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Direct heat transfer problems can be solved analytically or numerically to predict the temperature profile when the thermal properties, boundary conditions, and other relevant parameters are known. Though it is common practice to measure temperature experimentally, heat transfer parameters and boundary conditions are more challenging to measure and can instead be inferred through the use of inverse heat transfer (IHT) techniques, which can be solved through optimization. In this study, the IHT method with the conjugate gradient method is used to determine the energy consumption of bread during the cooking process in a developed baking oven with and without a reflector. A complex variable differentiation method is integrated to calculate the accurate sensitivity coefficient matrix. The results demonstrated that the estimated heat flux is very close to the exact heat flux and relative error is less than measurement errors. [ABSTRACT FROM AUTHOR]

With the development of intelligent manufacturing technology, robots have become more widespread in the field of milling processing. When milling difficult-to-machine alloy materials, the localized high temperature and large temperature gradient at the front face of the tool lead to shortened tool life and poor machining quality. The existing temperature field reconstruction methods have many assumptions, large arithmetic volume and long solution time. In this paper, an inverse heat conduction problem solution model based on Gated Convolutional Recurrent Neural Network (CNN-GRU) is proposed for reconstructing the temperature field of the tool during milling. In order to ensure the speed and accuracy of the reconstruction, we propose to utilize the inverse heat conduction problem solution model constructed by knowledge distillation (KD) and compression acceleration, which achieves a significant reduction of the training time with a small loss of optimality and ensures the accuracy and efficiency of the prediction model. With different levels of random noise added to the model input data, CNN-GRU + KD is noise-resistant and still shows good robustness and stability under noisy data. The temperature field reconstruction of the milling tool is carried out for three different working conditions, and the curve fitting excellence under the three conditions is 0.97 at the highest, and the root mean square error is 1.43°C at the minimum, respectively, and the experimental results show that the model is feasible and effective in carrying out the temperature field reconstruction of the milling tool and is of great significance in improving the accuracy of the milling machining robot. [ABSTRACT FROM AUTHOR]

HFITS is a software tool that supports experimental measurements of heat flux over planar surfaces using infrared thermography. This technique enables spatially and temporally resolved heat flux measurements at a higher resolution than arrays of traditional point sensors. The target audience is researchers and engineers in thermal engineering disciplines. Developed in Python with a graphical front end, the software is accessible both to advanced users as well as to users with a more fundamental knowledge of complex thermogram manipulation and heat transfer analysis methods. HFITS consists of two main components: pre-processing of infrared thermograms (obtained from heat transfer experiments), and inverse heat transfer analysis (to deduce heat flux over the planar surface in those experiments). The software offers comprehensive functionalities, including support for metadata handling, a graphical interface for selection of regions of interest, the ability to import additional temperature measurements to enhance convective heat transfer estimates, and the exporting of both computed field data and contour videos. This open-source software broadens access to advanced experimental and analytical techniques to support thermal analyses in a wide range of engineering and research applications.

The technology for obtaining sorbite by isothermal quenching of high-temperature molten salt has been used by more and more factories to produce wires with high tensile strength. In this paper, the controlling cap and bottom pipeline of the original salt bath are redesigned. The mathematical model previously proposed is used to simulate the redesigned salt bath model, and the flow field is analyzed in detail. The redesigned and original controlling cap are compared in detail by applying third-generation vortex identification technology. Then, by using the inverse heat transfer method, the heat transfer coefficient (HTC) during the boiling heat transfer stage of the wire rod in molten salt is calculated by taking advantage of quenching experimental data, on the basis of which the original model is corrected. Finally, a new salt bath design is proposed, which divides the salt bath into two parts. The first salt bath at 515 °C is used to cool the austenitized wire and complete the initial phase transformation. The second salt bath at 560 °C is used to prevent the transformation from retained austenite to bainite, and to induce its transformation from retained austenite to sorbite. [ABSTRACT FROM AUTHOR]

Objective. Thermal property (TP) maps of human tissues are useful for tumor treatment and diagnosis. In particular, the blood perfusion rate is significantly different for tumors and healthy tissues. Noninvasive techniques that reconstruct TPs from the temperature measured via magnetic resonance imaging (MRI) by solving an inverse bioheat transfer problem have been developed. A few conventional methods can reconstruct spatially varying TP distributions, but they have several limitations. First, most methods require the numerical Laplacian computation of the temperature, and hence they are sensitive to noise. In addition, some methods require the division of a region of interest (ROI) into sub-regions with homogeneous TPs using prior anatomical information, and they assume an unmeasurable initial temperature distribution. We propose a novel robust reconstruction method without the division of an ROI or the assumption of an initial temperature distribution. Approach. The proposed method estimates blood perfusion rate maps from relative temperature changes. This method avoids the computation of the Laplacian by using integral representations of the Helmholtz decomposition of the heat flux. Main Result. We compare the reconstruction results of the conventional and proposed methods using numerical simulations. The results indicate the robustness of the proposed method. Significance. This study suggests the feasibility of thermal property mapping with MRI using the robust proposed method. [ABSTRACT FROM AUTHOR]

