively studied in the last years. Many authors have estimated the heat fluxes at the evaporator and at the condenser area only in terms of the average values based on first principle considerations. In the present study the application of an inverse analysis technique to experimental infrared temperature data is proposed to investigate the local convective heat flux for forced convection flow inside these devices along the adiabatic zone. A PHP specifically designed to be hosted on board the heat transfer host of the International Space Station was tested in microgravity during the 67th Parabolic Flight Campaign organized by the European Space Agency. The device consists of an aluminium tube closed in a loop with 14 turns in the evaporator section, 3 mm inner diameter, half filled with FC-72 fluid. The external temperatures of the device are measured in the adiabatic zone with a high-speed infrared camera (50 Hz, 1280x1024 pixels). The images are thereafter post-processed and adopted as input data for the solution of the inverse heat conduction problem in the pipe wall (Tikhonov regularisation method) to extrapolate time-varying local heat fluxes on the tube internal surface in contact with the fluid.

Prediction identification method of time-varying internal heat source based on inverse heat transfer problem

Purpose This paper aims to discuss the inverse problems that arise in various practical heat transfer processes. The purpose of this paper is to provide an identification method for predicting the internal boundary conditions for thermal analysis of mechanical structure. A few examples of heat transfer systems are given to illustrate the applicability of the method and the challenges that must be addressed in solving the inverse problem. Design/methodology/approach In this paper, the thermal network method and the finite difference method are used to model the two-dimensional heat conduction inverse problem of the tube structure, and the heat balance equation is arranged into an explicit form for heat load prediction. To solve the matrix ill-conditioned problem in the process of solving the inverse problem, a Tikhonov regularization parameter selection method based on the inverse computation-contrast-adjustment-approach was proposed. Findings The applicability of the proposed method is illustrated by numerical examples for different dynamically varying heat source functions. It is proved that the method can predict dynamic heat source with different complexity. Practical implications The modeling calculation method described in this paper can be used to predict the boundary conditions for the inner wall of the heat transfer tube, where the temperature sensor cannot be placed. Originality/value This paper presents a general method for the direct prediction of heat sources or boundary conditions in mechanical structure. It can directly obtain the time-varying heat flux load and thtemperature field of the machine structure.

Experimental estimation of the local heat transfer coefficient for thin liquid film evaporation in a capillary tube

• Local heat transfer coefficient was estimated for thin liquid film evaporation in a capillary tube. • Temperature infrared measurements were employed as input data of the inverse heat conduction problem. • A robust estimation procedure was adopted. • Procedure validation through the application to both synthetic and experimental data. • Original insight of thin liquid film evaporation was given. Two-phase heat transfer devices consisting of mini and microtubes represent a powerful solution to the continuous reduction of electronic components' dimensions and to the increase of the power to dissipate. Despite many studies on the two-phase heat transfer phenomenon in minitubes, most provided outcomes regarding the average heat transfer coefficient or Nusselt number. A technique to assess the local convective wall heat flux and heat transfer coefficient is proposed, validated, and then applied to the experimental case of thin-film evaporation in a heated capillary tube. The evaporation of the thin film of liquid plays a vital part in the two-phase heat transfer phenomenon inside mini/microtubes. Our study investigated this phenomenon by examining a semi-infinite slug flow. The estimation method used is represented by the inverse heat conduction problem solution in the tube wall, applying the Tikhonov regularisation method. The temperature distributions on the outer surface of the channel measured by an infrared camera were employed as input data for the inverse problem. The estimated heat transfer coefficient distributions confirm the available correlations in average values and provide insight into these complex phenomena in local and instantaneous quantities.

PHYSICS-INFORMED NEURAL NETWORK FOR INVERSE HEAT CONDUCTION PROBLEM

PHYSICS-INFORMED NEURAL NETWORK FOR INVERSE HEAT CONDUCTION PROBLEM

Data-measuring device to determine the thermophysical properties of polymer composites: information support part

This paper deals with the problem of developing an information support subsystem of the data-measuring device for determining the thermophysical properties of polymer composites during cure, designed to identify the parameters of a mathematical model necessary to optimize the curing process of composites. Methods and algorithms for processing experimental data and calculating the thermophysical properties of polymer composites, based on an integral representation of the solution of the inverse heat conduction problem and a Kalman filter, has been developed. The structure of the construction, content, goals, parameters and functionality of the basic modules of the data-measuring device application software are presented. A subsystem of informational decision-making support has been developed for choosing the optimal method and algorithm for calculating the thermophysical properties of polymer composites, which allows minimization of the errors in determining properties under given experimental conditions. The subsystem is built on the alternative use of four algorithms for calculating thermophysical properties and is included as a module into the application software of an intelligent data-measuring device for studying the process of curing polymer composites.

