Heat Coefficient Research Articles

Heat kernel coefficients on Kähler manifolds

Polterovich proved a remarkable closed formula for heat kernel coefficients of the Laplace operator on compact Riemannian manifolds involving powers of Laplacians acting on the distance function. In the case of Kähler manifolds, we prove a combinatorial formula for powers of the complex Laplacian and use it to derive an explicit graph-theoretic formula for the numerics in heat coefficients as a linear combination of metric jets based on Polterovich’s formula.

Thermal performance analysis of a domestic-size absorption cooling system incorporating nanofluid with thermal insulation in hot climate of Algeria

The increased demand for energy consumption for air conditioning, due to rising temperatures, has created challenges related to thermal comfort in residential environments .In the present study, a simulation of an air conditioning system for a small building was conducted, considering various absorption cooling scenarios to assess system performance through dynamic and economic analysis. The proposed system employs a parabolic trough collector in conjunction with a storage tank, designed to cool a 12 m² room in Adrar, Algeria. The study aims to identify the optimal scenario based on temperature, heat, and system coefficient of performance indicators. A computer program was developed using characteristic equations and finite difference methods to analyze the system's behavior with different nanofluid concentrations and thermal insulation. Simulation results show that scenario with nanofluid and insulation the best performance is achieved with a 4% nanofluid concentration, a 9 m² solar collector, a 0.3 m³ storage tank, and 0.05 m thick polystyrene insulation. The system can operate for 9 h, maintaining an indoor temperature of 27°C with a peak cooling load of 3 kW. The economic analysis estimates an investment cost of 4535.4$ and Net Present Value 3,370.40$ with a payback period of 12 years and 3 months.

Predictions of windage heating and flow characteristics in a high-speed rotating seal of aero-engine

The labyrinth seal plays a crucial role within the secondary air system of an aeroengine, significantly impacting its safety and reliability. This paper presents a comprehensive evaluation of the complex windage heating phenomenon within a high-speed rotating labyrinth seal system. Employing similarity criteria and dimensional analysis, the multifactorial influences on the seal system are thoroughly characterized. A dedicated high-speed rotating labyrinth seal test rig was constructed to conduct an experimental investigation into the windage heating characteristics of a four-tooth, stepped-slanted labyrinth seal. The results demonstrate a peak windage heating of 11.8 K and windage heating coefficient of 1.14 when the inlet temperature rose from ambient to 100 °C, under the rotating Mach number of 0.418 and pressure ratio of 1.1. Conversely, as the seal clearance increased from 0.2 mm to 0.6 mm, with a rotating Mach number of 0.487 and a pressure ratio of 2.0, the windage heating coefficient decreased to 0.57. Furthermore, five dimensionless operating cases were analyzed using similarity principles to elucidate the correlation between system performance and the combined effects of strong rotating flow and windage heating characteristics. The analysis revealed that the windage heating coefficient exhibited a decreasing trend with increasing flow Reynolds number, effective pressure ratio, inlet swirl ratio, and dimensionless clearance, as the effective pressure ratio increase from 1.1 to 5.0, with the rotating Mach number of 0.624 and flowing Reynolds number of 9600, the windage heating coefficient decrease from 1.831 to 0.797, representing a 56 % reduction. Conversely, the windage heating coefficient increased with a rising rotating Mach number, while the flowing Reynolds number demonstrated a minor influence.

Comprehensive analysis of a novel sustainable photovoltaic/thermal assisted ground source heat pump system with energy storage

The imbalance of soil heat is a significant issue hindering the sustainable operation of ground source heat pump (GSHP) systems, especially under single-mode heating conditions. To address this challenge and develop a more energy-efficient, economical, and sustainable heating system, this paper proposes a novel PV/T-GSHP-PCM (photovoltaic/thermal-ground source heat pump-phase change material) system. A simulation model of the system was developed, and its performance was thoroughly analyzed. Furthermore, the comprehensive performance of four different system coupling configurations was compared. The study concluded that the PV/T-GSHP-PCM system increases energy efficiency by 13 % and reduces operating costs by 32 % compared to conventional GSHP systems. Furthermore, the PV/T-GSHP-PCM system achieves zero energy consumption, zero operational cost, and zero carbon dioxide emissions. After 10 years of continuous operation under single-mode heating, the soil heat imbalance rate stabilized at around 7 %, the heating coefficient of performance of the system decreased by only 0.04. This system demonstrates sustainable and efficient green heating. This study provides valuable insights for advancing research on sustainable and renewable energy-based heating systems.

