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Keywords = heat conduction equation

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22 pages, 5509 KiB  
Article
Kinetic Analysis of Thermal Degradation of Styrene–Butadiene Rubber Compounds Under Different Aging Conditions
by Imen Hamouda, Masoud Tayefi, Mostafa Eesaee, Meysam Hassanipour and Phuong Nguyen-Tri
J. Compos. Sci. 2025, 9(8), 420; https://doi.org/10.3390/jcs9080420 - 6 Aug 2025
Abstract
This study examined the impact of storage and operational aging on the thermal stability, structural degradation, and electrical properties of styrene–butadiene rubber (SBR) compound by analyzing three distinct materials: a laboratory-stored sample, an operationally aged one, and an original unaged reference. Thermal degradation [...] Read more.
This study examined the impact of storage and operational aging on the thermal stability, structural degradation, and electrical properties of styrene–butadiene rubber (SBR) compound by analyzing three distinct materials: a laboratory-stored sample, an operationally aged one, and an original unaged reference. Thermal degradation was analyzed through thermogravimetric analysis (TGA), which examined weight loss as a function of temperature and time at different heating rates. Results showed that the onset temperature and peak position in the 457 °C to 483 °C range remained stable. The activation energy (Ea) was determined using the Kissinger–Akahira–Sunose (KAS), Flynn–Wall–Ozawa (FWO), and Friedman methods, with the original unaged sample’s (OUS) Ea averaging 203.7 kJ/mol, decreasing to 163.47 kJ/mol in the laboratory-stored sample (LSS), and increasing to 224.18 kJ/mol in the operationally aged sample (OAS). The Toop equation was applied to estimate the thermal degradation lifetime at a 50% conversion rate. Since the material had been exposed to electricity, the evolution of electrical conductivity was studied and found to have remained stable after storage at around 0.070 S/cm. However, after operational aging, it showed a considerable increase in conductivity, to 0.321 S/cm. Scanning Electron Microscopy (SEM) was employed to analyze microstructural degradation and chemical changes, providing insights into the impact of aging on thermal stability and electrical properties. Full article
(This article belongs to the Special Issue Mechanical Properties of Composite Materials and Joints)
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12 pages, 2519 KiB  
Article
Mathematical Formulation of Causal Propagation in Relativistic Ideal Fluids
by Dominique Brun-Battistini, Alfredo Sandoval-Villalbazo and Hernando Efrain Caicedo-Ortiz
Axioms 2025, 14(8), 598; https://doi.org/10.3390/axioms14080598 - 1 Aug 2025
Viewed by 166
Abstract
We establish a rigorous kinetic-theoretical framework to analyze causal propagation in thermal transport phenomena within relativistic ideal fluids, building a more rigorous framework based on the kinetic theory of gases. Specifically, we provide a refined derivation of the wave equation governing thermal and [...] Read more.
We establish a rigorous kinetic-theoretical framework to analyze causal propagation in thermal transport phenomena within relativistic ideal fluids, building a more rigorous framework based on the kinetic theory of gases. Specifically, we provide a refined derivation of the wave equation governing thermal and density fluctuations, clarifying its hyperbolic nature and the associated characteristic propagation speeds. The analysis confirms that thermal fluctuations in a simple non-degenerate relativistic fluid satisfy a causal wave equation in the Euler regime, and it recovers the classical expression for the speed of sound in the non-relativistic limit. This work offers enhanced mathematical and physical insights, reinforcing the validity of the hyperbolic description and suggesting a foundation for future studies in dissipative relativistic hydrodynamics. Full article
(This article belongs to the Section Mathematical Physics)
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19 pages, 2954 KiB  
Article
Static Analysis of Temperature-Dependent FGM Spherical Shells Under Thermo-Mechanical Loads
by Zhong Zhang, Zhiting Feng, Zhan Shi, Honglei Xie, Ying Sun, Zhenyuan Gu, Jie Xiao and Jiajing Xu
Buildings 2025, 15(15), 2709; https://doi.org/10.3390/buildings15152709 - 31 Jul 2025
Viewed by 88
Abstract
Static analysis is conducted for functionally graded material (FGM) spherical shells under thermo-mechanical loads, based on the three-dimensional thermo-elasticity theory. The material properties, which vary with both the radial coordinate and temperature, introduce nonlinearity to the problem. To address this, a layer model [...] Read more.