Using a linear inverse heat conduction model to estimate the boundary heat flux with a material undergoing phase transformation

Modeling heat conduction during steel-cooling processes is challenging because solid–solid phase transformations can take place, introducing highly non-linear phenomena to the heat equation. Using a linear model for the inverse problem can be helpful for estimating the dissipated heat flux, especially because complex phase transformations models that use empirical parameters are not always available. However, the performance and applicability of such a simplified inverse model for a strongly non-linear process is still unclear. This study presents several numerical simulations to evaluate the accuracy and limitations of solving a linear inverse heat conduction problem (i.e. constant thermophysical properties and no internal heat source) to estimate the boundary heat flux during cooling of a material undergoing phase transformations. Preliminary simulations with stable materials but with temperature-dependent thermophysical properties showed that the linear model performs well to estimate the boundary heat flux, except when the material has a highly temperature-dependent specific heat, like pure iron near its Curie temperature. Then, we performed several simulations for 42CrMo4 steel, which undergoes phase transformations and, hence, has phase- and temperature-dependent thermophysical properties and latent heat of phase transformations as an internal heat source. The latent heat has a very small effect on the heat flux estimation for fast cooling conditions; however, it can lead to an interpretation bias in medium and slow cooling conditions due to temporary underestimates of the heat flux, reaching errors up to 100%. Even when the estimated heat fluxes seem accurate (average errors smaller than 10%), further estimates of the temperature evolution or phase transformations kinetics are inaccurate (range of uncertainties as large as 200 °C and 20%, respectively) because of the phase-dependent thermophysical properties. Hence, using a linear inverse heat conduction problem for a material undergoing phase transformations is acceptable only for fast cooling conditions ( h > 1500 Wm −2 K −1 ) and exclusively to estimate the boundary heat flux without further simulations. • Numerical simulations of a coupled heat conduction-phase transformation model. • Simulated temperature data were used in a linear inverse model to estimate the heat flux. • The inverse model performs well for AISI 304 and Ni201, which do not undergo phase transformations. • For the 42CrMo4 steel, which undergoes phase transformation, it performs well only for h > 1500 Wm − 2 K − 1 . • For lower h, the latent heat plays an important role, so the simplified model is no longer acceptable.

Теплофизические характеристики стали и огнезащитных покрытий при нормированных температурных режимах пожара

PURPOSE. The article is devoted to the experimental study of thermophysical characteristics of steel on an experimental model – a metal plate of 600×600×5 mm, and to determining effective thermophysical characteristics of a fireproof coating made of a two-component epoxy composition under standardized temperature conditions. METHODS. In this work the finite element method implemented in the Ansys Mechanical software complex was applied for numerical thermotechnical calculation. The inverse heat conduction problem method was also applied for determining thermophysical characteristics of fireproof coatings. FINDINGS. As a result of the study the temperature fields were obtained in the cross section of steel structures with a fireproof coating under various fire temperature conditions. The conducted analysis showed that the discrepancies between numerical modeling and experimental data were satisfactory. RESEARCH APPLICATION FIELD. The results obtained can be applied for designing passive fire protection systems for building structures at construction facilities. As a result of the calculations, a number of values of fire resistance limits of structures with a fireproof coating from a two-component epoxy composition were obtained, taking into account the influence of standardized temperature fire regimes. All these data are put down in the tables of structures fire resistance ratings for three critical temperatures values based on which the corresponding nomograms were built. CONCLUSIONS. The study confirms the effectiveness of epoxy-based fireproof coatings to improve fire resistance of steel structures. Thermotechnical calculation and experimental modeling make it possible to determine the effectiveness of fireproof materials and justify their application in buildings and structures designed in accordance with standardized temperature fire modes requirements.

Reconstruction of the Thermal Source from the Temperature Measured Case of Surface Heat Treatment of Steel by Laser Beam

The problem posed in the surface heat treatment industry of metallic materials is the knowledge of the amount of energy required and its correct distribution on the treated surface for the achievement of a better quality of the metallurgical structure of treated parts. To succeed in this operation, manufacturers are required to carry out many expensive and time-consuming experiments. This work consists in predicting the energy density applied to the surface of a metal part, during surface heat treatment by a laser beam, based solely on temperature measurements taken under the treated surface. This problem in the mathematical sense is called the reverse heat transfer problem. The solution of this inverse problem of heat conduction allows us to predict the density of the energy necessary to be applied to the surface from the desired metallurgic structure characterized by a well-defined temperature distribution. The optimization method used in this work is that of the conjugate gradient thanks to its speed of convergence, its quality of precision and also to stability. Many similar works have been developed in the literature using the inverse method but only to estimate thermo-physical characteristics such as thermal conductivity, thermal capacity mass, point heat source, etc. using conventional numerical methods. But in no case to estimate the complex profile of an energy density applied to the real processing of steel using the conjugate gradient algorithm.