Microstructure and Properties of Aluminum Alloy/Diamond Composite Materials Prepared by Laser Cladding.

In this article, AlSi10Mg aluminum alloy was used as the substrate to prepare aluminum alloy/diamond composite materials with laser cladding technology. The effects of the composition and laser power on the microstructure and thermal properties of the composite materials were studied. The results show that the prefabrication of tungsten carbide layer on the diamond surface enhances the wettability of diamond with aluminum alloy and reduces the laser reflection, which ensures the implementability of laser cladding technology for the preparation of aluminum alloy/diamond composites. The laser power and components determine the temperature of the molten pool and thus the state of the organization of the composite material to be formed by cladding. With the increase in the diamond content, the density, specific heat, mechanical properties, and average linear thermal expansion coefficient of the composite material gradually decrease, while the thermal conductivity first increases and then decreases. The thermal conductivity of the aluminum alloy/diamond composite material prepared by laser cladding is 200.68 W/mK, and the linear thermal expansion coefficient is 1.904 × 10-5/K, which are superior to those of the matrix AlSi10Mg aluminum alloy.

Phase-transition metamaterial smart window for radiative cooling and privacy protection

This paper proposes a smart window for radiative cooling with adjustable transparency by leveraging the phase transition property of VO2. The proposed smart window exhibits daytime visible light transmission and near-infrared light reflection, all-day radiative cooling, and a nighttime privacy protection feature. It comprises a bottom layer of VO2/Ag/VO2 and top cubic two-dimensional SiO2 gratings, with structural parameters optimized by the genetic algorithm to ensure excellent optical performance. In the daytime, 75.4% visible light transmittance and 87.8% near-infrared reflectance can be achieved by utilizing the dielectric state of VO2. It also achieves low light transmission of 9.8% by using the metallic state of VO2, which is suitable for nighttime privacy protection. Furthermore, it has an all-day outside emissivity of 98.2% for radiative cooling, together with a low inside emissivity of 1.9% for effectively inhibiting the radiation heat transfer. In addition, the proposed structure is insensitive to the angles of incidence and the polarization of light, making it advantageous for radiative cooling. During the daytime, it reduces the temperature by 17.7 K compared to a glass of equal thickness when the non-radiative heat coefficient is 12 W/m2/K. At night, it achieves a cooling power of 124.7 W/m2, achieving a cooling effect of 8.9 K below ambient temperature. The proposed smart window is promising for various application scenarios for radiative cooling and privacy protection and could be used as windows for buildings and vehicles.

Graph Curvature Flow-Based Masked Attention.

Graph neural networks (GNNs) have revolutionized drug discovery in chemistry and biology, enhancing efficiency and reducing resource demands. However, classical GNNs often struggle to capture long-range dependencies due to challenges like oversmoothing and oversquashing. Graph Transformers address these issues by employing global self-attention mechanisms that allow direct information exchange between any pair of nodes, enabling the modeling of long-range interactions. Despite this, Graph Transformers often face difficulties in capturing the nuanced structural information on graphs. To overcome these challenges, we introduce the CurvFlow-Transformer, a novel graph Transformer model incorporating a curvature flow-based masked attention mechanism. By leveraging a topologically enhanced mask matrix, the attention layer can effectively detect subtle structural differences within graphs, balancing the focus between global mutual information and local structural details of molecules. The CurvFlow-Transformer demonstrates superior performance on the MoleculeNet data set, surpassing several state-of-the-art models across various tasks. Moreover, the model provides unique insights into the relationship between molecular structure and chemical properties by analyzing the attention heat coefficients of individual atoms.