Static analysis is conducted for functionally graded material (FGM) spherical shells under thermo-mechanical loads, based on the three-dimensional thermo-elasticity theory. The material properties, which vary with both the radial coordinate and temperature, introduce nonlinearity to the problem. To address this, a layer model is proposed, wherein the shell is discretized into numerous concentric spherical layers, each possessing uniform material properties. Within this framework, the nonlinear heat conduction equations are first solved iteratively. The resulting temperature field is then applied to the thermo-elastic equations, which are subsequently solved using a combined state space and transfer matrix method to obtain displacement and stress solutions. Comparison with existing literature results demonstrates good agreement. Finally, a parametric study is presented to investigate the effects of material temperature dependence and gradient index on the thermo-mechanical behaviors of the FGM spherical shells. Full article
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20 pages, 3271 KiB  
Article
Calculation Model for the Degree of Hydration and Strength Prediction in Basalt Fiber-Reinforced Lightweight Aggregate Concrete
by Yanqun Sun, Haoxuan Jia, Jianxin Wang, Yanfei Ding, Yanfeng Guan, Dongyi Lei and Ying Li
Buildings 2025, 15(15), 2699; https://doi.org/10.3390/buildings15152699 - 31 Jul 2025
Viewed by 217
Abstract
The combined application of fibers and lightweight aggregates (LWAs) represents an effective approach to achieving high-strength, lightweight concrete. To enhance the predictability of the mechanical properties of fiber-reinforced lightweight aggregate concrete (LWAC), this study conducts an in-depth investigation into its hydration characteristics. In [...] Read more.
The combined application of fibers and lightweight aggregates (LWAs) represents an effective approach to achieving high-strength, lightweight concrete. To enhance the predictability of the mechanical properties of fiber-reinforced lightweight aggregate concrete (LWAC), this study conducts an in-depth investigation into its hydration characteristics. In this study, high-strength LWAC was developed by incorporating low water absorption LWAs, various volume fractions of basalt fiber (BF) (0.1%, 0.2%, and 0.3%), and a ternary cementitious system consisting of 70% cement, 20% fly ash, and 10% silica fume. The hydration-related properties were evaluated through isothermal calorimetry test and high-temperature calcination test. The results indicate that incorporating 0.1–0.3% fibers into the cementitious system delays the early hydration process, with a reduced peak heat release rate and a delayed peak heat release time compared to the control group. However, fitting the cumulative heat release over a 72-h period using the Knudsen equation suggests that BF has a minor impact on the final degree of hydration, with the difference in maximum heat release not exceeding 3%. Additionally, the calculation model for the final degree of hydration in the ternary binding system was also revised based on the maximum heat release at different water-to-binder ratios. The results for chemically bound water content show that compared with the pre-wetted LWA group, under identical net water content conditions, the non-pre-wetted LWA group exhibits a significant reduction at three days, with a decrease of 28.8%; while under identical total water content conditions it shows maximum reduction at ninety days with a decrease of 5%. This indicates that pre-wetted LWAs help maintain an effective water-to-binder ratio and facilitate continuous advancement in long-term hydration reactions. Based on these results, influence coefficients related to LWAs for both final degree of hydration and hydration rate were integrated into calculation models for degrees of hydration. Ultimately, this study verified reliability of strength prediction models based on degrees of hydration. Full article
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953 KiB  
Proceeding Paper
Lie Optimal Solutions of Heat Transfer in a Liquid Film over an Unsteady Stretching Surface with Viscous Dissipation and an External Magnetic Field
by Haris Ahmad, Chaudhry Kashif Iqbal, Muhammad Safdar, Bismah Jamil and Safia Taj
Mater. Proc. 2025, 23(1), 7; https://doi.org/10.3390/materproc2025023007 - 30 Jul 2025
Abstract
A lie point symmetry analysis of flow and heat transfer under the influence of an external magnetic field and viscous dissipation was previously conducted using a couple of lie point symmetries of the model. In this article, we construct a one-dimensional optimal system [...] Read more.