Experimental Investigations of Heat-Flux and Temperature Predictions by New Inverse Technique

This paper describes the developed method for predictions of transient internal surface temperatures and heat-flux obtained from thermocouples, which are installed through the wall of the rocket motor nozzle. Heat-Flux was estimated by using the prediction of internal surface temperatures from numerical solutions of the inverse heat conduction problem (IHCP). Three Heat-Flux gauges are manufactured and used in convergent, throat, and divergent sections. The temperatures are measured with starting operation of the rocket motor along the gauges where the thermocouples are connected to the data acquisition system interfacing with the PC. The measured unsteady temperature behavior is approximated by polynomials third degree in space and time. The measurement results indicate that the maximum reading temperatures are at the throat section. No differences in time were appearing in curves to reach maximum prediction surface temperatures.

Real-Time Solution of Unsteady Inverse Heat Conduction Problem Based on Parameter-Adaptive PID with Improved Whale Optimization Algorithm

To solve the problem of the common unsteady inverse heat conduction problem in the industrial field, a real-time solution method of improving the whale optimization algorithm (IWOA) and parameter-adaptive proportional-integral-differential (PID) is proposed in the paper. A feedback control system with IWOA-PID, which can inversely solve the boundary heat flux, is established. The deviation between the calculated temperature and the measured temperature of the measured point obtained by solving the direct heat conduction problem (DHCP) is used as the system input. The heat flux which is iteration-solved by IWOA-PID is used as system output. The method improves the initial solution distribution, global search capability and population diversity generalization of the traditional whale optimization algorithm (WOA), which effectively improves the parameter-adaptive capability of PID. The experimental results show that the solution method of inverse heat transfer proposed in the paper can accurately retrieve the variation of the boundary heat flux in real time and has good resistance and self-adaptability.

A New Approach to Identifying an Arbitrary Number of Inclusions, Their Geometry and Location in the Structure Using Topological Optimization

In the present paper, a new approach to identifying an arbitrary number of inclusions, their geometry and their location in 2D and 3D structures using topological optimization was proposed. The new approach was based on the lack of initial information about the geometry of the inclusions and their location in the structure. The numerical solutions were obtained by the finite element method in combination with the method of moving asymptotes. The convergence of the finite element method at the coincidence of functions and their derivatives was analyzed. Results with an error of no more than 0.5%, i.e., almost exact solutions, were obtained. Identification at impact on the plate temperature and heat flux by solving the inverse problem of heat conduction was produced. Topological optimization for identifying an arbitrary number of inclusions, their geometry and their location in 2D problems was investigated.

Local heat flux estimation inside tubes through conjugate gradient method with adjoint operator: application to the pulsating heat pipes case

PurposeThe purpose of this paper is to apply the conjugate gradient (CG) method, together with the adjoint operator (AO) to the pulsating heat pipe problem, including some quite interesting experimental results. The CG method, together with the AO, was able to estimate the unknown functions more efficiently than the other techniques presented in this paper. The estimation of local heat transfer coefficients, rather than the global ones, in pulsating heat pipes is a relatively new subject and presenting a robust, efficient and self-regularized inverse tool to estimate it, supported also by some experimental results, is the main purpose of this paper. To also increase the visibility and the general use of the paper to the heat transfer community, the authors include, as supplemental material, all numerical and experimental data used in this paper.Design/methodology/approachThe approach was established on the solution of the inverse heat conduction problem in the wall by using as starting data the temperature measurements on the outer surface. The procedure is based on the CG method with AO. The here proposed approach was first verified adopting synthetic data and then it was validated with real cases regarding pulsating heat pipes.FindingsAn original fast methodology to estimate local convective heat flux is proposed. The procedure has been validated both numerically and experimentally. The procedure has been compared to other classical methods presenting some peculiar benefits.Practical implicationsThe approach is suitable for pulsating heat pipes performance evaluation because these devices present a local heat flux distribution characterized by an important variation both in time and in space as a result of the complex flow patterns that are generated in this type of devices.Originality/valueThe procedure here proposed shows these benefits: it affords a general model of the heat conduction problem that is effortlessly customized for the particular case, it can be applied also to large datasets and it presents reduced computational expense.

