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Search Results (887)

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Keywords = thermal time constant

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24 pages, 3043 KB  
Article
Friction-Induced Thermal Effects in an FGM Layer in Contact with a Homogeneous Layer
by Katarzyna Topczewska
Materials 2026, 19(7), 1299; https://doi.org/10.3390/ma19071299 (registering DOI) - 25 Mar 2026
Abstract
An analytical model of frictional heat transfer during the uniform sliding of two layers is proposed. One layer is composed of a functionally graded material (FGM) with a thermal conductivity coefficient that varies exponentially across its thickness, while the second layer is homogeneous, [...] Read more.
An analytical model of frictional heat transfer during the uniform sliding of two layers is proposed. One layer is composed of a functionally graded material (FGM) with a thermal conductivity coefficient that varies exponentially across its thickness, while the second layer is homogeneous, with constant thermophysical properties. The thermal problem of friction is formulated as an initial boundary value problem of heat conduction, accounting for the thermal contact conductance and convective heat exchange with the environment. An exact solution for constant friction power was obtained using the Laplace integral transform, supplemented by an asymptotic form for the initial stage of heating. Based on these analytical solutions, a comprehensive study was carried out for a frictional system comprising a ceramic–metal FGM composite in contact with a homogeneous friction material. A dimensional analysis allowed for both a qualitative and quantitative investigation into the influence of contact conductance, convective heat exchange, layer thickness and the FGM gradient parameter on the temperature evolution and distribution, as well as the time to reach the steady state. It was demonstrated that the implementation of an appropriately graded material can substantially improve thermal operating conditions by enhancing heat dissipation into the material bulk and intensifying convective cooling. Full article
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20 pages, 4075 KB  
Article
Data-Driven Thermal Optimization of Drill Geometry in Titanium Machining: FEM Modeling and Experimental Insights
by Ahmet Atak, Haider Khazal, Baydaa K. Khudhair, Raheem Al-Sabur, Hassanein I. Khalaf and Mahmood Alhafadhi
J. Manuf. Mater. Process. 2026, 10(3), 109; https://doi.org/10.3390/jmmp10030109 - 21 Mar 2026
Viewed by 159
Abstract
The current study offers a deeper understanding of the thermal behavior of AISI 420 stainless-steel drill bits during titanium alloy machining. It utilizes non-linear simulations with the finite element method (FEM) to analyze heat generation, accumulation, and dissipation. The FEM formulation displays the [...] Read more.
The current study offers a deeper understanding of the thermal behavior of AISI 420 stainless-steel drill bits during titanium alloy machining. It utilizes non-linear simulations with the finite element method (FEM) to analyze heat generation, accumulation, and dissipation. The FEM formulation displays the time-dependent temperatures for the tool and hole during the drilling process. The simulation was examined during drilling and subsequent stages, up to room temperature. The study explored a wide range of drill bit lengths (60–160 mm) and tool diameters (2–10 mm). Significant convergence of 4.1% was achieved when compared to infrared thermography data. Furthermore, increasing the tool length beyond 120 mm did not significantly increase the thermal effect. Moreover, increasing the tool diameter up to 10 mm also did not significantly increase the thermal efficiency compared to tool diameters between 2 and 5 mm based on a constant tool length. An exploratory data analysis (EDA) heatmap correlation matrix was used to examine the most efficient variables and the optimum tool geometry. The results obtained provide a clear understanding of the optimal geometry choice for steel drilling tools when used in drilling titanium alloys. Full article
(This article belongs to the Special Issue Advances in Metal Cutting and Cutting Tools, 2nd Edition)
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15 pages, 2181 KB  
Article
A Flexible and Thermally Uniform TiO2/Ag/SiO2 Transparent Heater for Skin-Integrated Applications
by Jaejeong Jo, Geonwoo Kang, Chankyoung Lee, Tran Thi Bao Vo and Dooho Choi
J. Funct. Biomater. 2026, 17(3), 151; https://doi.org/10.3390/jfb17030151 - 18 Mar 2026
Viewed by 336
Abstract
Transparent heaters intended for skin-contacting applications must simultaneously satisfy optical transparency, mechanical compliance, thermal uniformity, and operational safety under biologically relevant temperature ranges. Here, we evaluate the applicability of a TiO2/Ag/SiO2 (TAS) dielectric–metal–dielectric transparent heater as a functional biomaterial platform [...] Read more.