A lie point symmetry analysis of flow and heat transfer under the influence of an external magnetic field and viscous dissipation was previously conducted using a couple of lie point symmetries of the model. In this article, we construct a one-dimensional optimal system for the flow model to extend the previous analysis. This optimal system reveals all the solvable classes of the flow model by deducing similarity transformations, reducing flow equations, and solving the obtained equations analytically. A general class of solutions that encompasses all the previously known lie similarity solutions is provided here. Full article
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23 pages, 2950 KiB  
Article
Thermal Conductivity of UO2 with Defects via DFT+U Calculation and Boltzmann Transport Equation
by Jiantao Qin, Min Zhao, Rongjian Pan, Aitao Tang and Lu Wu
Materials 2025, 18(15), 3584; https://doi.org/10.3390/ma18153584 - 30 Jul 2025
Viewed by 249
Abstract
Accurate evaluation of the thermal conductivity of UO2 with defects is very significant for optimizing fuel performance and enhancing the safety design of reactors. We employed a method that combines the Boltzmann transport equation with DFT+U to calculate the thermal conductivity of [...] Read more.
Accurate evaluation of the thermal conductivity of UO2 with defects is very significant for optimizing fuel performance and enhancing the safety design of reactors. We employed a method that combines the Boltzmann transport equation with DFT+U to calculate the thermal conductivity of UO2 containing fission products and irradiation-induced point defects. Our investigation reveals that the thermal conductivity of UO2 is influenced by defect concentration, defect type, and temperature. Fission products and irradiation defects result in a decrease in thermal conductivity, but they have markedly different impacts on phonon scattering mechanisms. Metal cations tend to scatter low-frequency phonons (less than 5.8 THz), while the fission gas xenon scatters both low-frequency and high-frequency phonons (greater than 5.8 THz), depending on its occupancy at lattice sites. Uranium vacancies scatter low-frequency phonons, while oxygen vacancies scatter high-frequency phonons. When uranium and oxygen vacancies coexist, they scatter phonons across the entire frequency spectrum, which further results in a significant reduction in the thermal conductivity of UO2. Our calculated results align well with experimental data across a wide temperature range and provide fundamental insights into the heat transfer mechanisms in irradiated UO2. These findings are essential for establishing a thermal conductivity database for UO2 under various irradiation conditions and benefit the development of advanced high-performance UO2 fuel. Full article
(This article belongs to the Section Energy Materials)
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21 pages, 6272 KiB  
Article
Numerical Study of Gas Dynamics and Condensate Removal in Energy-Efficient Recirculation Modes in Train Cabins
by Ivan Panfilov, Alexey N. Beskopylny, Besarion Meskhi and Sergei F. Podust
Fluids 2025, 10(8), 197; https://doi.org/10.3390/fluids10080197 - 29 Jul 2025
Viewed by 175
Abstract
Maintaining the required relative humidity values in the vehicle cabin is an important HVAC task, along with considerations related to the temperature, velocity, air pressure and noise. Deviation from the optimal values worsens the psycho-physiological state of the driver and affects the energy [...] Read more.
