Heat Conduction Research Articles

Ultra-Efficient Heat Transport Across a "2.5D" All-Carbon sp2/sp3 Hybrid Interface.

Single- and few-layer graphene-based thermal interface materials (TIMs) with extraordinary high-temperature resistance and ultra-high thermal conductivity are very essential to develop the next-generation integrated circuits. However, the function of the as-prepared graphene-based TIMs would undergo severe degradation when being transferred to chips, as the interface between the TIMs and chips possesses a very small interfacial thermal conductance. Here, a "2.5D" all-carbon interface containing rich covalent bonding, namely a sp2/sp3 hybrid interfaces is designed and realized by a plasma-assisted chemical vapor deposition with a function of ultra-rapid quenching. The interfacial thermal conductance of the 2.5D interface is excitingly very high, up to 110-117 MWm-2 K-1 at graphene thickness of 12-25 nm, which is even more than 30 % higher than various metal/diamond contacts, and orders of magnitude higher than the existing all-carbon contacts. Atomic-level simulation confirm the key role of the efficient heat conduction via covalent C-C bonds, and reveal that the covalent-based heat transport could contribute 85 % to the total interfacial conduction at a hybridization degree of 22 at %. This study provides an efficient strategy to design and construct 2.5D all-carbon interfaces, which can be used to develop high performance all-carbon devices and circuits.

Ultra‐Efficient Heat Transport Across a “2.5D” All‐Carbon sp2/sp3 Hybrid Interface

AbstractSingle‐ and few‐layer graphene‐based thermal interface materials (TIMs) with extraordinary high‐temperature resistance and ultra‐high thermal conductivity are very essential to develop the next‐generation integrated circuits. However, the function of the as‐prepared graphene‐based TIMs would undergo severe degradation when being transferred to chips, as the interface between the TIMs and chips possesses a very small interfacial thermal conductance. Here, a “2.5D” all‐carbon interface containing rich covalent bonding, namely a sp2/sp3 hybrid interfaces is designed and realized by a plasma‐assisted chemical vapor deposition with a function of ultra‐rapid quenching. The interfacial thermal conductance of the 2.5D interface is excitingly very high, up to 110–117 MWm−2 K−1 at graphene thickness of 12–25 nm, which is even more than 30 % higher than various metal/diamond contacts, and orders of magnitude higher than the existing all‐carbon contacts. Atomic‐level simulation confirm the key role of the efficient heat conduction via covalent C−C bonds, and reveal that the covalent‐based heat transport could contribute 85 % to the total interfacial conduction at a hybridization degree of 22 at %. This study provides an efficient strategy to design and construct 2.5D all‐carbon interfaces, which can be used to develop high performance all‐carbon devices and circuits.

Contact metamorphism and dolomitization overprint on Cambrian carbonates from the Ossa-Morena Zone (SW Iberian Massif): implications to Sr-chronology of carbonate rocks

AbstractThe Cambrian Series 2 Carbonate Formation from the Alter do Chão Elvas-Cumbres Mayores unit (Ossa-Morena Zone, SW Iberian Massif) is composed of regionally metamorphosed marbles and marlstones that underwent chlorite zone metamorphism and preserve the primaeval limestone 87Sr/86Sr ratios (0.7083–0.7088). These are consistent with the established Lower Cambrian seawater curve, and therefore used for age constraints in formations lacking fossil contents. The regional mineralogical and Sr-isotopic features of the carbonate rocks are frequently overprinted by the effects of contact metamorphism induced by magmatic bodies emplaced during rift-related and synorogenic events of the Palaeozoic, as well as by post-metamorphic dolomitization processes. The development of calc-silicate minerals due to contact metamorphism is common in the rocks of the Carbonate Formation and apparently results from the interaction of the protolith with fluids of different origin: (i) internally produced fluids released by conductive heating (observed in external contact aureoles) and (ii) external intrusion-expelled fluids that, besides leading to the appearance of distinctive assemblages, also promote an influx of strontium content (observed in roof pendants). Calc-silicate mineralogy varies substantially throughout the region, likely due to the heterogeneous distribution of silicate minerals of the protolith, progression of intrusion-driven fluids, and the irregular effect of thermal gradients. Results suggest that high-grade contact metamorphism (hornblende facies or higher) and dolomitization processes imposed on the Carbonate Formation significantly influence the isotopic signatures of the carbonates, providing limitations in applying Sr-isotopic chronology. Graphical abstract