Transparent heaters intended for skin-contacting applications must simultaneously satisfy optical transparency, mechanical compliance, thermal uniformity, and operational safety under biologically relevant temperature ranges. Here, we evaluate the applicability of a TiO2/Ag/SiO2 (TAS) dielectric–metal–dielectric transparent heater as a functional biomaterial platform for wearable and skin-integrated thermal systems. By systematically optimizing each layer thickness of the TAS structure, the heater achieves high visible-light transmittance (average of 86.6%) together with low sheet resistance on the order of 7.7 Ω/sq for low-voltage operation. The TAS heater demonstrates rapid and reproducible Joule-heating behavior, showing fast thermal response with short thermal time constants and spatially homogeneous temperature distributions without localized hot spots. Stable electrothermal performance is maintained under repeated on/off cycling and during cyclic mechanical bending down to small radii, confirming excellent mechanical stability under repeated bending relevant to wearable applications. Importantly, direct on-skin evaluations conducted by attaching the device to a human elbow reveal conformal contact, uniform heating at therapeutically relevant temperatures (50–70 °C), and stable operation under dynamic bending and extension. The absence of thermal inhomogeneity during motion highlights the intrinsic stability of the TAS architecture for skin-interfaced use. Given the high optical visibility, mechanical compliance, thermal uniformity, and electrothermal stability, the proposed TAS architecture represents a promising functional biomaterial platform for wearable thermotherapy, skin-mounted healthcare devices, and human-interactive thermal systems operating under continuous mechanical deformation and direct skin contact. Full article
(This article belongs to the Special Issue Advanced Materials and Devices for Medical Interventions)
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12 pages, 2262 KB  
Article
Insights into the Oxidation Mechanism and Oxidative Stability of Nettle (Urtica dioica L.) Seed Oil: Differential Scanning Calorimetry and Ozawa–Flynn–Wall Method
by Jelena Mitrović, Nada Nikolić, Ivana Karabegović, Ivan Ristić, Dani Dordevic, Saša Savić and Bojana Danilović
Processes 2026, 14(6), 887; https://doi.org/10.3390/pr14060887 - 10 Mar 2026
Viewed by 231
Abstract
Oxidation of oils is a free-radical cascade of reactions leading to the formation of undesirable odors and tastes, nutrient degradation, and potentially harmful compounds. To better understand the oxidation process, the kinetic parameters were examined depending on the degree of conversion (0 ≤ [...] Read more.
Oxidation of oils is a free-radical cascade of reactions leading to the formation of undesirable odors and tastes, nutrient degradation, and potentially harmful compounds. To better understand the oxidation process, the kinetic parameters were examined depending on the degree of conversion (0 ≤ α ≤ 1) in this study. This approach provides insight into the complexity of the oxidative mechanism and allows a more reliable evaluation of the oxidative stability of nettle seed oil and its behavior during thermal treatment. A non-isothermal DSC method was applied, and kinetic parameters including the activation energy (Ea), the pre-exponential factor (A), and the reaction rate constant (k) were evaluated by applying the isoconversional Ozawa–Flynn–Wall method. Based on kinetic parameters, a simulation of oil oxidation at constant temperature (22 °C) was performed and the oil induction time was estimated. This value was compared to the ones obtained by OXITEST method. The observed conversion-dependent kinetic parameters demonstrate the complex oxidation behavior of nettle seed oil and justify the application of conversion-sensitive kinetic models to accurately describe its thermal stability. The induction period obtained under accelerated oxidation conditions suggests satisfactory oxidative stability of oil and highlights its potential suitability for nutritional and functional applications. Full article
(This article belongs to the Section Food Process Engineering)
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22 pages, 22545 KB  
Article
Effect of OLED Waste Glass Powder on Early Strength Performance of Rapid-Hardening Concrete
by Ngan Thanh Vu, Seong-Kyum Kim and Jae-Min Lee
Materials 2026, 19(5), 1004; https://doi.org/10.3390/ma19051004 - 5 Mar 2026
Viewed by 350
Abstract
Rapid-hardening concrete is widely used for rapid repairs but can suffer from accelerated hydration, shrinkage-related cracking, and durability concerns. This study evaluates the feasibility of replacing cement with OLED waste glass powder (0–30%) in CSA-type rapid-hardening concrete as a low-impact repair material. Mixtures [...] Read more.