Maintaining the required relative humidity values in the vehicle cabin is an important HVAC task, along with considerations related to the temperature, velocity, air pressure and noise. Deviation from the optimal values worsens the psycho-physiological state of the driver and affects the energy efficiency of the train. In this study, a model of liquid film formation on and removal from various cabin surfaces was constructed using the fundamental Navier–Stokes hydrodynamic equations. A special transport model based on the liquid vapor diffusion equation was used to simulate the air environment inside the cabin. The evaporation and condensation of surface films were simulated using the Euler film model, which directly considers liquid–gas and gas–liquid transitions. Numerical results were obtained using the RANS equations and a turbulence model by means of the finite volume method in Ansys CFD. Conjugate fields of temperature, velocity and moisture concentration were constructed for various time intervals, and the dependence values for the film thicknesses on various surfaces relative to time were determined. The verification was conducted in comparison with the experimental data, based on the protocol for measuring the microclimate indicators in workplaces, as applied to the train cabin: the average ranges encompassed temperature changes from 11% to 18%, and relative humidity ranges from 16% to 26%. Comparison with the results of other studies, without considering the phase transition and condensation, shows that, for the warm mode, the average air temperature in the cabin with condensation is 12.5% lower than without condensation, which is related to the process of liquid evaporation from the heated walls. The difference in temperature values for the model with and without condensation ranged from −12.5% to +4.9%. We demonstrate that, with an effective mode of removing condensate film from the window surface, including recirculation modes, the energy consumption of the climate control system improves significantly, but this requires a more accurate consideration of thermodynamic parameters and relative humidity. Thus, considering the moisture condensation model reveals that this variable can significantly affect other parameters of the microclimate in cabins: in particular, the temperature. This means that it should be considered in the numerical modeling, along with the basic heat transfer equations. Full article
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22 pages, 5231 KiB  
Article
Exploring Ibuprofen–Menthol Eutectic Systems: Physicochemical Properties and Cytotoxicity for Pharmaceutical Applications
by Álvaro Werner, Estefanía Zuriaga, Marina Sanz, Fernando Bergua, Beatriz Giner, Carlos Lafuente and Laura Lomba
Pharmaceutics 2025, 17(8), 979; https://doi.org/10.3390/pharmaceutics17080979 - 29 Jul 2025
Viewed by 277
Abstract
Backgroun/Objectives: Recent pharmaceutical research has increasingly focused on eutectic systems to improve the formulation and delivery of active pharmaceutical ingredients (APIs). This study presents the preparation and characterization of three therapeutic eutectic systems (THEESs) based on ibuprofen and menthol at various molar ratios. [...] Read more.
Backgroun/Objectives: Recent pharmaceutical research has increasingly focused on eutectic systems to improve the formulation and delivery of active pharmaceutical ingredients (APIs). This study presents the preparation and characterization of three therapeutic eutectic systems (THEESs) based on ibuprofen and menthol at various molar ratios. Methods: The THEESs were prepared and analyzed by assessing their physicochemical properties and rheological properties were evaluated to determine flow behavior. Cytotoxicity assays were conducted on HaCaT and HepG2 cell lines to assess biocompatibility. Results: All systems formed monophasic, homogeneous, clear and viscous liquids. Key physicochemical properties, including density, refractive index, surface tension, speed of sound and isobaric heat capacity, showed a temperature-dependent, inverse proportional trend. Viscosity followed the Vogel–Fulcher–Tammann equation, and rheological analysis revealed non-Newtonian behavior, which is important for pharmaceutical processing. Notably, cytotoxicity assays revealed that Ibu-M3 and Ibu-M4 showed lower toxicity than pure compounds in HaCaT cells, while Ibu-M5 was more toxic; in HepG2 cells, only Ibu-M3 was less toxic, whereas Ibu-M4 and Ibu-M5 were more cytotoxic than the pure compounds. Conclusions: These findings highlight the potential of ibuprofen–menthol eutectic systems for safer and more effective pharmaceutical formulations. Full article
(This article belongs to the Section Physical Pharmacy and Formulation)
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23 pages, 1585 KiB  
Article
The Key Role of Thermal Relaxation Time on the Improved Generalized Bioheat Equation: Analytical Versus Simulated Numerical Approach
by Alexandra Maria Isabel Trefilov, Mihai Oane and Liviu Duta
Materials 2025, 18(15), 3524; https://doi.org/10.3390/ma18153524 - 27 Jul 2025
Viewed by 360
Abstract
The Pennes bioheat equation is the most widely used model for describing heat transfer in living tissue during thermal exposure. It is derived from the classical Fourier law of heat conduction and assumes energy exchange between blood vessels and surrounding tissues. The literature [...] Read more.