Investigation of internal thermal distribution in inverted perovskite solar cell and improvement of its heat dissipation performance

Abstract COMSOL Multiphysics software was used to construct a numerical opto-electro-thermal coupling model to investigate the mechanisms of internal heat generation, conduction, and dissipation in inverted (p-i-n architecture) perovskite solar cells (PSCs). The research results indicate that Joule heating and Shockley-Read-Hall (SRH) recombination are the primary sources of heat, leading to significant accumulation of heat at the interfaces between the perovskite and the electron transport layer (ETL), as well as between the ETL and the electrode. This concentration of heat not only affects the performance of the device but also poses challenges for overall thermal management. Therefore, we compared four different top electrode materials (Ag, Cu, Al, and reduced graphene oxide) to assess their performance in terms of heat dissipation efficiency. The results showed that reduced graphene oxide (RGO) performed exceptionally well in heat dissipation efficiency, primarily due to its high thermal conductivity, which enables it to effectively reduce heat accumulation at the interfaces, thereby improving performance of PSCs. This finding provides important material selection criteria for optimizing the thermal management of PSCs.

Heat Transfer Characteristics of Cryogenically Frozen Kulfi (A Dairy Dessert)

Kulfi was frozen from concentrated milk as well as from reconstituted dry mix with solids content of 60%. The convective heat transfer coefficients during freezing of kulfi by deep freeze and cryogenic methods were determined using one-dimensional transient heat conduction equation. The heat transfer coefficient for cryogenic freezing of kulfi from milk and dry mix concentrates was 210.57 W m-2K-1 and 216.84 W m-2K-1, respectively when compared to 8.33 W m-2K-1 for conventional deep-frozen kulfi. Freezing was achieved in 267 min in deep freeze method, while it reduced to just 185-190 s under cryogenic conditions. The freezing time was predicted using empirical equations, and the prediction accuracies were compared. Cryogenic freezing was nearly 87.66 times faster than deep freezing, and Pham’s model best-predicted the freezing time. Organoleptic evaluation using fuzzy-logic revealed that the order of ranking of quality attributes of kulfi was body and texture (highly important) > melting characteristics (highly important) > flavour and taste (highly important) > colour and appearance (important), and cryogenically frozen kulfi was statistically (p<0.05) superior to conventionally frozen kulfi.

ON THE HEAT CONDUCTION EQUATION AND THE HEAT DISSIPATION FUNCTION IN ANISOTROPIC REACTING FLUID MIXTURES WITH MAGNETIC RELAXATION

In some previous papers, within the framework of the thermody namics of irreversible processes with internal variables, a linear theory for magnetic relaxation phenomena in anisotropic mixtures, consisting of n reacting fluid components, was developed. In particular, assuming that the macroscopic magnetization m can be split in two irreversible parts m = m(0) + m(1) a generalized Snoek equation was derived. In this paper we derive for these reacting anisotropic mixtures the heat conduction equation. We show that the heat dissipation function is due to the chemical reactions, the magnetic relaxation, the electric conduc tion, the viscous, magnetic, temperature fields and the diffusion and the concentrations of the n fluid components. Also, the Snoek and De Groot special cases are studied. The obtained results find applications in nuclear resonance, in biology, in medicine and other fields, where different species of molecules have different magnetic susceptibilities and relaxation times and contribute to the total magnetization.