In this work, we consider the problem of recovering the heat source term for the heat equation with a nonlocal Wentzell-Neumann boundary condition subject to an integral overdetermination condition. Conditions for the existence and uniqueness of the classical solution of the inverse problem are revisited, and a numerical method for practical source reconstruction is introduced. Unlike all of the source reconstruction methods found in literature, the method introduced in this work computes regularized solutions from a triangular linear system arising from a semi-discretization in the space of the continuous model. Regularization is introduced by applying the generalized singular value decomposition of a proper matrix pair along with truncation. Numerical results illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

The technology for obtaining sorbite by isothermal quenching of high-temperature molten salt has been used by more and more factories to produce wires with high tensile strength. In this paper, the controlling cap and bottom pipeline of the original salt bath are redesigned. The mathematical model previously proposed is used to simulate the redesigned salt bath model, and the flow field is analyzed in detail. The redesigned and original controlling cap are compared in detail by applying third-generation vortex identification technology. Then, by using the inverse heat transfer method, the heat transfer coefficient (HTC) during the boiling heat transfer stage of the wire rod in molten salt is calculated by taking advantage of quenching experimental data, on the basis of which the original model is corrected. Finally, a new salt bath design is proposed, which divides the salt bath into two parts. The first salt bath at 515 °C is used to cool the austenitized wire and complete the initial phase transformation. The second salt bath at 560 °C is used to prevent the transformation from retained austenite to bainite, and to induce its transformation from retained austenite to sorbite.

The objective of an inverse heat transfer problem is to address unknown parameters or boundary conditions using the temperature distributions obtained from measurement. While several approaches are proposed specifically for this purpose, utilizing deep learning algorithms has proved to produce promising results in such regression problems. In order to compare the effectiveness and efficiency of a developed deep learning model and two efficient inverse heat transfer techniques in determining the convective heat transfer coefficient and the generated temperature of an industrial heat gun, several experiments have been conducted. The experiments involved measuring the temperature at two specified points of two aluminum and steel rods heated by the given heat gun from various distances for greater comparability. The deep learning model is developed based on recently proposed one-dimensional convolutions and is trained by the results of direct numerical solution (with the target parameters as labels and their resulting temperature distributions as training data). This is to the best of the authors knowledge the first work using one-dimensional deep learning architectures in inverse heat transfer analysis. The results show that while the chosen inverse heat transfer methods produce similar results, the Levenberg–Marquardt method converges considerably faster (with a convergence rate of up to 7 times higher), especially in cases, where its initial guess requires more correction in order to yield the desired result. Furthermore, the temperature distributions obtained from the estimated parameters of all three approaches are in close agreement with the measured temperature profiles. [ABSTRACT FROM AUTHOR]

In this study, the unknown boundary heat fluxes in a square enclosure containing a cylinder were estimated by an inverse technique. A series of computations was conducted for the two-dimensional, steady-state, and buoyancy-driven heat transfer in a square section containing a cylinder with variable heat fluxes and at a Rayleigh number (Ra) of 106 and Prandtl number (Pr) of 0.7. The generated datasets were used to construct a physics-based neural network, which acted as a proxy model for natural convection to reduce the computational time for inverse estimation. The trained network was embedded in a genetic algorithm and Bayesian framework to estimate the boundary conditions of the heat fluxes from synthetic experimental temperatures. The results indicated that the genetic algorithm accurately predicted the heat flux, but the estimation failed with increasing measurement error/noise. The solutions of the genetic algorithm were then used as informative priors for the Bayesian framework, which outperformed the genetic algorithm at estimating unknown boundary heat fluxes with measurement noise. The estimated heat fluxes were then used as input for the direct problem and investigated the thermal and flow characteristics in an enclosure containing a cylinder. [ABSTRACT FROM AUTHOR]

The present work provides an experimental and numerical procedure to obtain the geometrical position of the hotspots of a microprocessor using the thermal images obtained from the transient thermal response of this processor subject to pulsating stress tests. This is performed by the solution of the steady inverse heat transfer problem using these thermal images, resulting in qualitative heat source distributions; these are analyzed using the mean heat source gradients to identify the elements that can be considered hotspots. This procedure identified that the processor INTEL Core 2 Quad Q8400S contains one hotspot located in the center of its left die and four hotspots located near the lower left corner of its right die, which is consistent with the thermal response obtained for both the stress test applied to each core of this processor and the stress test applied to all of its cores. [ABSTRACT FROM AUTHOR]

In aerospace industry, turbine engine blades made of nickel-based superalloys are commonly machined by creep-feed grinding processes. In order to pre-design grinding processes and avoid grinding burn, a method for calibrating a thermal finite element model was developed. For this purpose, the heat flux distribution and heat partition were evaluated by solving an optimization problem with the BOBYQA algorithm. A heat flux distribution differing from the frequently used triangular distribution was found and, further, a regression model estimating the heat partition was calibrated. The findings were compared to the experimental results, which showed a good agreement of the transient temperatures and maximum temperature rise. Subsequently, the findings were transferred to the grinding process of a fir tree profile. [ABSTRACT FROM AUTHOR]