A self-scaling sequential quasi-Newton method for estimating the heat transfer coefficient distribution in the air jet impingement

Accurate knowledge of the heat transfer coefficient (HTC) distribution is of great significance to the control and optimization of the heat transfer system in the air jet impingement. For this purpose, the estimation of the temporally-spatially varying HTC in the air jet impingement is studied based on the inverse heat conduction problem. The transient two-dimensional heat conduction model of the target disc under a single cooling air jet is established and utilized as the direct problem. A self-scaling sequential quasi-Newton method (SS-SQNM) is developed for accurately and efficiently solving the inverse problem. As a modification of the sequential quasi-Newton method (SQNM), the SS-SQNM adopts the self-scaling updating equation to accelerate the single-step convergence rate during iteration, and thus attains higher inversion efficiency than the SQNM. A series of numerical tests are carried out to investigate the performance of the SS-SQNM and the effects of the regularization parameters on inverse results. The results reveal that the SS-SQNM can give stable and accurate estimates of the HTC when regularization parameters are appropriately selected through the discrepancy principle. The mean absolute percentage error of the estimated HTC distribution is generally less than 10.2% in the presence of measurement noises. Additionally, the iteration number required by the SS-SQNM for inversion is only about 7.81%∼27.78% of that of the SQNM under the same conditions, which saves lots of computational time for the SS-SQNM. Therefore, the SS-SQNM developed in this study is a promising inverse algorithm, which can be employed to estimate the HTC distribution in the air jet impingement with reasonable accuracy and efficiency.

Volumetric heat source calibration for laser powder bed fusion

Computationally efficient models that consider only conduction are increasingly used in powder bed fusion (PBF) to predict the thermal history for relatively large build volumes. We propose a systematic method to calibrate experimentally representative heat sources for use in such models. An inverse heat conduction problem (IHCP) methodology is applied to determine the parameters that characterise a double-ellipsoid volumetric heat source, based on temperature measurements taken from the solidification boundary of the melt pool. We demonstrate that these fitted parameters follow well-defined trends across a range of laser powers and scan speeds, for melt pools in the conduction and transition modes typically used in laser PBF. Furthermore, we found that these trends in the fitted parameters are related to the energy density of the scanning laser beam, enabling an appropriate source to be calculated even at intermediate laser powers and scan speeds where calibration experiments have not been undertaken. These results enable a heat source to be selected for conduction-only models that incorporates experimentally calibrated effects such as the laser absorption and the penetration of the vapour depression into the melt pool, which are computationally expensive to calculate from first principles. The approach could also be used to characterize laser PBF systems, for example to monitor the drift in process settings that occur over time. The datasets generated and/or analysed during the current study are available in the PURE repository, with the identifier https://doi.org/10.17861/a1b95c12-5734-47f9-a469-ea75e73eb143 . • Experimental calibration of heat sources for conduction-only numerical models • Source is related to laser energy density for conduction and transition melt pools • Source can be interpolated for process settings between calibration experiments • Melt pool evolution during island scans inferred from heat source from first track

Effects of vacuum oil quenching on distortion of 42CrMo Navy C-ring

To better analyse the process parameters effects on distortion, a multi-field coupling simulation of the 42CrMo Navy C-ring vacuum oil quenching process is performed using DEFORM software. The cooling curves of different processes are measured using a stainless-steel probe, and the heat transfer coefficients are calculated by solving the inverse heat conduction problem to accurately predict the transient temperature field. The numerical analysis results demonstrate that increasing the oil temperature rarely affects the distortion. Decreasing the agitation frequency from 50 to 10 Hz can reduce the distortion by 48%. The pressure above the quenching tank has the most effect on distortion, as increasing the pressure from 10 to 50,000 Pa increases the gap by 1.5 times.