Qualitative Analysis of the Heat Transfer in a Package of Square Steel Sections

During the heat treatment of square or rectangular steel sections, a heated charge, arranged in regular packages, is placed inside a furnace. This type of charge forms a porous medium through which a complex heat flow occurs during heating. Several heat transfer mechanisms act simultaneously within this medium: conduction through the section walls, conduction and natural convection within the gas, thermal radiation between the section walls, and complex heat transfer (mainly contact conduction) at the joints between the adjacent sections. This article presents a qualitative analysis of heat transfer, aiming to determine the contribution of individual heat transfer mechanisms to the overall process. For this purpose, an analytical model of complex heat transfer within the package was employed, based on the thermo-electric analogy. The results from experimental studies were used to calculate the natural convection and heat transfer at the joints. It was assumed that the material of the sections was low-carbon steel, and the gas was air. Calculations were performed for the temperature range of 25 °C to 700 °C, considering three different geometrical configurations of the sections. It was shown that the effective thermal conductivity (ETC) of the package for the considered geometrical cases varies between 2.2 and 10.6 W/(m·K), which is an order of magnitude lower than the thermal conductivity of the individual sections. This parameter increased dynamically with the temperature. Moreover, the heat transfer intensity within the package of sections was nearly an order of magnitude lower than the heat conduction observed in a solid steel charge. Additionally, it was shown that the primary heat transfer mechanisms governing the heating process were thermal conduction (in the lower temperature range—up to approximately 350 °C) and thermal radiation (in the higher temperature range—above 350 °C). The gas convection inside the sections had a minimal impact on the heating process of the package. The primary parameters influencing the quality of the results were the joint resistance between the adjacent sections and the emissivity of the sections. The presented model can be used for the optimization of heat treatment processes for the considered charge.

Research on temperature rise prediction model for circuit breaker based on numerical laplace transform

Abstract The temperature rise in circuit breakers' thermal paths is a critical indicator influencing their tripping characteristics, directly affecting response speed, reliability, and safety. Existing models for predicting circuit breaker temperature rise are often structurally limited, lack generality, and exhibit low predictive accuracy. Addressing this issue, this paper investigates an efficient, precise, and widely applicable theoretical model for predicting circuit breaker temperature rise. This model focuses on the thermal conduction mechanisms within small-scale circuit breakers, establishing a fundamental numerical heat transfer model based on Newton's cooling formula and Fourier's heat conduction law. By applying numerical Laplace transformation, the model is simplified into the complex frequency domain, and employing residue theorem for solving, it is transformed back into the time domain using Laplace inverse transformation to derive the predictive model. Experimental validation using a 32A rated current circuit breaker demonstrates the model's high predictive accuracy, suitability across various circuit breaker structures, with an average deviation below the permissible deviation in industry standards. This research holds significant implications for enhancing the thermal tripping characteristics of circuit breakers.

A Monte Carlo Approach for Simulating Electrical Conductivity in Highly Porous Ceramic Composites: Impact of Internal Structure.

Porous ceramic composites play an important role in several applications. This is due to their unique properties resulting from a combination of various materials. Determination of the composite properties and structure is crucial for their further development and optimization. However, composite analysis often requires complex, expensive, and time-demanding experimental work. Mathematical modeling represents an effective tool to substitute experimental approach. The present study employs a Monte Carlo 3D equivalent electronic circuit network model developed to analyze a highly porous composite on the basis of minimum easily obtainable input parameters. Solid oxide cell electrodes were used as a model example, and this study focuses primarily on materials with a porosity of 55% and higher, characterized by deviation of behavior from those of lower void fraction share. This task is approached by adding to the original Monte Carlo model an additional parameter defining the void phase coalescence phenomenon. The enhanced model accurately simulates electrical conductivity for experimental samples of up to 75% porosity. Using sample composition, single-phase properties, and experimentally determined conductivity, this model allows us to estimate data of the internal structure of the material. This approach offers a rapid and cost-effective method to study material microstructure, providing insights into properties, such as electrical conductivity and heat conductivity. The present research thus contributes to advancing predictive capabilities in understanding and optimizing the performance of composite materials with potential in various technological applications.

Hydrodynamic heat conduction based on eigenvalues and eigenvectors of the normal collision operator

Abstract Although the Guyer-Krumhansl equations has opened up the study of phonon hydrodynamics in ultra-low temperature and low dimensional non-metallic crystals, it still cannot explain the high thermal conductivity of low dimensional non-metallic materials in adiabatic environments. In this work, the analytical solution of the linear Boltzmann transport equation with the Callaway approximation is obtained by expanding the nonequilibrium distribution function into a series of the orthogonal eigenvectors of the normal-process collision operator. By assuming the normal scatterings dominate the heat conduction in an anisotropic non-metallic crystal allowing the different branches of the phonon frequency spectrum having different group velocity, the macroscopic energy and momentum balance equations are developed for describing the phonon hydrodynamic transport. For an isotropic and dispersionless system, these balance equations reduce to the improved Guyer-Krumhansl equations. The thermal conductivity in these balance equations includes not only the contribution of the resistive scatterings, but also the contribution of the normal scatterings. Therefore, the improved Guyer-Krumhansl equations is capable for explaining the high thermal conductivity of suspended graphene, which is validated by the experimental results. Finally, the improved Guyer-Krumhansl equations is employed to derive the occurrence condition of the second sound in suspended single-layer graphene.