In this article, the decentralized fuzzy inference method (DFIM) is applied to reconstruct the distributions of surface laser power and internal temperature of the biological tissue during laser-induced thermal therapy. The Pennes bioheat equation is used to describe the heat transfer in the tissue with laser irradiation, and it is solved by finite volume method. The reconstruction task is formulated as an inverse problem which is solved by the DFIM. Reconstruction results demonstrate that the DFIM can accurately reconstruct the surface laser power and internal temperature distribution of the tissue. Furthermore, the influences of the number of measurement points, laser irradiance form and measurement error on reconstruction results are discussed. Retrieval results showed that the DFIM is robust to reconstruct different forms of laser irradiances and internal temperature fields, even with noisy data. [ABSTRACT FROM AUTHOR]

The hardness and phase composition are, among other things, the critical material properties considered in the quality control of aerospace gears made from Pyrowear 53 steel after high-pressure gas quenching. The low availability of data on and applications of such demanding structures justify investigating the choice of the material and the need to improve its manufacturability. In this study, computational finite-element analyses of low-pressure carburizing followed by oil and gas quenching of Pyrowear 53 steel were undertaken, the objective of which was to examine the influence of the process parameters on the materials' final phase composition and hardness. The material input was prepared using JMatPro. The properties computed by the CALPHAD method were calibrated by the values obtained from physical experiments. The heat transfer coefficient was regarded as an objective variable to be optimized. A 3D model of the Standard Navy C-ring specimen was utilized to predict the phase composition after the high-pressure gas quenching of the steel and the hardness at the final stage. These two parameters are considered good indicators of the actual process parameters and are used in the industry. The results of the simulation, e.g., optimized heat transfer coefficients, cooling curves, and hardness and phase composition, are presented and compared with experimental values. The accuracy of the simulation was validated, and a good correlation of the data was found, which demonstrates the quality of the input data and setup of the numerical procedure. A computational approach to heat treatment processes' design could contribute to accelerating new procedures' implementation and lowering the development costs. [ABSTRACT FROM AUTHOR]

Radiative heating furnaces are widely used for heat treatment applications in manufacturing industries. Strict requirements on heat treatment characteristics of the workpieces require precise control of furnace heater temperatures. Numerical techniques for the solution of inverse heat transfer problems can be used for the optimization of the radiant heater temperatures. In gradient-based optimization techniques, the optimization is carried out using the sensitivity coefficients between the heater and workpiece temperatures. In this study, we present a methodology for calculating the sensitivity coefficients for the solution of inverse boundary design problems involving transient heating of solid workpieces in a three-dimensional radiant furnace. In our methodology, the sensitivity coefficients on the selected design points within the workpieces are calculated by analytical differentiation of design point temperature formulations derived utilizing the floating random walk method and radiative heat flux formulation with exchange factors. The methodology for calculating sensitivity coefficients has been verified through applications to both a one-dimensional scenario and the three-dimensional radiant furnace model. The developed methodology was integrated into a gradient-based optimization algorithm in two test cases, to determine the furnace heater temperatures required to achieve the desired temperature histories at design points within the workpieces. First test case focuses reconstruction of an assumed heater temperature and examines the impact of design point configuration and input data noise on convergence behavior and calculated estimation. The findings reveal that increasing the number of design points in the workpieces increases solution accuracy, with transverse positioning of the design points in the workpieces resulting in heater temperatures closest to the assumed values. Second test case focused on estimating required heater temperatures for spatially uniform heating pattern on the workpieces. With 72 transversely positioned design points, we achieved uniform heating at these points with a maximum relative temperature deviation of 0.26%. • Sensitivity coefficient calculation methodology in gradient-based optimization. • Developed an inverse methodology to estimate furnace heater temperatures. • Design condition defined at design points within workpieces. • Demonstrated the impact of design point layouts on convergence and estimation. • Required heater temperatures for uniform heating show checkerboard-like pattern. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In orthopedic surgery, the drilling process is used to internally fix the fracture zone. During bone drilling, if the temperature exceeds the limit of 47 °C, it results in altered bone alkaline phosphatase nature, occurrence of thermal necrosis, non-fixation and inadequate bone fusion In order to investigate the effective parameters of the drilling process, after three-dimensional modeling of the femur bone in Mimics software and determination of bone coefficients based on the Johnson-Cook model, numerical simulation of the cortical and trabecular bone oblique drilling process have been performed. The drilling process was performed in both normal and high speed modes based on reverse heat transfer theory using DEFORM-3D software. The results of numerical simulation after validation with experimental results showed that this theory is capable of estimating the temperature and heat flux in this process and the occurrence of necrosis in both processes (normal and high speed) is imminent. The temperature in the drilling area of the trabecular bone is higher than the cortical bone at all speeds and feed rates and the axial force of the trabecular bone is less than the cortical bone at all speeds and feed rates. The optimum point leading to the minimum temperature in normal drilling of trabecular and cortical bone is the feed rate of 150 mm/min and the rotational speed of 2000 rpm. This optimum point is obtained in the high-speed drilling of trabecular and cortical bone at the feed rate of 150 mm/min and rotational speed of 4,000 rpm and 7,000 rpm. [ABSTRACT FROM AUTHOR]