Correction to: Determination of Heat and Mass Emission Coefficients in a Hybrid Cooling Tower with Transversely Finned Radiator Pipes

Correction to: Determination of Heat and Mass Emission Coefficients in a Hybrid Cooling Tower with Transversely Finned Radiator Pipes

Experimental determination of the entropic heat coefficient of a lithium-ion cell through immersion in a dielectric fluid

The heat generation of a lithium-ion cell is predominantly comprised of irreversible and reversible heating, with the latter term dictated by the entropic heat coefficient which describes the variation of the cell’s open circuit voltage with respect to temperature. The entropic heat coefficient is also dependent upon the cell’s state of charge, and the correct description of its behaviour is required to implement numerical and analytical models which accurately describe the heat generation rate of lithium-ion cells. In this study, the entropic heat coefficient of a single 26,650 LiFePO4 cylindrical lithium-ion cell is determined through a novel liquid immersion experimental set-up, offering greater thermal uniformity and control in comparison to the environmental chambers typically utilised. The arrangement is more cost effective and easily implemented in a laboratory setting, with a thermal non-uniformity of 0.2 °C and setpoint stability of ± 0.1 °C achieved. The entropic heat coefficient is determined for six setpoint temperatures in the range of 15 °C to 40 °C across the cell’s entire state of charge, which is adjusted in increments of 10 %. This work also details the influence of open circuit voltage instability arising from cell self-discharge and relaxation, and a method to adjust for its effect is proposed and implemented. The entropic heat coefficient is subsequently utilised to determine the heat generation rate of the cell under two-phase liquid immersion cooling conditions.

Recent Advances in High-Entropy Ceramics: Synthesis Methods, Properties, and Emerging Applications

High-entropy ceramics (HECs) represent an emerging class of materials composed of at least five different cations or anions in near-equiatomic proportions, garnering significant attention due to their extraordinary functional and structural properties. While multi-component ceramics have played a crucial role for many years, the concept of high-entropy materials was first introduced eighteen years ago with the synthesis of high-entropy alloys, and the first high-entropy nitride films were reported in 2014. These newly developed materials exhibit superior properties over traditional ceramics, such as enhanced thermal stability, hardness, and chemical resistance, making them suitable for a wide range of applications. High-entropy carbides, borides, oxides, oxi-carbides, oxi-borides, and other systems fall within the HEC category, typically occupying unique positions within phase diagrams that lead to novel properties. HECs are particularly well suited for high-temperature coatings, for tribological applications where low thermal conductivity and similar heat coefficients are critical, as well as for energy storage and dielectric uses. Computational tools like CALPHAD streamline the element selection process for designing HECs, while innovative, energy-efficient synthesis methods are being explored for producing dense specimens. This paper provides an in-depth analysis of the current state of the compositional design, the fabrication techniques, and the diverse applications of HECs, emphasizing their transformative potential in various industrial domains.

Performance analysis of a solar-assisted ground source heat pump with a single vertical U-tube ground heat exchanger

Owing to higher heat loads than cooling loads in cold climates, the performance of ground source heat pumps (GSHPs) can significantly degrade over time, leading to eventual system failure for systems not properly sized or when there is insufficient regeneration. Solar-assisted ground source heat pump (SAGSHP) systems are receiving increasing interest as a means of enhancing heating performance and maintaining ground thermal balance in cold regions. However, a critical gap remains in the literature: no study has comprehensively analyzed configurations of SAGSHP systems to enhance their overall performance considering long-term performance and realistic operating conditions. For this purpose, a comprehensive investigation of the long-term performance of single U-tube and double U-tube ground heat exchangers (GHEs) for solar-assisted ground source heat pump systems (SAGSHPs) was carried out and compared with the conventional GSHP. The effect of collector tilt angles (0–90°) on the performance of the single U-tube SAGSHP was also examined. A finite volume computational fluid dynamic model was developed and coupled with an actual building energy load profile and a solar irradiation profile based on Calgary’s weather conditions using a novel custom-coded thermodynamic model. Results show that the yearly average heating coefficient of performance (COP) increases by a factor of 1.21 and 1.18 for the single U-tube SAGSHP and double U-tube SAGSHP, respectively, when compared with the conventional GSHP. However, the average annual cooling COP reduces by 0.65 for the single U-tube and 0.72 for the double U-tube SAGSHPs. Moreover, considering the effect of tilt angle on the single U-tube SAGSHP, it is possible to improve the cooling COP when the collector tilt angle is 90°, at the expense of lower heating COP. However, the highest heating COP and annual energy savings are achieved with a tilt angle of 45°. This study provides practical insight into SAGSHP performance enhancements in cold climates.

