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Search Results (944)

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Keywords = complex heat transfer

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24 pages, 892 KB  
Review
Recent Progress in Experimental Techniques for Thin Liquid Film Evaporation
by Yu Zhang, Chengwei He, Yanwen Xiao, Weichao Yan and Xin Cui
Energies 2026, 19(3), 664; https://doi.org/10.3390/en19030664 - 27 Jan 2026
Abstract
Thin liquid film evaporation leverages latent heat and low thermal resistance to achieve superior heat transfer capabilities, making it pivotal for next-generation high-heat-flux thermal management systems. This paper presents a systematic review of the fundamental mechanisms, interfacial transport behaviors, and experimental techniques associated [...] Read more.
Thin liquid film evaporation leverages latent heat and low thermal resistance to achieve superior heat transfer capabilities, making it pivotal for next-generation high-heat-flux thermal management systems. This paper presents a systematic review of the fundamental mechanisms, interfacial transport behaviors, and experimental techniques associated with static thin films and falling liquid films. This work elucidates the complex coupling of Marangoni convection, van der Waals disjoining pressure, and contact line dynamics. These mechanisms collectively govern film stability and the intensity of non-equilibrium phase change in the micro-region. The influence of surface wettability and dynamic contact angle hysteresis on hydraulic replenishment and dry spot formation is critically analyzed, offering insights into optimizing surface engineering strategies. In addition, the review categorizes advanced non-intrusive diagnostics, including optical interferometry, laser-induced fluorescence (LIF), and infrared thermography, evaluating their capacity to resolve spatiotemporal variations in film thickness (ranging from 10 nm to several μm) and temperature under complex boundary conditions. Special attention is directed toward falling film evaporation over horizontal tubes, addressing flow regime transitions and the impact of interfacial shear from external airflow. The work concludes by identifying key challenges in multi-physics coupling and proposing future directions for synchronized diagnostics and adaptive surface design. Full article
(This article belongs to the Special Issue Innovations in Thermal Energy Processes and Management)
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27 pages, 3203 KB  
Article
Machine Learning and Physics-Informed Neural Networks for Thermal Behavior Prediction in Porous TPMS Metals
by Mohammed Yahya and Mohamad Ziad Saghir
Fluids 2026, 11(2), 29; https://doi.org/10.3390/fluids11020029 - 23 Jan 2026
Viewed by 112
Abstract
Triply periodic minimal surface (TPMS) structures provide high surface area to volume ratios and tunable conduction pathways, but predicting their thermal behavior across different metallic materials remains challenging because multi-material experimentation is costly and full-scale simulations require extremely fine meshes to resolve the [...] Read more.
Triply periodic minimal surface (TPMS) structures provide high surface area to volume ratios and tunable conduction pathways, but predicting their thermal behavior across different metallic materials remains challenging because multi-material experimentation is costly and full-scale simulations require extremely fine meshes to resolve the complex geometry. This study develops a physics-informed neural network (PINN) that reconstructs steady-state temperature fields in TPMS Gyroid structures using only two experimentally measured materials, Aluminum and Silver, which were tested under identical heat flux and flow conditions. The model incorporates conductivity ratio physics, Fourier-based thermal scaling, and complete spatial temperature profiles directly into the learning process to maintain physical consistency. Validation using the complete Aluminum and Silver datasets confirms excellent agreement for Aluminum and strong accuracy for Silver despite its larger temperature gradients. Once trained, the PINN can generalize the learned behavior to nine additional metals using only their conductivity ratios, without requiring new experiments or numerical simulations. A detailed heat transfer analysis is also performed for Magnesium, a lightweight material that is increasingly considered for thermal management applications. Since no published TPMS measurements for Magnesium currently exist, the predicted Nusselt numbers obtained from the PINN-generated temperature fields represent the first model-based evaluation of its convective performance. The results demonstrate that the proposed PINN provides an efficient, accurate, and scalable surrogate model for predicting thermal behavior across multiple metallic TPMS structures and supports the design and selection of materials for advanced porous heat technologies. Full article
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23 pages, 7133 KB  
Article
Energy Transfer Characteristics of Surface Vortex Heat Flow Under Non-Isothermal Conditions Based on the Lattice Boltzmann Method
by Qing Yan, Lin Li and Yunfeng Tan
Processes 2026, 14(2), 378; https://doi.org/10.3390/pr14020378 - 21 Jan 2026
Viewed by 124
Abstract
During liquid drainage from intermediate vessels in various industrial processes such as continuous steel casting, aircraft fuel supply, and chemical separation, free-surface vortices commonly occur. The formation and evolution of these vortices not only entrain surface slag and gas, but also lead to [...] Read more.
