Search Results (26)

Newton’s law of cooling requires a reference temperature ($T_{ref}$) to define the heat-transfer coefficient ($h$). For external flows with multiple temperatures in the freestream, obtaining $T_{ref}$ is a challenge. One widely used method, referred to as the adiabatic-wall (AW) method, obtains $T_{ref}$ by requiring the surface of the solid exposed to convective heat transfer to be adiabatic. Another widely used method, referred to as the linear-extrapolation (LE) method, obtains $T_{ref}$ by measuring/computing the heat flux ($q_s^{\prime \prime }$) on the solid surface at two different surface temperatures ($T_s$) and then linearly extrapolating to $q_s^{\prime \prime }=0$. A third recently developed method, referred to as the state-space (SS) method, obtains $T_{ref}$ by probing the temperature space between the highest and lowest in the flow to account for the effects of $T_s$ or $q_s^{\prime \prime }$ on $T_{ref}$. This study examines the foundation and accuracy of these methods via a test problem involving film cooling of a flat plate where $q_s^{\prime \prime }$ switches signs on the plate’s surface. Results obtained show that only the SS method could guarantee a unique and physically meaningful $T_{ref}$ where $T_s=T_{ref}$ on a nonadiabatic surface $q_s^{\prime \prime }=0$. The AW and LE methods both assume $T_{ref}$ to be independent of $T_s$, which the SS method shows to be incorrect. Though this study also showed the adiabatic-wall temperature, $T_{AW}$, to be a good approximation of $T_{ref}$ (<10% relative error), huge errors can occur in $h$ about the solid surface where $|T_s-T_{AW}|$ is near zero because where $T_s=T_{AW}$, $q_s^{\prime \prime }\ne 0$. Full article

Effective postharvest cooling of olive fruit is increasingly critical under rising harvest temperatures driven by climate change. This study models passive cooling dynamics using a trait-based, mixed-effects statistical framework. Ten olive groups—representing seven cultivars and different ripening or size stages—were subjected to controlled cooling conditions. Surface temperature was recorded using infrared thermal imaging, and morphological and compositional traits were quantified. Temperature decay was modeled using Newton’s Law of Cooling, extended with a quadratic time term to capture nonlinear trajse thectories. A linear mixed-effects model was fitted to log-transformed, normalized temperature data, incorporating trait-by-time interactions and hierarchical random effects. The results confirmed that fruit weight, specific surface area (SSA), and specific heat capacity (SHC) are key drivers of cooling rate variability, consistent with theoretical expectations, but quantified here using a trait-based statistical model applied to olive fruit. The quadratic model consistently outperformed standard exponential models, revealing dynamic effects of traits on temperature decline. Residual variation at the group level pointed to additional unmeasured structural influences. This study demonstrates that olive fruit cooling behavior can be effectively predicted using interpretable, trait-dependent models. The findings offer a quantitative basis for optimizing postharvest cooling protocols and are particularly relevant for maintaining quality under high-temperature harvest conditions. Full article

This study focuses on the phenomenon of boiling heat transfer during fluid flow (Fluorinert FC-72) in minichannels. The research stand was built around a specially designed test section incorporating sets of aligned minichannels, each 1 mm deep. These channel arrays varied in number, comprising configurations with 7, 15, 17, 19, 21, and 25 parallel channels. The test section was vertically orientated with upward fluid flow. To address the heat transfer problem associated with transient flow boiling, two numerical approaches grounded in the finite element method (FEM) were employed. One used the Trefftz function formulation, while the other relied on simulations performed using the commercial software ADINA (version 9.2). In both approaches, the heat transfer coefficient at the interface between the heated foil and the working fluid was determined by applying a Robin-type boundary condition, which required knowledge of the temperatures in both the foil and the fluid, along with the temperature gradient within the foil. The outcomes of both FEM-based models, as well as those of a simplified 1D method based on Newton’s cooling law, yielded satisfactory results. Full article

Federated learning is a distributed machine learning technique that allows multiple devices to collaborate on learning a shared model without exchanging data. It can be used to improve model accuracy while protecting user privacy. However, traditional federated learning is vulnerable to attacks from generative adversarial networks (GANs). As a new privacy protection method, differential privacy enhances privacy protection capabilities by sacrificing some data accuracy. To optimize the privacy budget allocation scheme in traditional differential privacy, we propose a differential privacy method called ADP-FL, which dynamically adjusts the privacy budget based on Newton’s Law of Cooling. While maintaining the overall privacy budget, it dynamically tunes adaptive parameters to improve training accuracy. Additionally, we propose an asynchronous federated learning aggregation scheme that combines privacy budget with data freshness, thereby reducing the impact of differential privacy on accuracy. We conducted extensive experiments on differential privacy algorithms based on Gaussian mechanisms and Laplace mechanisms. The experimental results show that, under the same privacy budget, our algorithm achieves higher accuracy and lower communication overhead compared to the baseline algorithm. Full article