The Pennes bioheat equation is the most widely used model for describing heat transfer in living tissue during thermal exposure. It is derived from the classical Fourier law of heat conduction and assumes energy exchange between blood vessels and surrounding tissues. The literature presents various numerical methods for solving the bioheat equation, with exact solutions developed for different boundary conditions and geometries. However, analytical models based on this framework are rarely reported. This study aims to develop an analytical three-dimensional model using MATHEMATICA software, with subsequent mathematical validation performed through COMSOL simulations, to characterize heat transfer in biological tissues induced by laser irradiation under various therapeutic conditions. The objective is to refine the conventional bioheat equation by introducing three key improvements: (a) incorporating a non-Fourier framework for the Pennes equation, thereby accounting for the relaxation time in thermal response; (b) integrating Dirac functions and the telegraph equation into the bioheat model to simulate localized point heating of diseased tissue; and (c) deriving a closed-form analytical solution for the Pennes equation in both its classical (Fourier-based) and improved (non-Fourier-based) formulations. This paper investigates the nuanced relationship between the relaxation time parameter in the telegraph equation and the thermal relaxation time employed in the bioheat transfer equation. Considering all these aspects, the optimal thermal relaxation time determined for these simulations was 1.16 s, while the investigated thermal exposure time ranged from 0.01 s to 120 s. This study introduces a generalized version of the model, providing a more realistic representation of heat exchange between biological tissue and blood flow by accounting for non-uniform temperature distribution. It is important to note that a reasonable agreement was observed between the two modeling approaches: analytical (MATHEMATICA) and numerical (COMSOL) simulations. As a result, this research paves the way for advancements in laser-based medical treatments and thermal therapies, ultimately contributing to more optimized therapeutic outcomes. Full article
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21 pages, 4524 KiB  
Article
Rotational Influence on Wave Propagation in Semiconductor Nanostructure Thermoelastic Solid with Ramp-Type Heat Source and Two-Temperature Theory
by Sayed M. Abo-Dahab, Emad K. Jaradat, Hanan S. Gafel and Eslam S. Elidy
Axioms 2025, 14(8), 560; https://doi.org/10.3390/axioms14080560 - 24 Jul 2025
Viewed by 271
Abstract
This study investigates the influence of rotation on wave propagation in a semiconducting nanostructure thermoelastic solid subjected to a ramp-type heat source within a two-temperature model. The thermoelastic interactions are modeled using the two-temperature theory, which distinguishes between conductive and thermodynamic temperatures, providing [...] Read more.