Rapid-hardening concrete is widely used for rapid repairs but can suffer from accelerated hydration, shrinkage-related cracking, and durability concerns. This study evaluates the feasibility of replacing cement with OLED waste glass powder (0–30%) in CSA-type rapid-hardening concrete as a low-impact repair material. Mixtures were prepared at a constant binder content (400 kg/m3) and water-to-binder ratio (0.425), and fresh properties (slump, air content, setting time) and mechanical performance (compressive and bond strength) were tested from 4 h to 56 d. Mercury intrusion porosimetry (MIP) and TG/DTG were additionally used to interpret changes in pore structure and hydration-related thermal indices. Increasing glass powder replacement improved workability but delayed setting. A 10% replacement (O-GP10) maintained 4 h compressive strength and showed slightly higher long-term strength and consistently higher long-term bond strength than the control, whereas 20–30% replacement caused pronounced strength loss due to dilution. MIP results indicated that O-GP10 suppressed large pores (>0.1 μm) and promoted a refined pore structure dominated by finer pores. TG/DTG trends were interpreted using temperature windows as comparative indicators, suggesting age-dependent bound-water development and a reduced apparent contribution in the Al-bearing-hydrate-related region for O-GP10. Overall, roughly 10% OLED waste glass powder is suggested for CSA rapid-hardening concrete to ensure early functioning while enhancing long-term bonding and microstructural stability. Full article
(This article belongs to the Special Issue Eco-Friendly and Low-Carbon Cement-Based Materials)
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23 pages, 1148 KB  
Article
Conservation-Consistent Modeling of Time-Varying Transfer Delays with Applications in Energy Systems
by Sara Bysko, Krzysztof Łakomiec and Krzysztof Fujarewicz
Energies 2026, 19(5), 1262; https://doi.org/10.3390/en19051262 - 3 Mar 2026
Viewed by 580
Abstract
Time delays are intrinsic to energy systems, arising from transport phenomena, communication latency, and control dynamics; however, their accurate modeling remains challenging, particularly under variable operating conditions. The most common delays are constant over time and are easy to model and simulate. However, [...] Read more.