During liquid drainage from intermediate vessels in various industrial processes such as continuous steel casting, aircraft fuel supply, and chemical separation, free-surface vortices commonly occur. The formation and evolution of these vortices not only entrain surface slag and gas, but also lead to deterioration of downstream product quality and abnormal equipment operation. The vortex evolution process exhibits notable three-dimensional unsteadiness, multi-scale turbulence, and dynamic gas–liquid interfacial changes, accompanied by strong coupling effects between temperature gradients and flow field structures. Traditional macroscopic numerical models show clear limitations in accurately capturing these complex physical mechanisms. To address these challenges, this study developed a mesoscopic numerical model for gas-liquid two-phase vortex flow based on the lattice Boltzmann method. The model systematically reveals the dynamic behavior during vortex evolution and the multi-field coupling mechanism with the temperature field while providing an in-depth analysis of how initial perturbation velocity regulates vortex intensity and stability. The results indicate that vortex evolution begins near the bottom drain outlet, with the tangential velocity distribution conforming to the theoretical Rankine vortex model. The vortex core velocity during the critical penetration stage is significantly higher than that during the initial depression stage. An increase in the initial perturbation velocity not only enhances vortex intensity and induces low-frequency oscillations of the vortex core but also markedly promotes the global convective heat transfer process. With regard to the temperature field, an increase in fluid temperature reduces the viscosity coefficient, thereby weakening viscous dissipation effects, which accelerates vortex development and prolongs drainage time. Meanwhile, the vortex structure—through the induction of Taylor vortices and a spiral pumping effect—drives shear mixing and radial thermal diffusion between fluid regions at different temperatures, leading to dynamic reconstruction and homogenization of the temperature field. The outcomes of this study not only provide a solid theoretical foundation for understanding the generation, evolution, and heat transfer mechanisms of vortices under industrial thermal conditions, but also offer clear engineering guidance for practical production-enabling optimized operational parameters to suppress vortices and enhance drainage efficiency. Full article
(This article belongs to the Section Energy Systems)
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18 pages, 1702 KB  
Article
Dynamic Modeling and Calibration of an Industrial Delayed Coking Drum Model for Digital Twin Applications
by Vladimir V. Bukhtoyarov, Ivan S. Nekrasov, Alexey A. Gorodov, Yadviga A. Tynchenko, Oleg A. Kolenchukov and Fedor A. Buryukin
Processes 2026, 14(2), 375; https://doi.org/10.3390/pr14020375 - 21 Jan 2026
Viewed by 101
Abstract
The increasing share of heavy and high-sulfur crude oils in refinery feed slates worldwide highlights the need for models of delayed coking units (DCUs) that are both physically meaningful and computationally efficient. In this study, we develop and calibrate a simplified yet dynamic [...] Read more.