Crystallization and crystal morphology of polymers: A multiphase-field study

In this paper, we introduce a coarse-grained model of polymer crystallization using a multiphase-field approach. The model combines a multiphase-field method, Nakamura’s kinetic equation, and the equation of heat conduction for studying microstructural evolution of crystallization under isothermal and non-isothermal conditions. The multiphase-field method provides flexibility in adding any number of phases with different properties making the model effective in studying blends or composite materials. We apply our model to systems of neat PA6 and study the impact of initial distribution of crystalline grains and cooling rate on the morphology of the system. The relative crystallinity (conversion) curves show qualitative agreement with experimental data. We also investigate the impact of including carbon fibers on the crystallization and grain morphology. We observe a more homogeneous crystal morphology around fibers. This is associated with the higher initial volume fraction of crystal grains and higher heat conductivity of the fiber (compared to the polymer matrix). Additionally, we observe that the crystalline grains at the fiber surface grow perpendicular to the surface. This indicates that the vertical growth observed in experiments is merely due to geometrical constraints imposed by the fiber surface and neighbouring crystalline regions.

Propagation, reflection, and transmission of nonlocal waves at the interface between semiconductor isotropic and diffusive porous semiconductors through a higher-order fractional derivative study

The current research paper investigates the transmission of nonlocal waves occurring at the interface between a semiconductor isotropic medium and a diffusive porous solid. A higher-order fractional-order derivative heat conduction model is utilized to account for thermal effects on wave propagation, reflection, and transmission. The interface generates five coupled and one independent transmitted wave in the lower medium, along with three coupled transmitted waves and one independent SV wave. Graphical analyses are conducted to examine the propagation speed of reflected waves in both porous and non-porous media. The impact of elastic non-locality and the fractional-order parameter on the propagation speed of all waves within the media is also assessed. The amplitude ratios are computed for the incident longitudinal displacement wave at the free boundary. The research explores the influence of physical parameters on reflection and transmission coefficients, and the results are validated through the conservation of energy. Additionally, the analysis yields deductions for certain special cases.

Flow behavior and heat transfer characteristics of liquid film on vertical hot surface by inclined jet impingement

In this study, the flow behavior and heat transfer characteristics of the liquid film on the hot wall by inclined jet impingement are experimentally studied in detail. The effects of jet parameters, such as jet inclination angle, impingement distance, jet Reynolds number (Rej), and nozzle diameter are explored. The liquid film flow is visualized using a high-speed camera, and the surface temperature and heat flux are obtained by solving the inverse heat conduction problem. The results indicate that the liquid film shape is strongly affected by jet inclination angle but is almost unaffected by other parameters. As the inclination angle increases, the liquid film shape changes from elliptical to fusiform. In addition, the onset, enhancement, and disappearance of boiling cause the expansion and contraction of liquid film. The splashing rate is barely affected by jet parameters and remains within the range of 80–95 % under all conditions. The propagation of wetting fronts exhibits anisotropy. Except for the impingement distance, the position of wetting fronts along y-axis direction displays a high dependence on all parameters. The Rej and nozzle diameter have a significant effect on the heat flux at the impingement point and parallel flow zone, while the jet inclination angle and impingement distance only effect the impingement point. The visualization image proves that the droplet impingement pattern is the main reason for the increase in heat flux at higher impingement distances. Optimizing jet parameters can promote the wall to enter the rapid cooling stage in advance and increase maximum heat flux, thereby improving the maximum cooling capacity of the jet. Finally, an empirical equation is proposed to predict the maximum Nusselt number.