A Novel Approach for Flow Analysis in Pulsating Heat Pipes: Cross-Correlation of Local Heat Flux

Pulsating heat pipe is a promising two-phase heat transfer device that has many advantages such as a simple wickless structure and high thermal performance. Its thermal behavior is inherently time-dependent, and it can also be characterized by substantial spatial variations. However, there are few studies investigating the interaction or similarity of the local physical quantities, such as heat fluxes exchanged between the working fluid and the device wall in adjacent branches. In the present work, a new approach based on the application of cross-correlation analysis to local heat fluxes is proposed to deepen the understanding of the flow characteristics in pulsating heat pipes. The temperature distribution in the condenser of a seven-turn pulsating heat pipe was measured with an infrared camera, changing the power input. The local heat flux distributions were estimated by solving the inverse heat conduction problem in the tube wall. The cross-correlation of the heat fluxes at different positions of central and edge tubes in the condenser was analyzed. The result revealed the different trends in the cross-correlation depending on the power input: there were no clear cross-correlations in 0.5 W, while it was shown more clearly on the diagonal line with increasing power input to 2 W and 3.5 W because of the more activated flow throughout the heat pipe than that of the low power input. Moreover, the results of 3.5 W indicated a synchronized flow. It is suggested that the original approach presented in this work would lead to a deeper understanding of the chaotic fluid oscillation in pulsating heat pipes.

Novel Infrared Approach for the Evaluation of Thermofluidic Interactions in a Metallic Flat-Plate Pulsating Heat Pipe

A novel and advanced analysis tool, based on the resolution of the inverse heat conduction problem, is used to evaluate wall-to-fluid heat fluxes in a metallic flat-plate pulsating heat pipe. The device under analysis is made of copper and formed by 16 channels having a squared section of 3 × 3 mm2 and filled with a water–ethanol mixture (20 wt.% of ethanol) with a volumetric filling ratio of 50%. One flat side of the device is externally coated with a highly emissive paint to perform temperature measurements by means of a medium-wave infrared camera. The acquired infrared maps are first processed by a three-dimensional Gaussian filter and then used as inputs for the inverse approach for the evaluation of heat fluxes locally exchanged between the fluid and the thin walls of each channel. The suggested procedure is successfully validated by means of synthetic data. The resulting space–time heat flux distributions are therefore statistically investigated in terms of amplitude and space–time variations, providing quantitative references for the identification of two-phase flow regimes. These unique data give an evaluation of the local heat transfer behavior, which is essential to provide empirical values for the numerical models of pulsating heat pipes.

New graphical user interface for an application to assist solution analysis with optimization of the 1D inverse heat conduction problem

Computer applications facilitate the analysis of large amounts of information. Currently, its development is a frequent activity for various fields of knowledge. Especially for those systems under study that require optimization processes to obtain precise answers to the solution of some approach. The answers must be reliable and offered at an increasingly higher speed since decision-making may depend on them. In particular, inverse analyzes are into these concepts. These approaches are ill-conditioned, so the control efforts are robust and complex to guarantee a unique solution. Some techniques are known, but new proposals will develop. In analyzing phenomena in materials, the solution to heat transfer problems helps improve the performance of the components manufactured with them. Therefore, to understand thermal phenomena, proposals for controlled experiments are developed. Where complicated working conditions can be implemented to the extent of mastery of the solution scope of mathematical formulations, in this work, an example is presented a whose analysis of results is successfully accepted. Likewise, a platform is established to evolve to more demanding systems.

Identification of the heterogeneous conductivity in an inverse heat conduction problem

AbstractThis work deals with the problem of determining a nonhomogeneous heat conductivity profile in a steady‐state heat conduction boundary‐value problem with mixed Dirichlet–Neumann boundary conditions over a bounded domain in , from the knowledge of the state over the whole domain. We develop a method based on a variational approach leading to an optimality equation which is then projected into a finite dimensional space. Discretization yields a linear although severely ill‐posed equation which is then regularized via appropriate ad‐hoc penalizers resulting a in a generalized Tikhonov–Phillips functional. No smoothness assumptions are imposed on the conductivity. Numerical examples for the case in which the conductivity can take only two prescribed values (a two‐materials case) show that the approach is able to produce very good reconstructions of the exact solution.

A wavelet-based collocation technique to find the discontinuous heat source in inverse heat conduction problems

This paper is devoted to an inverse problem of determining discontinuous space-wise dependent heat source in a linear parabolic equation from the measurements at the final moment. In the existing literature, a considerably accurate solution to the inverse problems with an unknown space-wise dependent heat source is impossible without introducing any type of regularization method but here we have to determine the unknown discontinuous space-wise dependent heat source accurately using the Haar wavelet collocation method (HWCM) without applying the regularization technique. This HWCM is based on finite-difference and Haar wavelets approximation to the inverse problem. In contrast to other numerical techniques, in HWCM, we used Haar functions that create a well-conditioned system of algebraic equations. The proposed method is stable and convergent because the numerical solution converges to the exact solution without observing any difficulty. Finally, some numerical examples are presented to verify the validity of the HWCM for different cases of the source term.