Carbon-textile-reinforced concrete (CTRC) is increasingly being used in the construction industry as a high-performance composite material combining non-metallic textile reinforcement with concrete. Known for its exceptional characteristics such as tensile strength, density, and durability, CTRC also exhibits electrical conductivity, enabling efficient electrical heat generation within building components. This study develops and validates a thermal model to predict the temperature evolution of electrically heated CTRC, incorporating Newton’s law of cooling and Joule’s heating principle. The proposed model segments the temperature development into three distinct phases: heating, constant, and cooling. The temperature calculation accounts for these phases, their boundary conditions, and material-specific parameters, which were determined through laboratory experiments. For the investigated CTRC material combinations, the model accurately predicts temperature profiles, demonstrating strong agreement between experimental and calculated results. Moreover, significant variations in electrical power requirements were observed among the tested materials. The investigated impregnation materials of the carbon textile reinforcement (CTR) significantly influence contact quality and resulting temperature behavior. This research bridges material science and thermal performance, expanding the potential for CTRC use in electrically heated construction solutions. Full article

The conservation of the olive ridley turtle (Lepidochelys olivacea) is increasingly critical due to declining global populations. This study investigates the influence of hydrometeorological conditions on the nesting season and annual hatchling sex ratios conducted at the Playón de Mismaloya Federal Reserve in Tomatlán, Jalisco, Mexico. The research specifically examines variations in sand temperature at both the beach surface and nesting depths, with extended measurements taken at multiple depths (20, 40, 60, 80, and 100 cm) to analyze the vertical temperature gradient along the beach. Atmospheric parameters were modeled using Newton’s Cooling Law and solved with the finite difference method to estimate heat loss rates from beach sand to its surroundings, shedding light on microclimatic effects on incubation and embryonic development. Meteorological data were gathered from an automatic weather station, while sand temperatures were monitored with thermographs. During the warm period (approximately 32 °C), sand temperature showed a negative correlation with depth (20–100 cm), indicating cooler temperatures at greater depths. These conditions were associated with female-biased hatchling production. Conversely, the cold period (approximately 28 °C) led to male-biased hatchling production, with a positive correlation between sand and air temperatures. This study emphasizes the importance of monitoring in situ environmental conditions and extending the protection season until February to avoid the loss of male hatchlings. Full article

Experiments on specimen cooling dynamics and possible film boiling around a body are very important in various industrial applications, such as nucleate boiling, to decrease drag reduction or achieve better surface properties in coating technologies. The objective of this study was to investigate the interaction between the heat transfer processes and cooling dynamics of a sample in different boundary conditions. This article presents new experimental data on specimens coated with Al–TiO₂ film and Leidenfrost phenomenon (LP) formation on the film’s surface. Furthermore, this manuscript presents numerical heat and mass transfer parameter results. The comparative analysis of new experiments on Al–TiO₂ film specimens and other coatings such as polished aluminium, Al–MgO, Al–MgH₂ and Al–TiH₂ provides further detail on oxide and hydride materials. In the experimental cooling dynamics experiments, specimens were heated up to 450 °C, while the sub-cooling water temperatures were 14*‒20 °C (room temperature), 40 °C and 60 °C. The specimens’ cooling dynamics were calculated by applying Newton’s cooling law, and heat transfer was estimated by calculating the heat flux $q$ transferred from the specimens’ surface and the Bi parameter. The metadata results from the performed experiments were used to numerically model the cooling dynamics curves for different material specimens. Approximated polynomial equations are proposed for the polished aluminium, Al–TiO₂, Al–MgO, Al–MgH₂ and Al–TiH₂ materials. The provided comparative analysis makes it possible to see the differences between oxides and hydrides and to choose materials for practical application in the industrial sector. The presented results could also be used in software packages to model heat transfer processes. Full article

The article aims to explore boiling heat transfer in mini-channels with a rectangular cross-section using various fluids (HFE-649, HFE-7000, HFE-7100, and HFE-7200). Temperature measurements were conducted using infrared thermography for the heated wall and K-type thermocouples for the working fluid. The 2D mathematical model for heat transfer in the test section was proposed. Local heat transfer coefficients between the heated wall and the working fluid were determined from the Robin condition. The problem was solved by means of the finite element method (FEM) with Trefftz functions. The values of the heat transfer coefficient that were obtained were compared with the results calculated from Newton’s law of cooling. The average relative differences between the obtained results did not exceed 4%. The study included uncertainty analyses for temperature measurements with K- and T-type thermocouples. Expanded uncertainties were calculated using the uncertainty propagation and Monte Carlo methods. Precisely determining the uncertainties in contact temperature measurements is crucial to ensure accurate temperature data for subsequent heat transfer calculations. The results of the heat transfer investigations were compared in terms of fluid temperature, heat transfer coefficients, and boiling curves. HFE-7200 consistently exhibited the highest fluid temperature and temperature differences at boiling incipience, while HFE-7000 demonstrated the highest heat transfer coefficients. HFE-649 showed the lowest heat transfer coefficients. The boiling curves exhibited a typical shape, with a notable occurrence of ‘nucleation hysteresis phenomena’. Upon the analysis of two-phase flow patterns, bubbly and bubbly-slug structures were observed. Full article