The increasing share of heavy and high-sulfur crude oils in refinery feed slates worldwide highlights the need for models of delayed coking units (DCUs) that are both physically meaningful and computationally efficient. In this study, we develop and calibrate a simplified yet dynamic one-dimensional model of an industrial coke drum intended for integration into digital twin frameworks. The model includes a three-phase representation of the drum contents, a temperature-dependent global kinetic scheme for vacuum residue cracking, and lumped descriptions of heat transfer and phase holdups. Only three physically interpretable parameters—the kinetic scaling factors for distillate and coke formation and an effective wall temperature—were calibrated using routinely measured plant data, namely the overhead vapor and drum head temperatures and the final coke bed height. The calibrated model reproduces the temporal evolution of the top head and overhead temperatures and the final bed height with mean relative errors of a few percent, while capturing the more complex bottom-head temperature dynamics qualitatively. Scenario simulations illustrate how the coking severity (represented here by the effective wall temperature) affects the coke yield, bed growth, and cycle duration. Overall, the results indicate that low-order dynamic models can provide a practical balance between physical fidelity and computational speed, making them suitable as mechanistic cores for digital twins and optimization tools in delayed coking operations. Full article
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28 pages, 3616 KB  
Article
Optimization of Cryogenic Gas Separation Systems Based on Exergetic Analysis—The Claude–Heylandt Cycle for Oxygen Separation
by Dănuț-Cristian Urduza, Lavinia Grosu, Alexandru Serban, Adalia Andreea Percembli (Chelmuș) and Alexandru Dobrovicescu
Entropy 2026, 28(1), 125; https://doi.org/10.3390/e28010125 - 21 Jan 2026
Viewed by 90
Abstract
In cryogenic air liquefaction systems, a major share of the mechanical energy consumption is associated with exergy destruction caused by heat transfer in recuperative heat exchangers. This study investigated the exergetic optimization of cryogenic gas separation systems by focusing on the Claude–Heylandt cycle [...] Read more.
In cryogenic air liquefaction systems, a major share of the mechanical energy consumption is associated with exergy destruction caused by heat transfer in recuperative heat exchangers. This study investigated the exergetic optimization of cryogenic gas separation systems by focusing on the Claude–Heylandt cycle as an advanced structural modification of the classical Linde–Hampson scheme. An exergy-based analysis demonstrates that minimizing mechanical energy consumption requires a progressive reduction in the temperature difference between the hot forward stream and the cold returning stream toward the cold end of the heat exchanger. This condition was achieved by extracting a fraction of the high-pressure stream and expanding it in a parallel expander, thereby creating a controlled imbalance in the heat capacities between the two streams. The proposed configuration reduces the share of exergy destruction associated with heat transfer in the recuperative heat exchanger from 14% to 3.5%, leading to a fourfold increase in the exergetic efficiency, together with a 3.6-fold increase in the liquefied air fraction compared with the Linde–Hampson cycle operating under identical conditions. The effects of key decision parameters, including the compression pressure, imposed temperature differences, and expander inlet temperature, were systematically analyzed. The study was further extended by integrating an air separation column into the Claude–Heylandt cycle and optimizing its configuration based on entropy generation minimization. The optimal liquid-air feeding height and threshold number of rectification trays were identified, beyond which further structural complexity yielded no thermodynamic benefit. The results highlight the effectiveness of exergy-based optimization as a unified design criterion for both cryogenic liquefaction and separation processes. Full article
(This article belongs to the Special Issue Thermodynamic Optimization of Industrial Energy Systems, 2nd Edition)
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17 pages, 2935 KB  
Article
Gas–Liquid Two-Phase Boiling Heat Transfer Mechanism in Cooling Water Jacket of Intense Thermal Load Engine and Its Improvement
by Gangzhi Tang and Chaojie Yuan
Appl. Sci. 2026, 16(2), 1081; https://doi.org/10.3390/app16021081 - 21 Jan 2026
Viewed by 71
Abstract
The results show that the numerical simulation error based on the RPI two-phase boiling heat transfer model is less than 5%, which is in good agreement with the test results. Compared with the original engine, the temperature near the spark plugs’ position of [...] Read more.