In this study, a combined method of Kalman filter (KF) and fuzzy logic is presented to solve the inverse problem of heat transfer in a R920K brake disc. The proposed algorithm uses the temperature data from a set of sensors for real-time reconstruction of the temperature field and the time-varying boundary heat flux for 10 different locomotive braking scenarios. The results show that the adaptive fuzzy type 2 Kalman filter (AFT2KF) algorithm is accurate and stable in estimating the temperature field and boundary heat flux. The use of adaptive fuzzy type 1 Kalman filter (AFT1KF) also significantly reduces the estimation error compared to the KF algorithm. The results show that the use of adaptive methods increases the time for parameter estimation compared to the KF algorithm, however can still be considered as real-time estimation. The performance of the AFT2KF method in parameter estimation is better than that of KF and AFT1KF, so it reduces the error in heat flux estimation by more than 80% compared to KF. [ABSTRACT FROM AUTHOR]

Inverse heat transfer problems are ill-posed problems and their solution is challenging. Conventional (hard computing) solution methods were developed for this purpose in the past, but they are not well applicable in cases including phase change, which contain strong non-linearity and bring additional computational difficulties. Soft computing methods, which currently experience very rapid development, are a promising tool for the solution of such problems. This paper addresses an inverse heat transfer problem with phase change, in which the boundary heat flux is estimated. Four methods based on distinct mathematical principles are applied to this problem and thoroughly compared. These methods include a conventional Levenberg–Marquardt method (LMM), a predictive fuzzy logic (PFL)-based method, a population-based meta-heuristic method called LSHADE (a state-of-the-art differential evolution variant), and a recently developed surrogate-assisted method coupled with differential evolution, referred to as LSADE method. Furthermore, a reformulation of the problem was developed, utilising a dimension reduction scheme and a decomposition scheme that led to sub-problems with different time frames. This reformulation brought extensive computational improvements. Results of the comparison of the methods then showed that the LMM and the PFL behave well in case without phase change but their performance deteriorates substantially in case with phase change. The LSHADE and the LSADE showed superior performance in the solution of the inverse problem with the phase change. Moreover, their performance was rather stable and insensitive to the location of the temperature sensor, which was the source of data for the estimation. • Inverse heat transfer problem with and without phase change was addressed. • Boundary heat flux was inversely identified from temperature readings. • Four solution methods were investigated and compared to each other. • Levenberg–Marquardt method (LMM) suffered from low performance due to non-linearity. • LSHADE and LSADE methods significantly outperformed LMM and fuzzy logic. [ABSTRACT FROM AUTHOR]

To deal with inverse nonlinear heat transfer problems in a two-dimensional heat conduction problem, this paper presents a hybrid approach combining fuzzy logic and the extended Kalman filter (EKF). The proposed algorithm has been applied to the real-time reconstruction of the temperature field, time-varying convective heat transfer coefficient, and time-varying boundary heat flux using temperature data from a set of sensors. The effects of the covariance of the initial estimation error, the time step of data acquisition by the sensors, and the number of installed sensors on the precision and stability of the estimation results has been investigated by numerical experiments. To compare and validate the results, all these parameters were investigated using the EKF method. The results show that the adaptive fuzzy extended Kalman filter (FEKF) method for estimating temperature, convection coefficient, and heat flux at the boundaries is precise and stable. The comparison shows that the performance of the FEKF method in parameter estimation is better than the EKF method, and the highest increase in precision and stability of the results is related to the convective heat transfer coefficient. [ABSTRACT FROM AUTHOR]

Accurate prediction of an off-normal event in a nuclear reactor is dependent upon the availability of sensory data, reactor core physical condition, and understanding of the underlying phenomenon. This work presents a method to project the data from some discrete sensory locations to the overall reactor domain during conduction cooldown scenarios similar to High Temperature Gas-cooled Reactors (HTGRs). The existing models for conductive cooldown in a heterogeneous multi-body system, such as an assembly of prismatic blocks or pebble beds relies on knowledge of the thermal contact conductance, requiring significant knowledge of local thermal contacts and heat transport possibilities across those contacts. With a priori knowledge of bulk geometry features and some discrete sensors, a machine learning approach was devised. The presented work uses an experimental facility to mimic conduction cooldown with an assembly of 68 cylindrical rods initially heated to 1200 K. High-fidelity temperature data were collected using an infrared (IR) camera to provide training data to the model and validate the predicted temperature data. The machine learning approach used here first converts the macroscopic bulk geometry information into Graph-Laplacian, and then uses the eigenvectors of the Graph-Laplacian to develop Kernel functions. Support vector regression (SVR) was implemented on the obtained Kernels and used to predict the thermal response in a packed rod assembly during a conduction cooldown experiment. The usage of SVR modeling differs from most models today because of its representation of thermal coupling between rods in the core. When trained with thermographic data, the average normalized error is less than 2 % over 400 s, during which temperatures of the assembly have dropped by more than 500 K. The rod temperature prediction performance was significantly better for rods in the interior of the assembly compared to those near the exterior, likely due to the model simplification of the surroundings. [ABSTRACT FROM AUTHOR]