A novel heating system of solar-assisted enhanced jet enthalpy air source heat pump for cold regions

Solar energy and air source heat pumps are common heat sources for clean heating, but at lower ambient temperatures, the performance of solar energy and air source heat pumps will decline significantly, which can be ameliorated by integrating the two heat sources. However, the range of solar radiation and ambient temperature variation is very wide, and the existing integration methods cannot guarantee that they are optimal over a wide range. Therefore, this paper proposes a novel integration method of solar energy and jet enthalpy air source heat pump suitable for cold regions, where solar energy is used to heat the refrigerant in the jet branch to increase the flow rate of the jet branch, which enhances the effect of jet enthalpy. Under varying outdoor temperatures and solar radiations, the performances of the new integrated system and the traditional integrated systems are compared by simulation method. The results show that within the scope of this study (outdoor temperatures ranging from −30 °C to 10 °C, and radiations from 200 to 800 W/m2), the heat output and coefficient of performance of the new system are higher than those of the existing integrated systems. At an outdoor temperature of −30 °C and a radiation of 500 W/m2, the new system increases heat output by 45.8 % and coefficient of performance by 22.5 % compared with the existing two systems. This research can promote the application of solar energy and air source heat pump heating in cold regions.

Impact of thermal conductivity of a Williamson’s nanofluid flow due to a stretching sheet

This paper intends to build a mathematical model of a two-dimensional Williamson nanofluid flow due to the stretching of a sheet linearly. The flow geometry is influenced by the magnetic field that is applied externally to the system. The induced magnetic field is infinitesimal and hence neglected. However, the flow structure is incorporated with the Brownian motion and thermophoresis effects as it alter the physics of the flow. The equations that model the flow comprise the highly nonlinear coupled simultaneous system. Thus, a numerical technique namely finite difference accompanied with the Thomas algorithm is adopted to approach the flow system. The motion, temperature, and concentration of the Williamson nanofluid flow are studied for the different flow controlling parameters. The co-efficient of skin-friction, heat, and mass transfer rates is also computed. The streamlines, isotherms, and iso-concentration are plotted to picturise the flow phenomena in the complete domain. The study reveals that the temperature of the flow raises with the Brownian motion of the nanoparticles and the trend is opposite with the concentration. The strength of the streamlines, isotherms, and the concentration contour is identified to be high for the least magnitude of Weissenberg number. The Brownian motion raises the heat transfer rate and slows down the mass transfer rate.

Effect of Sintering Temperature on the Microstructure and Mechanical and Tribological Properties of Copper Matrix Composite for Brake Pads

Copper-based powder metallurgy materials are frequently utilized in fabricating brake pads for high-speed trains. The preparation process involves mixing, ball milling, pressing, and sintering. Among these steps, hot-pressed sintering stands out as a rapid and efficient method that significantly influences the properties and performance of the products. In this study, four samples (S700/S750/S800/S850) were prepared using hot-pressed sintering at various temperatures, as follows: 700 °C, 750 °C, 800 °C, and 850 °C. The mechanical and physical properties of the four samples were tested, and the microstructure and compositions were investigated using scanning electron microscopy, energy dispersive spectroscopy, and X-ray diffraction. The findings highlighted the close relationship between sintering temperature and the mechanical and physical properties of the samples, as it impacts the porosity and interfacial bonding of the particles. Notably, Sample S800 demonstrated superior mechanical and thermal conductivity. Furthermore, the coefficient of friction (COF), friction heat, and wear rate of the four samples were also tested under different braking speeds ranging from 150 km/h to 350 km/h. The results indicated that the COFs of the four samples remained relatively stable below 300 km/h but decreased notably above 300 km/h due to heat fading. Sample S800 displayed consistent and high COF under varied braking speeds and exhibited the lowest wear rate. The observed wear mechanisms included abrasive wear and oxidation wear. Additionally, the friction test results underscored the close correspondence of the COF curve of S800 with the standard of the Ministry of Railways of the People’s Republic of China.