This study investigates the influence of rotation on wave propagation in a semiconducting nanostructure thermoelastic solid subjected to a ramp-type heat source within a two-temperature model. The thermoelastic interactions are modeled using the two-temperature theory, which distinguishes between conductive and thermodynamic temperatures, providing a more accurate description of thermal and mechanical responses in semiconductor materials. The effects of rotation, ramp-type heating, and semiconductor properties on elastic wave propagation are analyzed theoretically. Governing equations are formulated and solved analytically, with numerical simulations illustrating the variations in thermal and elastic wave behavior. The key findings highlight the significant impact of rotation, nonlocal parameters e0a, and time derivative fractional order (FO) α on physical quantities, offering insights into the thermoelastic performance of semiconductor nanostructures under dynamic thermal loads. A comparison is made with the previous results to show the impact of the external parameters on the propagation phenomenon. The numerical results show that increasing the rotation rate Ω=5 causes a phase lag of approximately 22% in thermal and elastic wave peaks. When the thermoelectric coupling parameter ε3 is increased from 0.8×1042 to 1.2×1042. The temperature amplitude rises by 17%, while the carrier density peak increases by over 25%. For nonlocal parameter values ε=0.30.6, high-frequency stress oscillations are damped by more than 35%. The results contribute to the understanding of wave propagation in advanced semiconductor materials, with potential applications in microelectronics, optoelectronics, and nanoscale thermal management. Full article
(This article belongs to the Section Mathematical Physics)
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17 pages, 3179 KiB  
Article
Changes in Physical Parameters of CO2 Containing Impurities in the Exhaust Gas of the Purification Plant and Selection of Equations of State
by Xinyi Wang, Zhixiang Dai, Feng Wang, Qin Bie, Wendi Fu, Congxin Shan, Sijia Zheng and Jie Sun
Fluids 2025, 10(8), 189; https://doi.org/10.3390/fluids10080189 - 23 Jul 2025
Viewed by 263
Abstract
CO2 transport is a crucial part of CCUS. Nonetheless, due to the physical property differences between CO2 and natural gas and oil, CO2 pipeline transport is distinct from natural gas and oil transport. Gaseous CO2 transportation has become the [...] Read more.
CO2 transport is a crucial part of CCUS. Nonetheless, due to the physical property differences between CO2 and natural gas and oil, CO2 pipeline transport is distinct from natural gas and oil transport. Gaseous CO2 transportation has become the preferred scheme for transporting impurity-containing CO2 tail gas in purification plants due to its advantages of simple technology, low cost, and high safety, which are well suited to the scenarios of low transportation volume and short distance in purification plants. The research on its physical property and state parameters is precisely aimed at optimizing the process design of gaseous transportation so as to further improve transportation efficiency and safety. Therefore, it has important engineering practical significance. Firstly, this paper collected and analyzed the research cases of CO2 transport both domestically and internationally, revealing that phase state and physical property testing of CO2 gas containing impurities is the basic condition for studying CO2 transport. Subsequently, the exhaust gas captured by the purification plant was captured after hydrodesulfurization treatment, and the characteristics of the exhaust gas components were obtained by comparing before and after treatment. By preparing fluid samples with varied CO2 content and conducting the flash evaporation test and PV relationship test, the compression factor and density of natural gas under different temperatures and pressures were obtained. It is concluded that under the same pressure in general, the higher the CO2 content, the smaller the compression factor. Except for pure CO2, the higher the CO2 content, the higher the density under constant pressure, which is related to the content of C2 and heavier hydrocarbon components. At the same temperature, the higher the CO2 content, the higher the viscosity under the same pressure; the lower the pressure, the slower the viscosity growth slows down. The higher the CO2 content at the same temperature, the higher the specific heat at constant pressure. With the decrease in temperature, the CO2 content reaching the highest specific heat at the identical pressure gradually decreases. Finally, BWRS, PR, and SRK equations of state were utilized to calculate the compression factor and density of the gas mixture with a molar composition of 50% CO2 and the gas mixture with a molar composition of 100% CO2. Compared with the experimental results, the most suitable equation of state is selected as the PR equation, which refers to the parameter setting of critical nodes of CO2 gas transport. Full article
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21 pages, 2049 KiB  
Article
Tracking Lava Flow Cooling from Space: Implications for Erupted Volume Estimation and Cooling Mechanisms
by Simone Aveni, Gaetana Ganci, Andrew J. L. Harris and Diego Coppola
Remote Sens. 2025, 17(15), 2543; https://doi.org/10.3390/rs17152543 - 22 Jul 2025
Viewed by 1033
Abstract
Accurate estimation of erupted lava volumes is essential for understanding volcanic processes, interpreting eruptive cycles, and assessing volcanic hazards. Traditional methods based on Mid-Infrared (MIR) satellite imagery require clear-sky conditions during eruptions and are prone to sensor saturation, limiting data availability. Here, we [...] Read more.