Time delays are intrinsic to energy systems, arising from transport phenomena, communication latency, and control dynamics; however, their accurate modeling remains challenging, particularly under variable operating conditions. The most common delays are constant over time and are easy to model and simulate. However, simulation tools of time-varying delay systems rely on signal-delay representations that fail to enforce conservation laws, leading to unphysical results in applications involving mass or energy transport. This study develops a physically consistent mathematical framework for time-varying transfer delays that explicitly couples kinematic evolution with conservation principles through a dynamic gain term. A systematic classification is introduced, distinguishing between signal delays (information transfer) and transfer delays (physical transport), further categorized by the source of variability in time delay into Types R (variable extraction), W (variable supply), and M (variable medium). The proposed formulation was implemented in Simulink through newly developed functional blocks supporting all delay variants and validated against representative heat transport scenarios. Comparative analysis demonstrates that standard signal-delay models violate energy conservation by generating spurious energy, whereas the proposed transfer-delay formulation preserves physical consistency under variable-flow conditions. The framework provides a rigorous foundation for accurate modeling of district heating networks, renewable energy integration with power-to-gas systems, thermal storage, and smart grid communications, supporting the development of reliable control strategies essential for the ongoing energy transition. Full article
(This article belongs to the Special Issue Advances in Heat and Mass Transfer)
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17 pages, 1164 KB  
Article
A Predictive Model and Comparative Analysis of Laser-Induced Phase Transition Thresholds for Four Key Engineering Alloys
by Lyubomir Lazov, Lyubomir Linkov, Nikolay Angelov, Edmunds Sprudzs and Arturs Abolins
Materials 2026, 19(5), 927; https://doi.org/10.3390/ma19050927 - 28 Feb 2026
Viewed by 202
Abstract
Laser-based manufacturing processes—including marking, hardening, cutting, and welding—demand the precise selection of processing parameters, as the resulting surface state is critically dependent on the delivered power density and beam–material interaction time. This study presents a unified predictive framework for estimating the critical surface [...] Read more.
Laser-based manufacturing processes—including marking, hardening, cutting, and welding—demand the precise selection of processing parameters, as the resulting surface state is critically dependent on the delivered power density and beam–material interaction time. This study presents a unified predictive framework for estimating the critical surface power density thresholds for melting qscm and evaporation qscv as functions of scanning speed v for the following four technologically important metallic materials: titanium, C26000 brass, SS304 stainless steel, and 42CrMo4 alloy steel. The principal novelty of this work is twofold. First, it provides the first directly comparative analysis of these four materials under identical, standardized laser conditions (λ = 1064 nm, d = 40 μm, constant absorptivity A = 0.4), eliminating the confounding effects of variable beam geometries and optical assumptions that hinder cross-study comparisons. Second, it translates fundamental thermophysical principles into a practical engineering tool, such as a validated spreadsheet calculator that outputs material-specific threshold curves in real time, enabling rapid, physics-based parameter estimation without recourse to complex numerical simulations. The computed threshold curves exhibit a consistent non-linear increase with scanning speed for all materials, governed by the inverse relationship between interaction time and required power density. The following clear material hierarchy emerges: C26000 brass exhibits the highest thresholds (e.g., qscm = 0.94 × 1010 W/m2, qscv = 10.74 × 1010 W/m2 at v = 100 mm/s) due to its high thermal conductivity, while titanium shows the lowest (qscm = 0.19 × 1010 W/m2, qscv = 0.48 × 1010 W/m2 at v = 100 mm/s) as a consequence of strong heat confinement. SS304 and 42CrMo4 occupy intermediate positions, with 42CrMo4 demonstrating notably higher evaporation resistance than SS304 despite similar melting thresholds. The resulting dual-threshold framework delineates three distinct process regimes—sub-melting heating, melting-dominant processing, and evaporation—providing a quantitative basis for parameter selection in applications ranging from surface hardening to micromachining. By bridging the gap between theoretical material science and applied manufacturing, this work offers a robust, first-order reference for process design and establishes a methodological template for future comparative studies of laser–material interactions. Full article
(This article belongs to the Section Materials Physics)
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21 pages, 4400 KB  
Article
What Is the Main Cause of Shrinkage Porosity in AlSi7Mg0.6 Alloy Castings Obtained with an Increased Share of Secondary Materials?
by Jaroslaw Piatkowski, Katarzyna Nowinska, Tomasz Matula and Andrzej Nowrot
Materials 2026, 19(5), 910; https://doi.org/10.3390/ma19050910 - 27 Feb 2026
Viewed by 306
Abstract
Determining the causes of shrinkage porosity in Al-Si-Mg alloy castings with an increased proportion of secondary materials is very important and poses many problems. The reason for this is the existence of two opposing theories. One assumes that plate-like α-Al5FeSi (β-Fe) [...] Read more.