The results show that the numerical simulation error based on the RPI two-phase boiling heat transfer model is less than 5%, which is in good agreement with the test results. Compared with the original engine, the temperature near the spark plugs’ position of improvement in scheme 2 decreased by 8.4 K, and the maximum temperature difference between the cylinder head intake and exhaust decreased by 14 K. Moreover, the overheating degree of the water jacket wall is the lowest, avoiding the occurrence of film boiling, and the local maximum vaporization rate is less than 50%. The prototype tests also confirmed that the improvement scheme effectively enhanced the heat transfer performance of the water jacket. The inlet flow rate and temperature of the coolant have significant and complex effects on two-phase boiling heat transfer. Both too low a flow rate and too high a temperature will lead to local film boiling, deteriorating heat transfer. Too high a flow rate will blow away bubbles, while too low an inlet temperature will not cause boiling, both of which can only enforce convective heat transfer. Appropriately reducing the flow rate and increasing the temperature can effectively utilize the enhanced heat transfer potential of subcooled boiling, while also save pump power consumption and improving engine fuel economy. The average heat flux density of boiling heat transfer in this paper is 13.9% higher than that of the forced convective heat transfer. When designing a water jacket with boiling heat transfer, attention should be paid to the transport effect of convective motion on bubbles, controlling subcooled boiling in the high-temperature zone and preventing film boiling. Full article
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24 pages, 2699 KB  
Article
Performance Analysis and Design of a Pulsating Heat Pipe-Based Thermal Management System for PEMFC
by Hongchun Zhao, Meng Zheng, Zheshu Ma, Yan Zhu and Liangyu Tao
Sustainability 2026, 18(2), 1047; https://doi.org/10.3390/su18021047 - 20 Jan 2026
Viewed by 119
Abstract
Given automotive PEMFCs’ susceptibility to thermal runaway and uneven temperature distribution under high-power-density operation, this study proposes a novel embedded pulsating heat pipe cooling system. The core innovations of this work are threefold, fundamentally distinguishing it from prior PHP cooling approaches: (1) an [...] Read more.
Given automotive PEMFCs’ susceptibility to thermal runaway and uneven temperature distribution under high-power-density operation, this study proposes a novel embedded pulsating heat pipe cooling system. The core innovations of this work are threefold, fundamentally distinguishing it from prior PHP cooling approaches: (1) an embedded PHP cooling plate design that integrates the heat pipe within a unified copper plate, eliminating the need for external attachment or complex bipolar plate channels and enhancing structural compactness; (2) a system-level modeling methodology that derives an effective thermal conductivity (k_eff ≈ 65,000 W·m−1·K−1) from a thermal resistance network for seamless integration into a full-stack CFD model, significantly simplifying the simulation of the passive PHP component; and (3) a parametric system-level optimization of the secondary active cooling loop. Numerical results demonstrate that the system achieves an exceptional maximum temperature difference (ΔT_max) of less than 1.7 K within the PEMFC stack at an optimal coolant flow rate of 0.11 m/s, far surpassing the performance of conventional liquid cooling baselines. This three-layer framework (PHP heat transfer, cooling plate conduction, liquid coolant convection) offers robust theoretical and design support for high-efficiency, passive-dominant thermal control of automotive fuel cells. Full article
(This article belongs to the Section Sustainable Engineering and Science)
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27 pages, 10006 KB  
Article
Analysis About the Leaks and Explosions of Alternative Fuels
by José Miguel Mahía-Prados, Ignacio Arias-Fernández, Manuel Romero Gómez and Sandrina Pereira
Energies 2026, 19(2), 514; https://doi.org/10.3390/en19020514 - 20 Jan 2026
Viewed by 127
Abstract
The maritime sector is under growing pressure to decarbonize, driving the adoption of alternative fuels such as methane, methanol, ammonia, and hydrogen. This study evaluates their thermal behavior and associated risks using Engineering Equation Solve software for heat transfer modeling and Areal Locations [...] Read more.