For the first time, a numerical solution code, based on Levenberg–Marquardt method is presented for solving non-linear problem of inverse heat transfer in axisymmetric stagnation flow impinging on a cylinder rod to determine time-dependent wall temperature by temperature distribution at a specific point in the fluid region. Also, the effect of noisy data on the final result has been studied. For this purpose, the numerical solution of the dimensionless temperature and the convective heat transfer in a radial incompressible flow on a cylinder axis is carried out as a direct problem. In the direct problem, the free stream is steady with an initial flow strain rate of k ¯ . Using similarity variable and appropriate transformations, momentum and energy equations are converted into semi-similar equations. The new equation systems are then discretized using an implicit finite difference method and solved by applying the tridiagonal matrix algorithm (TDMA). The wall temperature is then estimated by applying the Levenberg–Marquardt parameter estimation approach. This technique is an iterative approach based on minimizing the least-square summation of the error values, the error being the difference between the estimated and measured temperatures. Results of the inverse analysis indicate that the Levenberg–Marquardt algorithm is an efficient and acceptably stable technique for estimating wall temperature in axisymmetric stagnation flow. The maximum value of the sensitivity coefficient is related to the estimation of polynomial wall temperature and its value is 0.1952 also the minimum value of the sensitivity coefficient is 8.62 × 10–6 which is related to the triangular wall temperature. The results show that the parameter estimation error in calculating the triangular and trapezoidal wall temperature is greater than the others because the maximum value of RMS error is obtained for these two cases, which are 0.451 and 0.479, respectively, the reason for the increase in error in estimating these functions is the existence of points where the first derivative of the function does not exist. This method also exhibits considerable stability for noisy input data. [ABSTRACT FROM AUTHOR]

Pipeline systems are widely used in gas refineries, oil factories chemical power plants. It is important to measure the fluid temperature in this pipeline. Numerous cases, however, exist where the internal fluid temperature is not available and only an outside wall temperature measurement is feasible. Recently inverse heat transfer problems have been analyzed for the situations where a direct measurement of boundary/initial conditions, or thermophisical properties are difficult, or indeed impossible, to carry out. Various numerical approaches have been proposed to estimate fluid temperature in the pipes. In this study, the analytical method is applied to solve the one-dimensional inverse heat conduction problem, in order to estimate fluid temperature in the pipes, based on the exact outer wall temperature. The fluid temperature is assumed to be a polynomial. The unknown polynomial coefficients are found by combining the method of Duhamel's theorem and the least squares method. The results show that the fluid temperature in the pipes can be accurately estimated by using the inverse heat transfer method.

The hardness and phase composition are, among other things, the critical material properties considered in the quality control of aerospace gears made from Pyrowear 53 steel after high-pressure gas quenching. The low availability of data on and applications of such demanding structures justify investigating the choice of the material and the need to improve its manufacturability. In this study, computational finite-element analyses of low-pressure carburizing followed by oil and gas quenching of Pyrowear 53 steel were undertaken, the objective of which was to examine the influence of the process parameters on the materials’ final phase composition and hardness. The material input was prepared using JMatPro. The properties computed by the CALPHAD method were calibrated by the values obtained from physical experiments. The heat transfer coefficient was regarded as an objective variable to be optimized. A 3D model of the Standard Navy C-ring specimen was utilized to predict the phase composition after the high-pressure gas quenching of the steel and the hardness at the final stage. These two parameters are considered good indicators of the actual process parameters and are used in the industry. The results of the simulation, e.g., optimized heat transfer coefficients, cooling curves, and hardness and phase composition, are presented and compared with experimental values. The accuracy of the simulation was validated, and a good correlation of the data was found, which demonstrates the quality of the input data and setup of the numerical procedure. A computational approach to heat treatment processes’ design could contribute to accelerating new procedures’ implementation and lowering the development costs.

With the development of intelligent manufacturing technology, robots have become more widespread in the field of milling processing. When milling difficult-to-machine alloy materials, the localized high temperature and large temperature gradient at the front face of the tool lead to shortened tool life and poor machining quality. The existing temperature field reconstruction methods have many assumptions, large arithmetic volume and long solution time. In this paper, an inverse heat conduction problem solution model based on Gated Convolutional Recurrent Neural Network (CNN-GRU) is proposed for reconstructing the temperature field of the tool during milling. In order to ensure the speed and accuracy of the reconstruction, we propose to utilize the inverse heat conduction problem solution model constructed by knowledge distillation (KD) and compression acceleration, which achieves a significant reduction of the training time with a small loss of optimality and ensures the accuracy and efficiency of the prediction model. With different levels of random noise added to the model input data, CNN-GRU + KD is noise-resistant and still shows good robustness and stability under noisy data. The temperature field reconstruction of the milling tool is carried out for three different working conditions, and the curve fitting excellence under the three conditions is 0.97 at the highest, and the root mean square error is 1.43°C at the minimum, respectively, and the experimental results show that the model is feasible and effective in carrying out the temperature field reconstruction of the milling tool and is of great significance in improving the accuracy of the milling machining robot., Competing Interests: ZS was employed by Angang Heavy Machinery Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Ma, Wang, E, Sha, Wang, Cui and Yin.)