Determining the causes of shrinkage porosity in Al-Si-Mg alloy castings with an increased proportion of secondary materials is very important and poses many problems. The reason for this is the existence of two opposing theories. One assumes that plate-like α-Al5FeSi (β-Fe) phase segregations cause shrinkage porosity. At the same time, the other believes that thin, double-layered oxide films with air-filled voids are responsible for the porosity. To address this question, the popular commercial alloy AlSi7Mg0.6 (EN AC-42200) was selected for testing. This alloy was cast into three series: with increasing content from 0.3 to 0.8 wt.% Fe and a constant content of approx. 0.1 wt.% Mn, the second with increasing iron and manganese contents (Mn/Fe = 1/2) (both series cast by gravity), and the third series under low pressure (approx. 0.15 MPa) with increasing content from 0.8 wt.% to 1.3 wt.% Fe and a constant content of approx. 0.1 wt.% Mn. Based on DTA (Derivative Thermal Analysis) and DSC (Differential Scanning Calorimetry) tests, the order of crystallizing components in various Mn/Fe combinations was determined. It has been found that the most unfavorable phases in gravity castings are the primary crystallizing β-Al5FeSi (β-Fe) phases (over 0.7 wt.% Fe), which are the leading cause of shrinkage porosity. After adding manganese to the alloy, thermal tests indicate that after the formation of α(Al) dendrites but before the eutectic α(Al) + β(Si), the Al15(Fe,Mn)3Si2 phase crystallizes. In die-cast samples, plate-like α-Al5FeSi (β-Fe) phase precipitates were also observed, but their share is small, and their average length does not exceed 20–30 µm. However, microstructural tests revealed the presence of rare oxides. It can therefore be assumed that in the AlSi7Mg0.6 alloy cast under pressure, the primary source of shrinkage porosity is not plate-like α-Al5FeSi (β-Fe) phase precipitates, but double-layer oxide films. In all cases, it was found that the Mg2Si phase formed at the end of crystallization does not affect shrinkage porosity. Full article
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12 pages, 3134 KB  
Article
CO2 Sensing Using Symmetrical Three-Wavelength Precompensated Current-Modulated Tunable Diode Laser Absorption Spectroscopy
by Giacomo Zanetti, Peter John Rodrigo and Christian Pedersen
Sensors 2026, 26(5), 1420; https://doi.org/10.3390/s26051420 - 24 Feb 2026
Viewed by 249
Abstract
In this paper, a novel symmetrical three-wavelength toggling archetype for measuring the concentration of gases using a tunable diode laser absorption spectroscopy (TDLAS) system is introduced and demonstrated. The system was operated at 1.5714 µm with a 2 kHz update rate, targeting an [...] Read more.
In this paper, a novel symmetrical three-wavelength toggling archetype for measuring the concentration of gases using a tunable diode laser absorption spectroscopy (TDLAS) system is introduced and demonstrated. The system was operated at 1.5714 µm with a 2 kHz update rate, targeting an absorption line of gaseous CO2. Precompensated diode–current pulses are introduced to offset the inherent thermal time constants of the diode laser by orders of magnitude. Here, repetition rates matching that of contemporary methods can be achieved, while simultaneously providing a noteworthy wavelength stability of 0.6 pm for the three targeted wavelengths that are approximately 70 pm apart (142 pm maximum wavelength excursion). A 10 Hz current loop locks one of the wavelengths to a CO2 absorption peak, thus providing an absolute and stable wavelength reference. The flexibility in choosing the shape and repetition frequency of the current pulses makes this approach easily adaptable to other gases and/or absorption lines, since wavelength filters are avoided. The new method is benchmarked against a two-wavelength precompensated continuous-wave TDLAS technique, revealing a fourfold improvement in reproducibility with system restart over the span of 24 days, while outperforming other widespread spectroscopic techniques applied to comparable transmittance levels. The effect of the analytical model was further studied by thermally inducing baseline changes, showing a 7.9 ± 0.2 times weaker correlation between concentration and temperature with respect to the one observed using the two-wavelength TDLAS archetype. These results demonstrate the system’s suitability for sensitive applications. Full article
(This article belongs to the Special Issue Advanced Sensors for Gas Monitoring: 2nd Edition)
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20 pages, 4390 KB  
Article
Study on Temperature Response Characteristics of Gas Containing Coal at Different Freezing Temperatures
by Qiang Wu, Zhaofeng Wang, Liguo Wang, Shujun Ma, Yongxin Sun, Shijie Li and Boyu Lin
Fuels 2026, 7(1), 11; https://doi.org/10.3390/fuels7010011 - 19 Feb 2026
Viewed by 236
Abstract
In the process of using the freezing method to uncover coal from stone gates, the thermal evolution profiles of the coal body during the freezing process tend to be complex due to the presence of gas and moisture. To investigate the temperature response [...] Read more.