Accurate estimation of erupted lava volumes is essential for understanding volcanic processes, interpreting eruptive cycles, and assessing volcanic hazards. Traditional methods based on Mid-Infrared (MIR) satellite imagery require clear-sky conditions during eruptions and are prone to sensor saturation, limiting data availability. Here, we present an alternative approach based on the post-eruptive Thermal InfraRed (TIR) signal, using the recently proposed VRPTIR method to quantify radiative energy loss during lava flow cooling. We identify thermally anomalous pixels in VIIRS I5 scenes (11.45 µm, 375 m resolution) using the TIRVolcH algorithm, this allowing the detection of subtle thermal anomalies throughout the cooling phase, and retrieve lava flow area by fitting theoretical cooling curves to observed VRPTIR time series. Collating a dataset of 191 mafic eruptions that occurred between 2010 and 2025 at (i) Etna and Stromboli (Italy); (ii) Piton de la Fournaise (France); (iii) Bárðarbunga, Fagradalsfjall, and Sundhnúkagígar (Iceland); (iv) Kīlauea and Mauna Loa (United States); (v) Wolf, Fernandina, and Sierra Negra (Ecuador); (vi) Nyamuragira and Nyiragongo (DRC); (vii) Fogo (Cape Verde); and (viii) La Palma (Spain), we derive a new power-law equation describing mafic lava flow thickening as a function of time across five orders of magnitude (from 0.02 Mm3 to 5.5 km3). Finally, from knowledge of areas and episode durations, we estimate erupted volumes. The method is validated against 68 eruptions with known volumes, yielding high agreement (R2 = 0.947; ρ = 0.96; MAPE = 28.60%), a negligible bias (MPE = −0.85%), and uncertainties within ±50%. Application to the February-March 2025 Etna eruption further corroborates the robustness of our workflow, from which we estimate a bulk erupted volume of 4.23 ± 2.12 × 106 m3, in close agreement with preliminary estimates from independent data. Beyond volume estimation, we show that VRPTIR cooling curves follow a consistent decay pattern that aligns with established theoretical thermal models, indicating a stable conductive regime during the cooling stage. This scale-invariant pattern suggests that crustal insulation and heat transfer across a solidifying boundary govern the thermal evolution of cooling basaltic flows. Full article
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20 pages, 4023 KiB  
Article
Numerical Study on the Thermal Behavior of Lithium-Ion Batteries Based on an Electrochemical–Thermal Coupling Model
by Xing Hu, Hu Xu, Chenglin Ding, Yupeng Tian and Kuo Yang
Batteries 2025, 11(7), 280; https://doi.org/10.3390/batteries11070280 - 21 Jul 2025
Viewed by 444
Abstract
The escalating demand for efficient thermal management in lithium-ion batteries necessitates precise characterization of their thermal behavior under diverse operating conditions. This study develops a three-dimensional (3D) electrochemical–thermal coupling model grounded in porous electrode theory and energy conservation principles. The model solves multi-physics [...] Read more.
The escalating demand for efficient thermal management in lithium-ion batteries necessitates precise characterization of their thermal behavior under diverse operating conditions. This study develops a three-dimensional (3D) electrochemical–thermal coupling model grounded in porous electrode theory and energy conservation principles. The model solves multi-physics equations such as Fick’s law, Ohm’s law, and the Butler–Volmer equation, to resolve coupled electrochemical and thermal dynamics, with temperature-dependent parameters calibrated via the Arrhenius equation. Simulations under varying discharge rates reveal that high-rate discharges exacerbate internal heat accumulation. Low ambient temperatures amplify polarization effects. Forced convection cooling reduces surface temperatures but exacerbates core-to-surface thermal gradients. Structural optimization strategies demonstrate that enhancing through-thickness thermal conductivity reduces temperature differences. These findings underscore the necessity of balancing energy density and thermal management in lithium-ion battery design, proposing actionable insights such as preheating protocols for low-temperature operation, optimized cooling systems for high-rate scenarios, and material-level enhancements for improved thermal uniformity. Full article
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16 pages, 4062 KiB  
Article
Numerical Modeling of Charging and Discharging of Shell-and-Tube PCM Thermal Energy Storage Unit
by Maciej Fabrykiewicz, Krzysztof Tesch and Janusz T. Cieśliński
Energies 2025, 18(14), 3804; https://doi.org/10.3390/en18143804 - 17 Jul 2025
Viewed by 208
Abstract
This paper presents the results of a numerical study on transient temperature distributions and phase fractions in a thermal energy storage unit containing phase change material (PCM). The latent heat storage unit (LHSU) is a compact shell-and-tube exchanger featuring seven tubes arranged in [...] Read more.