The accurate and detailed measurement of the vertical temperature, humidity, pressure, and wind profiles of the atmosphere is pivotal for high-resolution numerical weather prediction, the determination of atmospheric stability, as well as investigation of small-scale phenomena such as urban heat islands. Traditional approaches, such as weather balloons, have been indispensable but are constrained by cost, environmental impact, and data sparsity. In this article, we investigate uncrewed aerial systems (UASs) as an innovative platform for in situ atmospheric probing. By comparing data from a drone-mounted semiconductor temperature sensor (TMP117) with traditional radiosonde measurements, we spotlight the UAS-collected atmospheric data’s accuracy and such system suitability for atmospheric surface layer measurement. Our research encountered challenges linked with the inherent delays in achieving ambient temperature readings. However, by applying specific data processing techniques, including smoothing methodologies like the Savitzky–Golay filter, iterative smoothing, time shift, and Newton’s law of cooling, we have improved the data accuracy and consistency. In this article, 28 flights were examined and certain patterns between different methodologies and sensors were observed. Temperature differentials were assessed over a range of 100 m. The article highlights a notable accuracy achievement of 0.16 ± 0.014 °C with 95% confidence when applying Newton’s law of cooling in comparison to a radiosonde RS41’s data. Our findings demonstrate the potential of UASs in capturing accurate high-resolution vertical temperature profiles. This work posits that UASs, with further refinements, could revolutionize atmospheric data collection. Full article

Centrifugal spray deposition forming technology, which is used in the preparation process of near-net-forming billets, not only reduces the macroscopic segregation and refines the microstructures of billets but also has the characteristics of a rapid solidification structure. The trajectory, velocity, heat transfer and solidification of metal droplets granulated by the centrifugal force during flight will affect the shape, precision and microstructure of the billet. Therefore, it is necessary to study the dynamics and thermal history of droplets in flight. In this study, a single droplet is taken as the object. Considering the resistance of ambient gas, Newton’s second law, classical nucleation theory, Newton’s cooling law and the energy conservation equation were used to establish a dynamic model and heat transfer solidification model of liquid metal droplets during flight. The influence of the centrifugal disc speed on the diameter of granulated droplets was analyzed. The variation law of droplet flight trajectory and velocity was explored. The supercooling degree in metal droplet nucleation was quantified, and the influence of droplet diameter, superheat and other factors on heat transfer and solidification was revealed. The results show that the numerical calculation results are basically consistent with the previous research results. The trajectory of the droplet is parabolic during flight. The initial velocity of the droplet, the environmental gas resistance and the convective heat transfer coefficient are positively correlated with the rotating speed of the centrifugal disc; however, the droplet diameter is negatively correlated with the rotating speed of the centrifugal disc. The super cooling degree at the time of droplet nucleation and the flight time required for solidification are negatively correlated with the droplet diameter. Among them, the droplet diameter has a linear relationship with the solidification start time and a quadratic curve relationship with the solidification end time. The effect of superheat on the heat transfer and solidification of droplets is not obvious. The conclusions obtained can provide a theoretical basis for the determination of the preparation process parameters. Full article

Determination of the heat transfer coefficient (HTC) distribution is important during the design and operation of many devices in microelectronics, construction, the car industry, drilling, the power industry and research on nuclear fusion. The first part of the manuscript shows works describing how a change in the coefficient affects the operation of devices. Next, various methods of determining the coefficient are presented. The most common method to determine the HTC is the use of Newton’s law of cooling. If this method cannot be applied directly, there are other methods that can be found in the open literature. They use analytical formulations, the lumped thermal capacity assumption, the 1D unsteady heat conduction equation for a semi-infinite wall, the fin model, energy conservation and the analogy between heat and mass transfer. The HTC distribution can also be calculated by means of computational fluid dynamics (CFD) modelling if all boundary conditions with fluid and solid properties are known. Often, the surface on which the HTC is to be determined is not accessible for any measuring sensors, or their installation might disturb the analysed phenomenon. It also happens that calculations using direct or CFD methods cannot be performed due to the lack of required boundary conditions or sufficiently proven models to analyse the considered physical phenomena. Too long a calculation time needed by CFD tools may also be problematic if the method should be used in the online mode. One way to solve the above problem is to assume an unknown boundary condition and include additional information from the sensors located at a certain distance from the investigated surface. The problem defined in this way can be solved by inverse methods. The aim of the paper is to show the current state of knowledge regarding the importance of the heat transfer coefficient and the variety of methods that can be used for its determination. Full article