An inverse heat transfer model based on Salp Swarm optimization algorithm is developed for prediction of heat flux at the hot faces of a mold in thin slab continuous casting. The industrial mold considered in this work is a funnel-shaped mold having complex arrangement of cooling slots and holes. Significant variations of heat flux along the casting direction, as well as across the width are observed. Subsequently, the obtained heat flux profile estimated by the inverse method is used to analyze the fluid flow and thermal characteristics of the solidifying steel strand inside the mold. Three different recirculatory zones are present due to molten steel flow, affecting the thermal and solidification characteristics significantly. The effect of these recirculatory flows on remelting phenomenon, and consequent formation of thinner shell at the mold outlet leading to quality control issues in the casting process have been discussed. Another practical issue of depression in the wide face shell thickness at the mold outlet has been identified, and its cause has been related to the location of the submerged entry nozzle and the high speed of the molten steel inflow. [ABSTRACT FROM AUTHOR]

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.

In this paper for the first time, a numerical code based on Levenberg–Marquardt method is presented for solving inverse heat transfer problem of axisymmetric stagnation flow impinging on a cylinder with uniform transpiration and to estimate the time-dependent heat flux using temperature distribution at a point. k ¯ The effect of noisy data on the final result is studied. The maximum value of the sensitivity coefficient is related to estimation of exponential heat flux and its value is 0.1718 also the minimum value of the sensitivity coefficient is 7.50 × 10−6 which is related to the triangular heat flux. The results show that the parameter estimation error in calculating the triangular and trapezoidal heat flux is greater than the exponential and sinus–cosines heat flux because the maximum value of RMS error is obtained for these two cases, which are 0.458 and 0.492, respectively the reason for the increase in error in estimating these functions is the existence of points where the first derivative of the function does not exist. This method also exhibits considerable stability for noisy input data. In most cases, surface blowing decreases the prediction accuracy by removing the boundary layers from the surface whereas suction acts vice versa. [ABSTRACT FROM AUTHOR]

Accurate prediction of an off-normal event in a nuclear reactor is dependent upon the availability of sensory data, reactor core physical condition, and understanding of the underlying phenomenon. This work presents a method to project the data from some discrete sensory locations to the overall reactor domain during conduction cooldown scenarios similar to High Temperature Gas-cooled Reactors (HTGRs). The existing models for conductive cooldown in a heterogeneous multi-body system, such as an assembly of prismatic blocks or pebble beds relies on knowledge of the thermal contact conductance, requiring significant knowledge of local thermal contacts and heat transport possibilities across those contacts. With a priori knowledge of bulk geometry features and some discrete sensors, a machine learning approach was devised. The presented work uses an experimental facility to mimic conduction cooldown with an assembly of 68 cylindrical rods initially heated to 1200 K. High-fidelity temperature data were collected using an infrared (IR) camera to provide training data to the model and validate the predicted temperature data. The machine learning approach used here first converts the macroscopic bulk geometry information into Graph-Laplacian, and then uses the eigenvectors of the Graph-Laplacian to develop Kernel functions. Support vector regression (SVR) was implemented on the obtained Kernels and used to predict the thermal response in a packed rod assembly during a conduction cooldown experiment. The usage of SVR modeling differs from most models today because of its representation of thermal coupling between rods in the core. When trained with thermographic data, the average normalized error is less than 2% over 400 s, during which temperatures of the assembly have dropped by more than 500 K. The rod temperature prediction performance was significantly better for rods in the interior of the assembly compared to those near the exterior, likely due to the model simplification of the surroundings.

Objective: Electrosurgical vessel sealing is a process commonly used to control bleeding during surgical procedures. Finite element (FE) modeling is often performed to obtain a better understanding of thermal spread during this process. The accuracy of the FE model depends on the implemented material properties. Thermal conductivity is one of the most important properties that affect temperature distribution. The goal of this study is to determine the tissue thermal conductivity as a function of thermal dose. Methods: We developed an iterative approach to correlating tissue thermal conductivity to more accurately calculated thermal dose, which cannot be experimentally measured. The resulting regression model was then implemented into an electrosurgical vessel sealing FE model to examine the accuracy of this FE model. Results: The results show that with the regression model, more reasonable temperature and thermal dose prediction can be achieved at the center of the sealed vessel tissue. The resulting electrical current and impedance from the FE model match with the experimental results. Conclusion: The developed approach can be used to determine the correlation between thermal dose and thermal conductivity. Describing the thermal conductivity as a function of thermal dose allows modeling of irreversible changes in tissue properties. Significance: By having a more accurate temperature estimation at the center of the sealed vessel, more insight is provided into how the tissue reacts during the vessel sealing process. [ABSTRACT FROM AUTHOR]