Adaptive fractional physics-informed neural networks for solving forward and inverse problems of anomalous heat conduction in functionally graded materials

In this paper, adaptive fractional physics-informed neural networks (PINNs) are employed to solve the forward and inverse problems of anomalous heat conduction in three-dimensional functionally graded materials. In adaptive fractional PINNs, the finite difference L1 scheme is employed to discretize the time fractional derivatives in anomalous heat conduction problems. By combining the finite difference L1 scheme with automatic differentiation technique, adaptive fractional PINNs minimize a loss function constructed based on the governing equation, initial and boundary conditions to obtain solutions to heat conduction problems. To avoid competition among various loss terms during the training process, an adaptive loss balancing algorithm is adopted to balance the interactions among different terms of the loss functions. In addition, polynomial basis functions are used to expand unknown functions characterizing material parameters or heat sources, aiming to enhance the performance of adaptive fractional PINNs in resolving inverse problems. Five numerical examples involving forward, inverse, and nonlinear problems related to anomalous heat conduction are carried out to demonstrate the feasibility and effectiveness of adaptive fractional PINNs.

Pressure-regulated rotational guests in nano-confined spaces suppress heat transport in methane hydrates

Materials with low lattice thermal conductivity are essential for various heat-related applications like thermoelectrics, and usual approaches for achieving this rely on specific crystalline structures. Here, we report a strategy for thermal conductivity reduction and regulation via guest rotational dynamics and their couplings with lattice vibrations. By applying pressure to manipulate rotational states, we find the intensified rotor-lattice couplings of compressed methane hydrate MH-III can trigger strong phonon scatterings and phonon localizations, enabling an almost three-fold suppression of thermal conductivity. Besides, the disorder in methane rotational dynamics results in anharmonic interactions and nonlinear pressure-dependent heat transport. The overall guest rotational dynamics and heat conduction changes can be flexibly regulated by the rotor-lattice coupling strength. We further underscore that this reduction mechanism can be extended to a wide range of systems with different structures. The results demonstrate a potentially universal method for reducing or controlling heat transport by developing a hybrid system with tailored molecular rotors.

Thermal processes affected by carbon dioxide near ground surface

This study provides penetrative investigation of the effects of carbon dioxide concentration on time-dependent temperature and energy fluxes on the ground surface subject to solar irradiation. While global warming significantly impacts human life, the factors responsible remain controversial. This work considers unsteady one-dimensional heat conduction and radiative heat transfer, including collimated and diffuse components as functions of longitude, latitude, and altitude. Diffuse radiation depends on the different absorption bands of carbon dioxide and water vapor, as functions of wavelength, temperature, concentrations or pressure. The predicted results using COMSOL computer code show that the effects of carbon dioxide concentration on ground surface temperature are negligibly small, for example, over a 5-year period. Time-dependent ground surface temperature strongly depends on the absorption or dissipation of diffuse radiation and heat conduction. Diffuse radiation has a damping effect on temperature variation. Temperature changes due to solar irradiation absorption in the atmosphere are also negligibly small, despite solar irradiation being much greater than diffuse radiation and heat conduction. The absorption or dissipation of diffuse radiation depends on the dominant absorption bands centered at 4.3 and 15 μm of carbon dioxide at different times. This study, from the viewpoint of energy conservation, identifies diffuse radiation as a critical factor influencing the rate of temperature change at the ground surface, without assuming radiative or thermal equilibrium or modeling convection. Poor management of this radiation would hinder efforts to avoid droughts, water scarcity, severe fires, rising sea levels, flooding, catastrophic storms, and biodiversity loss.

Impact of Pore Diameter on Heat Conduction Efficiency in Porous Media Based on Ansys

Abstract. To help advance the development of heat dissipation technologies, the research studies the effect of pore diameter on heat conduction within porous media. With the help of Ansys software, a cuboid with varying pore sizes is modelled to investigate its influence on effective thermal conductivity. Through analysing the data exported, an overall trend is derived: for a fixed number of nodes in a piece of porous material, the efficiency of heat conduction tends to be higher with the increase of pore sizes. The study is especially relevant for the design of radiators with porous plates, commonly used in cooling systems. Larger pores tend to facilitate more gas-phase conduction, which, when combined with solid-phase conduction, optimizes overall thermal conductivity. The results of the study can potentially advance the development of heat dissipation technologies.