The maritime sector is under growing pressure to decarbonize, driving the adoption of alternative fuels such as methane, methanol, ammonia, and hydrogen. This study evaluates their thermal behavior and associated risks using Engineering Equation Solve software for heat transfer modeling and Areal Locations of Hazardous Atmospheres software for dispersion and explosion analysis in pipelines and storage scenarios. Results indicate that methane presents moderate and predictable risks, mainly from thermal effects in fires or Boiling Liquid Expanding Vapor Explosion events, with low toxicity. Methanol offers the safest operational profile, stable at ambient temperature and easily manageable, though it remains slightly flammable even when diluted. Ammonia shows the greatest toxic hazard, with impact distances reaching several kilometers even when emergency shutoff systems are active. Hydrogen, meanwhile, poses the most severe flammability and explosion risks, capable of autoignition and generating destructive overpressures. Thermal analysis highlights that cryogenic fuels require complex insulation systems, increasing storage costs, while methanol and gaseous hydrogen remain thermally stable but have lower energy density. The study concludes that methanol is the most practical transition fuel, when comparing thermal behavior and associated risks, while hydrogen and ammonia demand further technological and regulatory development. Proper insulation, ventilation, and automatic shutoff systems are essential to ensure safe decarbonization in maritime transport. Full article
(This article belongs to the Special Issue Advances in Green Hydrogen Energy Production)
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27 pages, 10557 KB  
Article
Numerical and Experimental Estimation of Heat Source Strengths in Multi-Chip Modules on Printed Circuit Boards
by Cheng-Hung Huang and Hao-Wei Su
Mathematics 2026, 14(2), 327; https://doi.org/10.3390/math14020327 - 18 Jan 2026
Viewed by 126
Abstract
In this study, a three-dimensional Inverse Conjugate Heat Transfer Problem (ICHTP) is numerically and experimentally investigated to estimate the heat-source strength of multiple chips mounted on a printed circuit board (PCB) using the Conjugate Gradient Method (CGM) and infrared thermography. The interfaces between [...] Read more.
In this study, a three-dimensional Inverse Conjugate Heat Transfer Problem (ICHTP) is numerically and experimentally investigated to estimate the heat-source strength of multiple chips mounted on a printed circuit board (PCB) using the Conjugate Gradient Method (CGM) and infrared thermography. The interfaces between the PCB and the surrounding air domain are assumed to exhibit perfect thermal contact, establishing a fully coupled conjugate heat transfer framework for the inverse analysis. Unlike the conventional Inverse Heat Conduction Problem (IHCP), which typically only accounts for conduction within solid domains, the present ICHTP formulation requires the simultaneous solution of the governing continuity, momentum, and energy equations in the air domain, along with the heat conduction equation in the chips and PCB. This coupling introduces substantial computational complexity due to the nonlinear interaction between convective and conductive heat transfer mechanisms, as well as the sensitivity of the inverse solution to measurement uncertainties. The numerical simulations are conducted first with error-free measurement data and an inlet velocity of uin = 4 m/s; the recovered heat-sources exhibit excellent agreement with the true values. The computed average errors for the estimated temperatures ERR1 and estimated heat sources ERR2 are as low as 0.0031% and 1.87%, respectively. The accuracy of the estimated heat sources is then experimentally validated under various prescribed inlet air velocities. During experimental verification at an inlet velocity of 4 m/s, the corresponding ERR1 and ERR2 values are obtained as 0.91% and 3.34%, while at 6 m/s, the values are 0.86% and 2.81%, respectively. Compared with the numerical results, the accuracy of the experimental estimations decreases noticeably. This discrepancy arises because the numerical simulations are free from measurement noise, whereas experimental data inherently include uncertainties due to thermal picture resolutions, environmental fluctuations, and other uncontrollable factors. These results highlight the inherent challenges associated with inverse problems and underscore the critical importance of obtaining precise and reliable temperature measurements to ensure accurate heat source estimation. Full article
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25 pages, 5632 KB  
Article
Chaos-Enhanced, Optimization-Based Interpretable Classification Model and Performance Evaluation in Food Drying
by Cagri Kaymak, Bilal Alatas, Suna Yildirim, Ebru Akpinar, Gizem Gul Katircioglu, Murat Catalkaya, Orhan E. Akay and Mehmet Das
Biomimetics 2026, 11(1), 78; https://doi.org/10.3390/biomimetics11010078 - 18 Jan 2026
Viewed by 174
Abstract
Food drying is a widely used preservation technique; however, achieving high energy efficiency while maintaining product quality remains a significant challenge. This study aims to analyze comprehensive experimental data obtained during the hot-air drying process of the Paşa pear (regional pear) and the [...] Read more.