Growing concerns over the hazardous impact of mineral oil-based industrial quench media on human health and the environment have forced researchers to seek renewable and non-hazardous alternatives. Non-edible vegetable oil-based quench media are perceived to be a potential replacement for mineral-based industrial quench media. The present work focuses on assessing the cooling performance of neem oil as compared to commercial hot oil quench media. Inconel and steel probes were used to characterize the cooling performance of these quench media maintained at bath temperatures 100 °C, 150 °C and 200 °C. The heat extraction rates and uniformity of heat extraction in Inconel probes quenched in neem oil were observed to be substantially higher at all bath temperatures. The hardness of AISI 52100 steel probe quenched in neem oil at all bath temperatures was observed to be higher. The pearlitic microstructure was observed in the steel probe quenched in hot oil maintained at 200 °C bath temperature. In contrast to this, a mixture of bainite, martensite and carbide was observed in case of steel probes quenched in neem oil maintained at 200 °C. Oxidation experiments revealed that neem oil is susceptible to an increase in viscosity due to oxidation. An increase in the viscosity by about 15% was observed in the case of neem oil as compared to only 4% increase in viscosity of hot oil. However, after an initial increase, the viscosity of neem oil stabilized and further no significant change in viscosity due to oxidation were observed. Oxidation had no significant effect on the cooling performance hot neem oil quench medium, and thus, it can be considered as an effective replacement for hot oil. [ABSTRACT FROM AUTHOR]

In recent years, many studies have been done on heat transfer in the fin under unsteady boundary conditions using Fourier and non-Fourier models. In this paper, unsteady non-Fourier heat transfer in a straight fin having an internal heat source under periodic temperature at the base was investigated by solving numerically Dual-Phase-Lag and Fractional Single-Phase-Lag models. In this way, the governing equations of these models were presented for heat conduction analysis in the fin, and their results of the temperature distribution were validated using the theoretical results of Single and Dual-Phase-Lag models. After that, for the first time the order of fractional derivation and heat flux relaxation time of the fractional model were obtained for the straight fin problem under periodic temperature at the base using Levenberg-Marquardt parameter estimation method. To solve the inverse fractional heat conduction problem, the numerical results of Dual-Phase-Lag model were used as the inputs. The results obtained from Fractional Single-Phase-Lag model could predict the fin temperature distribution at unsteady boundary condition at the base as well as the Dual-Phase-Lag model could. [ABSTRACT FROM AUTHOR]

The boundary emissivity, thermal conductivity, and boundary time-varying heat flux in the participating media are retrieved in this work. In the forward model, the coupled radiation-conduction heat transfer in the participating medium is resolved by the finite volume method combined with discrete ordinates method. The inverse model utilizes the temperature signals at the appropriate position of the medium as the known information and uses the unscented Kalman filter (UKF) as an optimization tool to reconstruct the boundary emissivity, thermal conductivity, and boundary time-varying heat flux. It is found that when the emissivity, thermal conductivity, and boundary time-varying heat flux are reconstructed simultaneously, only the temperature information of two locations is required. The influence of the measurement noise, sampling interval, absorption coefficient, process noise covariance, measurement noise covariance on the accuracy and stability of the retrieval results is investigated in detail. All the reconstruction results indicate that the UKF technique is effective and robust for estimating the photothermal parameters and boundary condition of the radiation-conduction heat transfer problems. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent heat transfer coefficient is estimated efficiently and accurately. The functional form of the heat transfer coefficient is assumed unknown and the inverse heat transfer problem should be treated using a function estimation approach by solving sensitivity and adjoint problems during the minimization process. Based on proposing a new sensitivity matrix, however, the functional form can be estimated in an accurate and very efficient manner using a parameter estimation approach without the need for solving the sensitivity and adjoint problems and imposing extra computational cost, mathematical complexity, and implementation efforts. In the proposed sensitivity analysis scheme, all sensitivity coefficients can be computed in only one direct problem solution at each iteration. In this inverse heat transfer problem, the body shape is irregular and meshed using a body-fitted grid generation method. The direct heat conduction problem is solved using the finite-difference method. The steepest-descent method is used as a minimization algorithm to minimize the defined objective function and the termination of the minimization process is carried out based on the discrepancy principle. A test case with three different functional forms and two different measurement errors is considered to show the accuracy and efficiency of the used inverse analysis.