This paper presents the results of a numerical study on transient temperature distributions and phase fractions in a thermal energy storage unit containing phase change material (PCM). The latent heat storage unit (LHSU) is a compact shell-and-tube exchanger featuring seven tubes arranged in a staggered layout. Three organic phase change materials are investigated: paraffin LTP 56, fatty acid RT54HC, and fatty acid P1801. OpenFOAM software is utilized to solve the governing equations using the Boussinesq approximation. The discretization of the equations is performed with second-order accuracy in both space and time. The three-dimensional (3D) computational domain corresponds to the inner diameter of the LHSU. Calculations are conducted assuming constant thermal properties of the fluids. The experimental and numerical results indicate that for paraffin LTP56, the charging time is approximately 8% longer than the discharging time. In contrast, the discharging times for fatty acids RT54HC and P1801 exceed their charging times, with time delays of about 14% and 49% for RT54HC and 25% and 30% for P1801, according to experimental and numerical calculations, respectively. Full article
(This article belongs to the Special Issue Advancements in Energy Storage Technologies)
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22 pages, 323 KiB  
Article
The First- and Second-Order Features Adjoint Sensitivity Analysis Methodologies for Fredholm-Type Neural Integro-Differential Equations: An Illustrative Application to a Heat Transfer Model—Part II
by Dan Gabriel Cacuci
Processes 2025, 13(7), 2265; https://doi.org/10.3390/pr13072265 - 16 Jul 2025
Viewed by 197
Abstract
This work illustrates the application of the “First-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Fredholm-Type” (1st-FASAM-NIDE-F) and the “Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Fredholm-Type” (2nd-FASAM-NIDE-F) to a paradigm heat transfer model. This physically [...] Read more.
This work illustrates the application of the “First-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Fredholm-Type” (1st-FASAM-NIDE-F) and the “Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Fredholm-Type” (2nd-FASAM-NIDE-F) to a paradigm heat transfer model. This physically based heat transfer model has been deliberately constructed so that it can be represented either by a neural integro-differential equation of a Fredholm type (NIDE-F) or by a conventional second-order “neural ordinary differential equation (NODE)” while admitting exact closed-form solutions/expressions for all quantities of interest, including state functions and first-order and second-order sensitivities. This heat transfer model enables a detailed comparison of the 1st- and 2nd-FASAM-NIDE-F versus the recently developed 1st- and 2nd-FASAM-NODE methodologies, highlighting the considerations underlying the optimal choice for cases where the neural net of interest is amenable to using either of these methodologies for its sensitivity analysis. It is shown that the 1st-FASAM-NIDE-F methodology enables the most efficient computation of exactly determined first-order sensitivities of the decoder response with respect to the optimized NIDE-F parameters, requiring a single “large-scale” computation for solving the 1st-Level Adjoint Sensitivity System (1st-LASS), regardless of the number of weights/parameters underlying the NIDE-F decoder, hidden layers, and encoder. The 2nd-FASAM-NIDE-F methodology enables the computation, with unparalleled efficiency, of the second-order sensitivities of decoder responses with respect to the optimized/trained weights. Full article
(This article belongs to the Section Energy Systems)
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