Food drying is a widely used preservation technique; however, achieving high energy efficiency while maintaining product quality remains a significant challenge. This study aims to analyze comprehensive experimental data obtained during the hot-air drying process of the Paşa pear (regional pear) and the system’s autonomous control structure using an explainable artificial intelligence (XAI)-based method. The intelligent drying system, operating for approximately 17.5 h under two temperatures (50 °C and 65 °C) and two air speeds (0.63 m/s and 1.03 m/s), continuously adjusted the temperature and air speed using a PLC-based control mechanism; it ensured stable control throughout the process by monitoring parameters such as product weight, moisture, inlet–outlet temperatures, and air speed in real time. Experimental results showed that drying performance varied significantly with operating conditions, with product mass decreasing from 450 g to 103 g. The innovative aspect of the study is that it obtained quantitative, interpretable rules without discretization by applying the oscillatory chaotic sunflower optimization algorithm (OCSFO) to multidimensional control and process data for the first time. Thanks to its chaotic search mechanism, OCSFO accurately analyzed complex drying dynamics and created rules that achieved over 90% success for high, medium, and low performance classes. The obtained explainable rules clearly demonstrate that drying temperature and air velocity are the dominant determining parameters for drying efficiency, while energy consumption and cabin temperature distribution play a supporting role in distinguishing between efficiency classes. These rules clearly demonstrate how changes in controlled temperature and air velocity, combined with product weight and heat transfer, affect drying performance. Thus, the study offers a robust framework that identifies critical factors affecting drying performance through a transparent artificial intelligence approach that leverages both the autonomous control system and XAI-based rule mining. Full article
(This article belongs to the Section Biological Optimisation and Management)
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28 pages, 9150 KB  
Article
PhysGraphIR: Adaptive Physics-Informed Graph Learning for Infrared Thermal Field Prediction in Meter Boxes with Residual Sampling and Knowledge Distillation
by Hao Li, Siwei Li, Xiuli Yu and Xinze He
Electronics 2026, 15(2), 410; https://doi.org/10.3390/electronics15020410 - 16 Jan 2026
Viewed by 163
Abstract
Infrared thermal field (ITF) prediction for meter boxes is crucial for the early warning of power system faults, yet this method faces three major challenges: data sparsity, complex geometry, and resource constraints in edge computing. Existing physics-informed neural network-graph neural network (PINN-GNN) approaches [...] Read more.
Infrared thermal field (ITF) prediction for meter boxes is crucial for the early warning of power system faults, yet this method faces three major challenges: data sparsity, complex geometry, and resource constraints in edge computing. Existing physics-informed neural network-graph neural network (PINN-GNN) approaches suffer from redundant physics residual calculations (over 70% of flat regions contain little information) and poor model generalization (requiring retraining for new box types), making them inefficient for deployment on edge devices. This paper proposes the PhysGraphIR framework, which employs an Adaptive Residual Sampling (ARS) mechanism to dynamically identify hotspot region nodes through a physics-aware gating network, calculating physics residuals only at critical nodes to reduce computational overhead by over 80%. In this study, a ‘hotspot region’ is explicitly defined as a localized area exhibiting significant temperature elevation relative to the background—typically concentrated around electrical connection terminals or wire entrances—which is critical for identifying potential thermal faults under sparse data conditions. Additionally, it utilizes a Physics Knowledge Distillation Graph Neural Network (Physics-KD GNN) to decouple physics learning from geometric learning, transferring universal heat conduction knowledge to specific meter box geometries through a teacher–student architecture. Experimental results demonstrate that on both synthetic and real-world meter box datasets, PhysGraphIR achieves a hotspot region mean absolute error (MAE) of 11.8 °C under 60% infrared data missing conditions, representing a 22% improvement over traditional PINN-GNN. The training speed is accelerated by 3.1 times, requiring only five infrared samples to adapt to new box types. The experiments prove that this method significantly enhances prediction accuracy and computational efficiency under sparse infrared data while maintaining physical consistency, providing a feasible solution for edge intelligence in power systems. Full article
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16 pages, 3945 KB  
Article
Analysis of Multi-Physics Thermal Response Characteristics of Anchor Rod and Sealant Systems Under Fire Scenarios
by Kui Tian, Rui Rao, Yu Zeng, Sihang Chen and Qingyuan Xu
Buildings 2026, 16(2), 383; https://doi.org/10.3390/buildings16020383 - 16 Jan 2026
Viewed by 109
Abstract
During on-site welding operations, the sealant coated on anchor bolt surfaces can be ignited by hot particles or localized sparks, potentially triggering a fire hazard. This combustion process involves a complex multi-physics coupling among sealant combustion, convective and radiative heat transfer, and three-dimensional [...] Read more.