• The in-situ calibration method for temperature-sensitive-paint (TSP) heat-flux measurements is developed by using the data obtained with a heat-flux sensor based on the analytical inverse heat transfer solution. • The developed in-situ calibration method is used in TSP measurements in a high-enthalpy shock tube. • The proposed method is useful for TSP measurements in various facilities. This work incorporates in-situ calibration into the analytical inverse heat transfer solution for a finite base in temperature-sensitive-paint (TSP) measurements in high-enthalpy short-duration hypersonic wind tunnels. The thermal penetration parameter of the polymer layer (TSP) in the analytical inverse solution is determined by in-situ calibration based on the data obtained using a reliable heat flux sensor at a reference location. This method is applied to TSP images obtained on a wedge in a high-enthalpy shock tunnel. [ABSTRACT FROM AUTHOR]

• A simple method is developed for correction of the effect of the temperature-dependent thermal diffusivity on temperature-sensitive-paint (TSP) heat flux measurements. • This method is validated through simulations. • A correction factor is introduced. A simple method is developed for correcting the effect of the temperature-dependent thermal diffusivity on temperature-sensitive-paint (TSP) heat flux measurements in hypersonic wind tunnels. The relation between the heat flux obtained using the constant thermal diffusivity and the heat flux obtained using the temperature-dependent diffusivity is discussed based on an analysis of the nonlinear heat conduction equation. The non-dimensional correction factor is introduced and modeled as an approximate function of the measured surface temperature for the monotonically increasing heat flux histories, which can be determined in situ using the data at several selected points. The corrected heat flux field is obtained by multiplying the correction factor field with the heat flux field obtained using the analytical inverse heat transfer method for constant thermal properties. This method is validated through simulations. [ABSTRACT FROM AUTHOR]

This review provides a systematical description of the inverse heat transfer solutions applied to global heat-flux measurements using temperature-sensitive-coating techniques in hypersonic wind tunnels. The analytical inverse heat transfer solutions for a two-layer structure (typically a polymer sensor coating on a base) are focused to elucidate the effects of the relevant parameters including the polymer and base thicknesses, the thermal properties of materials, and the convective heat transfer at the base backside. Then, the numerical inverse heat transfer method is developed by incorporating the temperature-dependencies of the thermal properties in heat-flux calculation. Furthermore, correcting the lateral heat conduction effect is formulated as an image deconvolution problem based on a convolution-type integral equation with a Gaussian kernel. Other relevant topics are also discussed, including determining the non-uniform paint thickness distribution, in-situ correction for the effect of the temperature-dependent diffusivity, and in-situ calibration for the thermal penetration parameter of the polymer coating. Examples are given to demonstrate the applications of these inverse solutions in temperature-sensitive-paint (TSP) measurements. [ABSTRACT FROM AUTHOR]

Highlights • q (t) can be accurately estimated using SQP algorithm even with noisy data. • SQP algorithm is proved to be more efficient and robust than other techniques. • q (y) and h f (y) can be simultaneously and accurately reconstructed. • q (y) is easier to be estimated than h f (y) when measurement error is considered. • q (y , t) can be accurately reconstructed using SQP algorithm. Abstract The sequential quadratic programming (SQP) algorithm is applied to reconstruct the time- and space-dependent boundary conditions in 1D and 2D radiative-conductive systems in this study. The coupled radiation-conduction heat transfer in absorbing, scattering and emitting media is solved by the discrete ordinate method combined with finite volume method, and the simulated boundary temperature is served as input for the inverse analysis. The SQP algorithm is employed as the optimization technique, through which the time-dependent boundary heat flux in 1D heat transfer problems and the space-dependent boundary heat flux and convective heat transfer coefficient in 2D heat transfer problems are recovered. No prior information on the functional forms of the unknown boundary conditions is needed for inverse analysis. All the retrieval results show that the SQP algorithm is robust to the reconstruction of thermal boundary conditions in coupled radiative-conductive systems. The present inverse technique is proved to be more efficient and accurate than the conjugate gradient method, Levenberg-Marquardt method and particle swarm optimization algorithm. [ABSTRACT FROM AUTHOR]

Abstract Estimating the internal heat transfer coefficient in ducts is becoming increasingly important in many engineering applications. Unlike traditional estimation methods which seek to recover the unknown coefficient by using optimization tools such as iterative methods or linear system solvers, new solution methods based on forward/inverse analytical solutions have gained noticeable interest. Two recently proposed non traditional methods are an explicit Fourier analysis-based (EFA) reconstruction method of Bazán and Bedin and a filtered reciprocity functional (FRF) approach of Mocerino et al. Both methods provide approximate solutions that are expressed as a sum of weighted harmonics where the number of terms used in the reconstruction depends on the noise level in the data and is selected using the Morozov's discrepancy principle (DP). In the present work, these methods are analyzed to identify similarities and differences as well as to introduce improvements. In particular, limitations of the FRF method in determining the truncation parameter are discussed and circumvented. This gives rise to new methods for heat flux estimation that are easy to implement and extremely inexpensive when compared to existing techniques. To illustrate the effectiveness of the new methods we present numerical results on several test problems including an analytical model obtained by synthesizing experimental data reported by Bozzoli et al. and several benchmark problems reported by Mocerino et al. [ABSTRACT FROM AUTHOR]