Thermal management optimization strategy for lithium-ion battery based on phase change material and fractal fin

In order to solve the problem of temperature control of lithium-ion battery (LB) in electric vehicles, a new battery thermal management system (BTMS) based on phase change material (PCM) coupled fractal fin (FF) was proposed. The effects of latent heat, thickness, and thermal conductivity of PCM (paraffin) on the thermal properties of BTMS were investigated. Subsequently, the fin structure was added to the BTMS to improve the heat transfer capacity, and the number of fins, aspect ratio, material and structure morphology were explored. The results show that when the latent heat of PCM is 200 kJ/kg, the thickness is 2 cm, and the thermal conductivity is 0.8 W/(m·K), the temperature of LB is 34.9 K lower than that of LB without the BTMS at 4C. In addition, the BTMS has the best performance when FF-II with a fin count of 5, aspect ratio of 7:1, and material of carbon steel are used. The temperatures of LB are 301.8 K, 303.9 K, 305.4 K, and 307.3 K at 1 to 4C, respectively, and the temperature difference in BTMS can be controlled within 2.5 K. This study provides some guidance for the optimization of BTMS.

An investigation of the physic-mechanical properties of the expanded perlite mortars with thermal-activated concrete waste and microencapsulated paraffin

In the transition to zero waste and sustainable development, it becomes essential to use phase change materials and recycled cement in construction projects to improve energy efficiency and encourage sustainable building practices. The primary goal of this study is to determine how the properties of expanded perlite mortars are affected when Portland cement is partially replaced with recycled cement, produced by thermally treating concrete waste at 550˚C. Recycled cement substituted Portland cement in various percentages (10%, 30%, and 50%). Also, microencapsulated phase change material (m-PCM) was incorporated into the mortar in a proportion of 2 wt.% and 5 wt.%. Cement-based mortars with a 1:3 aggregate volume ratio have been developed for evaluation. The mortars were analyzed in terms of mechanical strength (flexural and compressive), water absorption, thermal properties, differential scanning calorimetry, and microstructure. The experimental results revealed a decrease in mechanical strength values when Portland cement is substituted by recycled cement, regardless of percentage. Recycled cement in proportion of 30% positively influenced the water absorption. The thermal conductivity of reference mortar was higher than that of 30% recycled cement. The reference mortar's specific thermal conductivity values were 0.466 W/(m·K) at 25°C, 0.525 W/(m·K) at 30°C, and 0.589 W/(m·K) at 35°C. On the other hand, the mortar containing 30% recycled cement exhibited much lower heat conductivity throughout these temperatures, suggesting superior insulating qualities. DSC analysis verified that adding m-PCM to the mortars increased their thermal storage capacity, which is essential for raising the energy efficiency of building materials. Nevertheless, the mechanical strength decreased as m-PCM was added. Despite decreases, all mortars satisfied the SR EN 998–1 standard's CS IV classification for interior plaster applications, which is based on compressive strength requirements. Overall, this study shows how using m-PCM and recycled materials can improve the performance of cement-based materials.

Experimental study on the low-temperature preheating performance of positive-temperature-coefficient heating film in the prismatic power battery module

The performance of a power battery directly affects the thermal safety performance of the vehicle. Aiming at the improvement of thermal safety of lithium-ion batteries under low temperature condition, this study focuses on the effect of the positive-temperature-coefficient (PTC) heating film on the heating performance of batteries through experimental testing. First, the side and bottom of the cell were heated, and the heat transfer path and mode of the single cell were analyzed. The effects of different power densities and geometric positions on the heating effect were studied by testing the heating time and temperature consistency. Second, for the battery module, a low-temperature heating thermal management heat transfer model was built to analyze the heating mechanism of the heating film under different heating power densities. Finally, the results of these studies were synthesized to obtain the optimal heating power density. The results show that for the cell, the optimum power density of side heating and bottom heating is 0.5 W /cm2 and 0.4 W /cm2, respectively. The time required for side heating from −20 °C to 10 °C is 730 s lower than that of bottom heating, and the maximum temperature difference is 1.885 °C lower. For battery modules, a power density of 0.5 W/cm2 was appropriate for both bottom and side heating methods. Due to the existence of heat conduction between battery packs, the battery modules will be quickly and evenly preheated. Under the optimal power density, the time length for side heating from –20 °C to 10 °C was 1459 s, and the maximum temperature difference was 6.32 °C; bottom heating time required slightly more time (1783 s), and the maximum temperature difference was 6.221 °C. Side heating can be beneficial for the rapid preheating of the battery module. This study will contribute to improving the performance and safety of batteries in cold environments.