During on-site welding operations, the sealant coated on anchor bolt surfaces can be ignited by hot particles or localized sparks, potentially triggering a fire hazard. This combustion process involves a complex multi-physics coupling among sealant combustion, convective and radiative heat transfer, and three-dimensional heat conduction in solids. To resolve this coupling, a simulation strategy is proposed that correspondingly integrates the Fire Dynamics Simulator (FDS, version 6.7.6) for modeling combustion and radiation with ABAQUS (2024) for simulating conductive heat transfer in solids. The proposed method is validated against experimental measurements, showing close agreement in temperature evolution. It also demonstrates robustness across varying geometric scales, thereby confirming its reliability for predicting thermal response. Using this validated method, simulations are performed to analyze the fire behavior of an anchor rod-sealant system. Results show that the burning sealant can raise anchor rod temperatures above 900 °C and lead to rapid flame spread between adjacent rods. Furthermore, a sensitivity analysis of thermophysical parameters identifies critical thresholds for fire safety optimization: sealants with an ignition temperature > 280 °C and thermal conductivity ≥ 0.26 W/(m·K) demonstrate effective self-extinguishing properties, while specific heat capacity can retard flame growth. These findings provide a robust numerical framework and quantitative guidelines for the fire-safe design of bridge anchorage systems. Full article
(This article belongs to the Special Issue Advances in Steel and Composite Structures)
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23 pages, 3212 KB  
Article
On the Heat Transfer Process in a System of Two Convex Bodies Separated by a Vacuum—Mathematical Description and Solution Construction
by Rogério Pazetto Saldanha da Gama, Rogério Martins Saldanha da Gama and Maria Laura Martins-Costa
Thermo 2026, 6(1), 6; https://doi.org/10.3390/thermo6010006 - 16 Jan 2026
Viewed by 184
Abstract
This work presents a straightforward procedure for constructing the solution to the steady-state energy-transfer process in a system of two convex, opaque, gray bodies, with the aim of determining the temperature distribution within these bodies when separated by a vacuum. The methodology proposed [...] Read more.