Thermodynamic and economic analysis of a solar-assisted ejector-enhanced flash tank vapor injection heat pump cycle with dual evaporators

This paper proposes a solar-assisted ejector-enhanced flash tank vapor injection heat pump cycle with dual evaporators (SEFVIC), designed for heat pump drying application. Compared to the standard flash tank vapor injection heat pump cycle (FVIC), the SEFVIC uses an additional high-temperature evaporator to further minimize irreversible losses during the heat transfer process. Moreover, it integrates solar energy to improve the drying quality and heating capacity of the cycle. Meanwhile, the introduction of an ejector improves the system's performance by reducing throttling loss. The advantages of SEFVIC over FVIC are evaluated using theoretical models based on the first and second laws of thermodynamics. Results show that SEFVIC reveals a 34.1 % improvement in the heating coefficient of performance and a 192.8 % enhancement in volumetric heating capacity compared to FVIC under typical operating condition. Notably, SEFVIC maintains superior performance even at lower evaporating temperatures. Moreover, exergy research indicates that 77.1 % of the total exergy destruction in SEFVIC is attributed to the solar collector. Economic analysis indicates that the integration of solar energy into the SEFVIC is economically beneficial. These findings highlight the prospective application of SEFVIC and guide combining the multi-temperature heat pump drying system and auxiliary solar source.

Experimental study on the impact of indoor unit airflow velocity on the performance of an automotive heat pump system with a suction line heat exchanger

This study aimed to investigate the effect of changing the indoor unit air flow rate on the performance of an automobile heat pump with a suction line heat exchanger. Using a four-way valve, the automotive heat pump system was developed by reversing the refrigerant direction in the automobile air conditioning system, excluding the compressor. A suction line heat exchanger was added to the test system to enhance heat transfer between the liquid and suction lines of the automotive heat pump system. Performance comparisons were first performed for R134a and R1234yf by disabling the suction line heat exchanger. Then, the suction line heat exchanger was activated for R1234yf, and the tests were repeated. Performance comparisons were made for two different compressor speeds and three different indoor unit airflow speeds. It was found that using the heat exchanger in R1234yf operations improved the heating capacity, compressor discharge temperature and coefficient of performance by approximately 1.8 %, 5.1 % and 5.9 %, respectively. The heating capacity of the heat pump system using R134a, R1234yf, and R1234yf with the suction line heat exchanger was determined to be in the range of 2.46–3.29 kW, 2.35–3.04 kW, and 2.39–3.11 kW, respectively. An increase in the airflow speed of the indoor unit from 1.4 m s−1 to 3.2 m s−1 resulted in an average decrease of approximately 12.3 % in the compressor discharge temperature. In contrast, the heating capacity and coefficient of performance increased by approximately 11.8 % and 14.4 % on average, respectively, for R1234yf operations with the heat exchanger. This study revealed that by optimizing the air flow rate in the R1234yf heat pump system with a suction line heat exchanger, improvements in the heating capacity and coefficient of performance can be achieved, thus providing better thermal comfort in the passenger compartment.

Investigation of a high-temperature combination heat pump for lower-cost electrification in multifamily buildings

The development of space and water heating combination heat pumps capable of generating water temperatures high enough for convective heat emitters will enable more cost-effective and equitable decarbonization solutions for electrifying multifamily buildings. In this paper, multifamily building models and a charge-sensitive mechanistic cycle model of a combination heat pump are developed, and the system performance is predicted based on the models. Unlike other state-of-the-art residential heat pumping equipment, the modeled combination heat pump using an economized, fluid-injected variable-speed compressor can achieve higher temperature lifts of 40° – 85°C, with lower installation costs and complexity. The model predicted heating coefficient of performance (COPh) is 2.1 at an ambient temperature of −15°C with a high-temperature lift of nearly 85°C, and a seasonal coefficient of performance in heating mode (SCOPh) ranges from 2 – 4 for different locations. The system shows 30% – 90% lower CO2eq emissions over a condensing gas boiler and 9% – 13% lower projected installation costs than two separate space and water heat pumping appliances.