In the process of using the freezing method to uncover coal from stone gates, the thermal evolution profiles of the coal body during the freezing process tend to be complex due to the presence of gas and moisture. To investigate the temperature response of coal containing gas under different freezing temperature conditions, a self-developed low-temperature freezing test system for coal containing water and gas was used to conduct freezing and cooling tests at different freezing temperatures (−5 °C to −30 °C). The temperature changes at various measuring points inside the coal over time were monitored in real time, and the temperature distribution, cooling law, and strain evolution process of the coal in the axial and radial directions were analyzed. The experimental results show that the cooling process of the center point of the coal can be divided into four stages: rapid cooling, extremely slow temperature drop, relatively slow cooling, and stable constant temperature. The time required to reach the stable constant temperature stage is inversely proportional to the freezing temperature, and corresponding prediction formulas have been established based on this. The standardized coal briquettes exhibit a gradient distribution characteristic of gradually increasing temperature from outside to inside in both axial and radial directions, with the radial temperature distribution being well matched by an exponential decay model. The strain of coal is affected by both thermal shrinkage and ice-induced expansion. The occurrence time of frost heave is positively correlated with freezing temperature, while the strain of frost heave is negatively correlated with freezing temperature. The axial frost heave effect is significantly stronger than the radial effect, but the radial frost heave occurs slightly earlier than the axial effect. This study reveals the thermal-mechanical coupling response mechanism of gas-containing coal during the low-temperature freezing process, and the research results can provide theoretical support for parameter optimization and engineering application of low-temperature freezing anti-outburst technology. Full article
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14 pages, 2353 KB  
Article
Synergistic Optimization of Thermoelectric Properties of Indium Oxide-Based Thermoelectric Materials by Calcium Doping Regulation
by Jie Zhang, Bo Feng, Zhiwen Yang, Yichen Li, Xuan Liu, Shilang Guo, Xiaoqi Nong, Junjie Zhang, Chenan Zhang, Xiaoqiong Zuo, Haoyu Zeng, Tongqiang Xiong, Jiang Zhu, Suoluoyan Yang and Ruolin Ruan
Inorganics 2026, 14(2), 55; https://doi.org/10.3390/inorganics14020055 - 12 Feb 2026
Viewed by 280
Abstract
The effects of Ca doping content on the crystal structure, electronic transport, thermal transport, and mechanical properties of In2O3 were systematically studied by means of X-ray diffraction (XRD), thermoelectric performance test, and first-principles calculation. XRD analysis shows that Ca2+ [...] Read more.