This work presents a straightforward procedure for constructing the solution to the steady-state energy-transfer process in a system of two convex, opaque, gray bodies, with the aim of determining the temperature distribution within these bodies when separated by a vacuum. The methodology proposed in this work combines a sequence of elements that are functions obtained from the solution of uncomplicated, well-known linear, uncoupled heat transfer problems, thereby enabling solutions to be obtained using tools found in basic engineering textbooks. Specifically, these well-known problems resemble classical conduction-convection heat transfer problems, in which the boundary condition is described by the noteworthy Newton’s law of cooling. The limit of sequences of elements that are solutions to straightforward linear problems corresponds to the original, complex, coupled nonlinear problem. The convergence of these sequences is mathematically proven. The phenomenon (considered in this work) encompasses those involving black bodies. Since each element of the sequence arises from a well-known linear problem, numerical approximations can be used to obtain it, yielding a simple and powerful tool for simulations. Some presented results highlight the importance of considering thermal interaction between the two bodies, even in the absence of physical contact. In particular, the alterations in the temperature distributions of two separate gray bodies are explicitly shown to result from their thermal interaction. Full article
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23 pages, 1151 KB  
Article
CNN–BiLSTM–Attention-Based Hybrid-Driven Modeling for Diameter Prediction of Czochralski Silicon Single Crystals
by Pengju Zhang, Hao Pan, Chen Chen, Yiming Jing and Ding Liu
Crystals 2026, 16(1), 57; https://doi.org/10.3390/cryst16010057 - 13 Jan 2026
Viewed by 188
Abstract
High-precision prediction of the crystal diameter during the growth of electronic-grade silicon single crystals is a critical step for the fabrication of high-quality single crystals. However, the process features high-temperature operation, strong nonlinearities, significant time-delay dynamics, and external disturbances, which limit the accuracy [...] Read more.
High-precision prediction of the crystal diameter during the growth of electronic-grade silicon single crystals is a critical step for the fabrication of high-quality single crystals. However, the process features high-temperature operation, strong nonlinearities, significant time-delay dynamics, and external disturbances, which limit the accuracy of conventional mechanism-based models. In this study, mechanism-based models denote physics-informed heat-transfer and geometric models that relate heater power and pulling rate to diameter evolution. To address this challenge, this paper proposes a hybrid deep learning model combining a convolutional neural network (CNN), a bidirectional long short-term memory network (BiLSTM), and self-attention to improve diameter prediction during the shoulder-formation and constant-diameter stages. The proposed model leverages the CNN to extract localized spatial features from multi-source sensor data, employs the BiLSTM to capture temporal dependencies inherent to the crystal growth process, and utilizes the self-attention mechanism to dynamically highlight critical feature information, thereby substantially enhancing the model’s capacity to represent complex industrial operating conditions. Experiments on operational production data collected from an industrial Czochralski (Cz) furnace, model TDR-180, demonstrate improved prediction accuracy and robustness over mechanism-based and single data-driven baselines, supporting practical process control and production optimization. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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23 pages, 24039 KB  
Article
Multi-Region Temperature Prediction in Grain Storage: Integrating WSLP Spatial Structure with LSTM–iTransformer Hybrid Framework
by Yongqi Xu, Peiru Li, Jin Qian, Limin Shi, Hui Zhang and Bangyu Li
Electronics 2026, 15(2), 357; https://doi.org/10.3390/electronics15020357 - 13 Jan 2026
Viewed by 193
Abstract
Grain security is a fundamental guarantee for social stability and sustainable development. Accurate monitoring and prediction of overall granary temperature are essential for reducing storage losses and improving warehouse management efficiency. As an integrated system, the temperature evolution of the grain pile is [...] Read more.
Grain security is a fundamental guarantee for social stability and sustainable development. Accurate monitoring and prediction of overall granary temperature are essential for reducing storage losses and improving warehouse management efficiency. As an integrated system, the temperature evolution of the grain pile is deeply affected by its inherent physical structure and heat transfer pathways. Therefore, a multi-level warehouse–surface–line–point (WSLP) structural modeling approach driven by the physical properties of the grain pile is proposed to extract the joint environmental and spatial characteristics. Building upon the WSLP framework, a dual-channel time-series prediction architecture integrating both long short-term memory (LSTM) and iTransformer through a mutual verification fusion mechanism is developed to enable synchronized temperature forecasting across different regions of the grain piles. Experiments are conducted using real granary data from Shandong, China. The results demonstrate that the proposed model achieves more than 30% improvement over baseline methods in terms of MAE and RMSE. Moreover, the WSLP-LSTM–iTransformer framework significantly improves prediction accuracy in complex warehouse environments and enhances the interpretability and applicability of deep learning models for grain condition forecasting by incorporating real environmental characteristics. Full article
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