A simple graphical method for sizing flat‐plate solar air heaters based on transversal and longitudinal aspect ratios

AbstractSolar air heaters (SAHs) are widely used for drying vegetables and fruits or for domestic heating. Certain sizing parameters are necessary to obtain the right dimensions for the required air temperature, flow rate, and thus useful thermal energy. The well‐known Hottel–Whillier–Bliss equation was used and made dimensionless by applying the collector longitudinal and transversal aspect ratios (rl and rt) of a double‐glazed flat plate solar air heater (DG‐FPSAH). The steady‐state equations are solved to determine the average temperatures. Thereafter, one could calculate the overall loss heat coefficient and efficiency factor, obtained analytically. A Matlab code was developed to estimate primarily unknown temperatures, useful energy, and the Nusselt number. An iterative numerical method is used until convergence occurs. The inlet cross‐sectional area and air flow velocity are defined as input data. The proposed sizing method depends on the output temperature required by the customer. This temperature can be determined from the plotted curves of the dimensionless ratios. Hence, the SAH‐needed dimensions are determined graphically depending on the functional requirements for construction planning, such as technology choice, work breakdown, and budgeting. In the present case study, based on the input parameters, an airflow rate of 1.2 kg/s entering a DG‐FPSAH with an output temperature of 41.5°C yields the dimensions of Lin = 3.824 m, Win = 2.735 m, and Hin = 0.1825, specifying the collector length, width, and air duct height. The gathered energy and thermohydraulic efficiency are: Qu = 7.91 kW, ηcol = 0.752, respectively.

The diamond-silicon carbide composite Skeleton® as a promising material for substrates of intense X-ray beam optics.

The paper considers the possibility of using the diamond-silicon carbide composite Skeleton® with a technological coating of polycrystalline silicon as a substrate for X-ray mirrors used with powerful synchrotron radiation sources (third+ and fourth generation). Samples were studied after polishing to provide the following surface parameters: root-mean-square flatness ≃ 50 nm, micro-roughness on the frame 2 µm × 2 µm σ ≃ 0.15 nm. The heat capacity, thermal conductivity and coefficient of linear thermal expansion were investigated. For comparison, a monocrystalline silicon sample was studied under the same conditions using the same methods. The value of the coefficient of linear thermal expansion turned out to be higher than that of monocrystalline silicon and amounted to 4.3 × 10-6 K-1, and the values of thermal conductivity (5.0 W cm-1 K-1) and heat capacity (1.2 J K-1 g-1) also exceeded the values for Si. Thermally induced deformations of both Skeleton® and monocrystalline silicon samples under irradiation with a CO2 laser beam have also been experimentally studied. Taking into account the obtained thermophysical constants, the calculation of thermally induced deformation under irradiation with hard (20 keV) X-rays showed almost three times less deformation of the Skeleton® sample than of the monocrystalline silicon sample.

Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition

This work investigates the thermal Casimir effect associated with a massive spinor field defined on a four-dimensional flat space with a circularly compactified spatial dimension whose periodicity is oriented along a vector in the xy plane. We employ the generalized zeta function method to establish a finite definition for the vacuum free energy density. This definition conveniently separates into the zero-temperature Casimir energy density and additional terms accounting for temperature corrections. The structure of existing divergences is analyzed from the asymptotic behavior of the spinor heat kernel function and removed in the renormalization by subtracting scheme. The only non-null heat coefficient is the one associated with the Euclidean divergence. We also address the need for a finite renormalization to treat the ambiguity in the zeta function regularization prescription associated with this Euclidean heat kernel coefficient and ensure that the renormalization procedure is unique. The high- and low-temperature asymptotic limits are also explored. In particular, we explicitly show that free energy density lacks a classical limit at high temperatures, and the entropy density agrees with the Nernst heat theorem at low temperatures. Published by the American Physical Society 2024