Soldering in a reflow oven is an important and efficient technical means to produce integrated circuit boards. The key to the quality of integrated circuit boards lies in the furnace temperature curve. In this paper, Newton’s law of cooling is used to establish the mechanism model of the temperature of each zone of the furnace and the curve of furnace temperature, which can reduce the number of experiments in actual production and obtain a better furnace temperature curve, thus improving production efficiency. Finally, several concrete examples are given to discuss and solve some common problems in the industry. Full article

One-dimensional heat-conduction models in a semi-infinite domain, although forced convection obeys Newton’s law of cooling, are challenging to solve using standard integral transformation methods when the boundary condition φ(t) is an exponential decay function. In this study, a general theoretical solution was established using Fourier transform, but φ(t) was not directly present in the transformation processes, and φ(t) was substituted into the general theoretical solution to obtain the corresponding analytical solution. Additionally, the specific solutions and corresponding mathematical meanings were discussed. Moreover, numerical verification and sensitivity analysis were applied to the proposed model. The results showed that T(x,t) was directly proportional to the thermal diffusivity (a) and was inversely proportional to calculation distance (x) and the coefficient of cooling ratio (λ). The analytical solution was more sensitive to the thermal diffusivity than other factors, and the highest relative error between numerical and analytical solutions was roughly 4% under the condition of 2a and λ. Furthermore, T(x,t) grew nonlinearly as the material’s thermal diffusivity or cooling ratio coefficient changed. Finally, the analytical solution was applied for parameter calculation and verification in a case study, providing the reference basis for numerical calculation under specific complex boundaries, especially for the study of related problems in the fields of fluid dynamics and peridynamics with the heat-conduction equation. Full article

The performance and efficiency of green energy sources in electric vehicles (EVs) are significantly affected by operation temperatures. To maintain the optimal temperatures of a hybrid energy system (HES), an innovative hybrid thermal management system (IHTMS) was designed. The IHTMS contains a coolant pump, a heat exchanger, a proportional valve for hybrid flow rates, five coolant pipes, and three electromagnetic valves to form two mode-switch coolant loops. A Matlab/Simulink-based simulator of the IHTMS was constructed by formulating a set of first-ordered dynamics of temperatures of coolant pipes and energy bodies using the theories of Newton’s law of cooling and the lumped-parameter technique. Parameters were majorly derived by measured performance maps and data from the experimental platform of the IHTMS. To properly manage the optimal temperatures, four control modes were designed for inner-loop form and outer-loop form. For the experimental platform to verify the simulator, two power supplies generated the waste heat of dual energy sources calculated by the driving cycle and vehicle dynamics. Simulation results show that the temperatures were controlled at their optimal ranges by proper mode/loop switch. With the inner-loop mechanism, the rise time of optimal temperature decreased 27.4%. The average simulation-experiment temperature error of the battery was $0.898$ °C; the average simulation-experiment temperature error of the PEMFC was $4.839$ °C. The IHTMS will be integrated to a real HES in the future. Full article

The operating conditions during the braking process in an automobile affect the tribological contact between the pad and disc brake, thus, influencing the times and distances of braking and, in a more significant way, the safety of the braking process. This mathematical work aimed to provide a general visualization of the disc brake’s mechanical, dynamic, and thermal behavior under different operating conditions through 2D maps of the power dissipated, braking time, and braking distance of a disc brake with a ventilation blade N- 38 type. However, the dissipated energy on the disc brake in terms of temperature was analyzed considering Newton’s cooling law and mathematical calculations through classical theories of the dynamic and mechanical behavior of the disc brakes. For this purpose, the Response Surface Methodology (RSM) and Distance Weighted Least Squares (DWLS) fitting model considered different operating conditions of the disc brake. The results demonstrate that the disc brakes can be used effectively in severe operational requirements with a speed of 100 km/h and an ambient temperature of 27 °C, without affecting the occupant’s safety or the braking system and the pad. For the different conditions evaluated, the instantaneous temperature reaches values of 182.48 and 82.94 °C, where the high value was found for a total deceleration to 100 km/h to 0, which represent a total braking distance of around 44.20 to 114.96 m depending on the inclination angle (θ). Furthermore, the energy dissipation in the disc brakes depends strongly on the disc, blades and pad geometry, the type of material, parameters, and the vehicle operating conditions, as can be verified with mathematical calculation to validate the contribution of the effectiveness of the braking process during its real operation. Full article