The effects of Ca doping content on the crystal structure, electronic transport, thermal transport, and mechanical properties of In2O3 were systematically studied by means of X-ray diffraction (XRD), thermoelectric performance test, and first-principles calculation. XRD analysis shows that Ca2+ can be completely solid-dissolved into the In2O3 lattice to form a single-phase solid solution without the formation of impurity phases, and the lattice constant increases linearly with the increase in doping content, confirming that Ca2+ successfully replaces In3+ and triggers lattice expansion. The results of thermoelectric performance tests show that Ca doping can significantly improve the electrical conductivity of the material. The essence is that Ca doping introduces a large number of free electrons through the charge compensation effect, and coordinately regulates the carrier concentration and mobility to optimize the electronic transport performance. In terms of thermal transport performance, Ca doping leads to a decreasing trend of the total thermal conductivity of the material. The core mechanism is that the difference in ionic radius between Ca2+ and In3+ causes lattice distortion, enhanced mass fluctuation scattering, and defect scattering. At the same time, the decrease in Young’s modulus intensifies phonon scattering, resulting in a significant decrease in lattice thermal conductivity (dominating the change in total thermal conductivity), while the electronic thermal conductivity increases slightly but accounts for a very low proportion. Under the synergistic optimization of electrical and thermal transport, the thermoelectric figure of merit (ZT) of the material increases from ~0.05 to ~0.239, with particularly prominent effects in the medium and high-temperature range. Full article
(This article belongs to the Special Issue Inorganic Thermoelectric Materials: Advances and Applications)
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18 pages, 8380 KB  
Article
An Experimental and Numerical Investigation into Compressor Casing Heat Shield Effectiveness
by Andrew Pilkington, Vinod Gopalkrishna, Christopher Barnes, Leo Lewis and Marko Bacic
Int. J. Turbomach. Propuls. Power 2026, 11(1), 9; https://doi.org/10.3390/ijtpp11010009 - 2 Feb 2026
Viewed by 332
Abstract
An investigation was conducted into the effectiveness of heat shields in an aero-engine compressor casing to slow down thermal time constants. The investigation used a combination of experimental measurements from a full-size compressor casing rig, combined with numerical analysis using CFD and thermal [...] Read more.
An investigation was conducted into the effectiveness of heat shields in an aero-engine compressor casing to slow down thermal time constants. The investigation used a combination of experimental measurements from a full-size compressor casing rig, combined with numerical analysis using CFD and thermal modelling. Experiments were performed on a compressor casing both with and without heat shielding in order to determine the heat shield effectiveness. Temperature measurements were taken throughout the casing in order to determine the thermal time constants. The experimental data was then used to validate a thermal model and CFD simulations of the compressor casing. The modelling allowed the heat transfer coefficients in the compressor casing to be determined from the experimentally measured time constants. It was found that the heat shields gave an increase in thermal time constant at each measured location. With a doubling in the time constant at some locations compared to the unshielded case. It was also found that the heat shields need to be fully sealed, as leakage flows significantly reduce their effectiveness. Full article
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17 pages, 1648 KB  
Article
Soil Microbial Responses to Starch-g-poly(acrylic acid) Copolymers Addition
by Katarzyna Sroka and Paweł Sroka
Sustainability 2026, 18(3), 1498; https://doi.org/10.3390/su18031498 - 2 Feb 2026
Viewed by 277
Abstract
Superabsorbent polymers (SAPs) are materials that can absorb and retain water solutions with a mass of several hundred times greater than their own. This work aimed to synthesise and evaluate the effects of highly absorbent starch phosphate-g-poly(acrylic acid) copolymers on the microbiological activity [...] Read more.
Superabsorbent polymers (SAPs) are materials that can absorb and retain water solutions with a mass of several hundred times greater than their own. This work aimed to synthesise and evaluate the effects of highly absorbent starch phosphate-g-poly(acrylic acid) copolymers on the microbiological activity of soils previously used for agriculture. The biopolymers studied were obtained by thermal and chemical oxidation of starch phosphates and copolymerized with potassium salts of acrylic acid. Basic physicochemical parameters were determined in the applied soil. Following SAP application, the basal respiration rate was measured at 22 °C with a constant soil moisture content of 60% WHC. The incubation time in constant temperature and moisture conditions was 78 days. After this period, their microbiological activity (microbial and organic phosphorus fractions) was assessed, thereby enabling the determination of the direction of change in the soil environment. The addition of SAP increases the soil’s water-holding capacity and respiration. The SP-g-PAA polymers serve as slow-release sources of potassium and phosphorus ions. These elements were bound to the polymer network by ionic and covalent bonds. Analysis of the results shows that within two weeks, 47–80% of the starch hydrogel undergoes microbial degradation. No differences were found in the content of labile forms of phosphorus in soils with SAP additions compared to soils without polymer additions. The use of modified starch reduces the consumption of vinyl monomers, while the resulting product is characterised by high absorbency and low water content, which reduces the amount of energy needed to obtain the finished product, thus contributing to sustainable development. Full article
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8 pages, 1118 KB  
Article
Conformable Fractional Newton’s Law of Cooling for Extended Time Periods
by Pablo Moreira and Othón Ortega
Symmetry 2026, 18(2), 250; https://doi.org/10.3390/sym18020250 - 30 Jan 2026
Viewed by 368
Abstract
This article presents an improved formulation of Newton’s law of cooling using the conformable fractional derivative to model long-term thermal behavior more accurately. A key feature of our approach is the use of the fractional time variable tγ, which introduces a [...] Read more.
This article presents an improved formulation of Newton’s law of cooling using the conformable fractional derivative to model long-term thermal behavior more accurately. A key feature of our approach is the use of the fractional time variable tγ, which introduces a simple scaling symmetry: the structure of the model remains unchanged even when time is proportionally stretched or compressed. This symmetry-based property provides additional flexibility compared to the classical formulation and enables the derivation of analytical solutions under both constant and non-constant ambient temperature. In particular, we incorporate sinusoidal models for ambient temperature to capture realistic environmental fluctuations over extended periods. Experimental measurements confirm that the conformable model achieves significantly better accuracy than traditional integer-order models. These results highlight the relevance of symmetry and fractional calculus in describing physical processes and demonstrate the potential of conformable methods for improving long-term thermal predictions. Full article
(This article belongs to the Section Mathematics)
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13 pages, 2876 KB  
Article
Kinetic and Machine Learning Modeling of Heat-Induced Colloidal Size Changes in Camel Milk
by Akmal Nazir, Reem Zapin, Raneem Abudayeh, Asma Obaid Hamdan Alkaabi, Anuj Niroula, Khaja Mohteshamuddin and Nayef Ghasem
Colloids Interfaces 2026, 10(1), 14; https://doi.org/10.3390/colloids10010014 - 28 Jan 2026
Viewed by 468
Abstract
This study investigated heat-induced protein aggregation in skim camel milk by monitoring changes in the volume-weighted mean particle size (d4,3) during isothermal heating (60–90 °C, up to 60 min, four temperature levels and 25 time–temperature conditions). Pronounced increases in d [...] Read more.
This study investigated heat-induced protein aggregation in skim camel milk by monitoring changes in the volume-weighted mean particle size (d4,3) during isothermal heating (60–90 °C, up to 60 min, four temperature levels and 25 time–temperature conditions). Pronounced increases in d4,3 with both time and temperature confirmed significant thermal aggregation. The reaction kinetics were described using a generalized exponential growth model, which fitted well at intermediate temperatures (e.g., coefficient of determination (R2) = 0.901 at 70 °C and 0.959 at 80 °C) but deviated at the lower (60 °C) and upper (90 °C) extremes, reflecting more complex behavior. Arrhenius analysis of the rate constant yielded an activation energy of 50.61 kJ mol−1, lower than values typically reported for bovine milk systems, indicating that camel milk proteins require less thermal input to aggregate. In parallel, a machine learning model implemented as an artificial neural network (ANN) predicted d4,3 from time-temperature inputs with high accuracy (R2 > 0.97 across training, validation, and testing), capturing nonlinear patterns without mechanistic assumptions. Together, the kinetic and ANN approaches provide complementary insights into the heat sensitivity of camel milk proteins and offer predictive tools to support the optimization of thermal processing, formulation, and quality control in dairy applications. Full article
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