Thermal Conduction Research Articles

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 32 A 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.

Transport Properties of Liquid Pentaerythritol Tetranitrate (PETN) from Molecular Dynamics Simulations.

We have used molecular dynamics simulations to determine the transport properties of liquid pentaerythritol tetranitrate (PETN), an important energetic material. The density, ρ, self-diffusion coefficient, D, thermal conductivity, κ, and shear viscosity, μ, have been computed over pressures and temperatures relevant to the subshock regime (up to 1000 K and a few GPa), where PETN is known to melt prior to initiation. We find that the thermal conductivity κ(P, T) can be represented by a simple analytical function that fits the data points with very good accuracy, even beyond the subshock regime, up to 2000 K and 20 GPa. The self-diffusion coefficient, D, exhibits nonmonotonic behavior, with notably the temperature-independent prefactor decreasing by several orders of magnitude between 0 and 2 GPa before remaining nearly constant after, and the activation energy varying little in the subshock regime before increasing linearly beyond. Lastly, the viscosity, μ, is well described by Nahme's law, which is fitted to the MD results and allows us to predict μ(P, T) for temperatures and pressures corresponding to the subshock regime. These results can be used to model the response of PETN to low-velocity impacts, where the material melts prior to the first reactions, and thermal conduction and viscosity play a crucial role.

Side-heated Rayleigh–Bénard convection

Unlike in solids, heat transfer in fluids can be greatly enhanced due to the presence of convection. Under gravity, an unevenly distributed temperature field results in differences in buoyancy, driving fluid motion that is seen in Rayleigh–Bénard convection (RBC). In RBC, the overall heat flux is found to have a power-law dependence on the imposed temperature difference, with enhanced heat transfer much beyond thermal conduction. In a bounded domain of fluid such as a cube, how RBC responds to thermal perturbations from the vertical sidewall is not clear. Will sidewall heating or cooling modify flow circulation and heat transfer? We address these questions experimentally by adding heat to one side of the RBC. Through careful flow, temperature and heat flux measurements, the effects of adding side heating to RBC are examined and analysed, where a further enhancement of flow circulation and heat transfer is observed. Our results also point to a direct and simple control of the classical RBC system, allowing further manipulation and control of thermal convection through sidewall conditions.

Simulators for Conversing Power to Thermal on Green Data Centers: A Review

This paper aims to help data center administrators choose thermal simulation tools, which manage thermal conduction from power for energy savings. When evaluating and suggesting data center thermal simulators for users, questions such as “What are the simulator’s differences? Are they easy to use? Which is the best choice?” are frequently asked. To answer these questions, this paper reviews the thermal simulation works for data centers in the last ten years. After that, it proposes the versatility and dexterity metrics for these simulators and discovers that it is difficult to choose them despite their similar design purpose and functions. Empowered by the survey, we claim that the widespread practice simulators still need more enhancement in data center scenarios. We back up our claim by comparing typical simulators and propose improvements to thermal simulators for future studies.

Densifying Conduction Networks of Vertically Aligned Carbon Fiber Arrays with Secondary Graphene Networks for Highly Thermally Conductive Polymer Composites

AbstractThermally conductive polymer composites hold great potential for thermal management applications in the electronics industry, but achieving metal‐like thermal conductivity (>200 W m−1 K−1) remains challenging due to the inevitable phonon scattering and the thermal resistance at filler‐filler and filler‐matrix interfaces. Herein, an efficient approach is presented to overcome this long‐standing barrier by designing a densified interconnecting filler framework, featuring a macro‐level carbon fiber (CF) array welded with a high‐quality, self‐assembled graphene network. In this framework, vertically aligned continuous CFs function as primary through‐plane thermal conduction paths, minimizing phonon scattering and thermal resistance. Meanwhile, the secondary graphene network interconnects the CFs into a more integrated and densified framework while introducing supplementary thermal conduction paths. Following polymer backfilling, the resulting epoxy nanocomposite exhibits an unprecedented through‐plane thermal conductivity of 262 W m−1 K−1 at a filler loading of 23.3 vol%, establishing a new benchmark among the thermally conducting polymer composites. When employed as a thermal interface material, this composite offers a 68.2% enhancement in cooling efficiency compared to standard commercial counterparts. Furthermore, the functional composite presents excellent Joule heating and interfacial adhesion properties, making it promising for thermal interface healing and multifunctional thermal management applications in complex environments.

Preparation of phosphorous ionic liquids and its effect on the properties of ABS

AbstractTo improve the thermal conductivity and mechanical properties of graphene‐acrylonitrile butadiene‐styrene plastic (ABS) composite, sub‐phosphite‐based ionic liquid (IL) was synthesized, and its structure was characterized by FTIR, NMR, and mass spectrometry. IL was as a modifier, and graphite powder (G powder) was modified by the ball milling method to obtain functional graphene thermal conductive filler (G‐IL). The structure and morphology of G‐IL were characterized by FTIR, X‐ray photoelectron spectroscopy (XPS), XRD, scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The results of the Molau test showed that the presence of IL improved the interfacial interaction of G‐IL and ABS, enhanced the dispersion of G‐IL in the ABS matrix, made G‐IL contact with each other, and it was easier to establish a thermal conduction network and promote phonon transfer. The thermal conductivity of 9 wt% G‐IL/ABS composite was 0.392 W·m−1·k−1, which was 96% and 14% higher than that of pure ABS and G/ABS composite, respectively. The tensile strength and bending modulus of 9 wt% G‐IL/ABS composite were 44.89 and 2124.37 MPa, which were 13% and 11% higher than those of pure ABS, respectively. The impact strength of 9 wt% G‐IL/ABS composite was 34.17 kJ/m2. It was 18% and 7% higher than that of pure ABS and 9 wt% G‐IL/ABS, respectively.Highlights Phosphorus imidazole ionic liquids were prepared. Graphene was modified by ionic liquids through non‐covalent. Enhanced mechanical properties and thermal conductivity of G‐IL/ABS composites.

Enhanced thermal performance of phase change mortar using multi-scale carbon-based materials

Incorporating phase change material (PCM) into construction materials is an effective method for modifying building energy regulations throughout their service life. However, the effectiveness of PCM is constrained by its low thermal conductivity, highlighting the need for efficient enhancement methods. This study introduces thermally conductive carbon-based additions at both the nano-scale and meso-scale with different shapes, including carbon nano-tube (CNT), carbon black nano-particle (CB), and carbon fibre (CF) in PCM mortar. The mixed hydrated inorganic salt serves as the core PCM, while expanded perlite acts as the supporting material for the stable PCM composite, based on the presented research. The multi-scale additions establish thermal conduction pathways that improve temperature regulation performance. The modified samples exhibited a temperature difference of 2.2 °C and a time lag of up to 20 min under natural cooling conditions. Notably, CB positively influenced thermal conductivity, while CNT demonstrated an unexpected minor reduction. The enhancement in thermal conductivity increased with the content of CB, reaching an optimal enhancement of 18 %, except at a CNT content of 0.5 %. Conversely, both CB and CNT consistently improved thermal diffusivity. Furthermore, the compressive strength of the modified samples was significantly enhanced by up to 24 % compared to PCM mortar without carbon modifications. The modification method proposed in this study significantly improves both the thermal and mechanical properties of PCM mortar.

Suppressing the thermal conduction in glass–ceramic foams by controlling crystallization

AbstractGlass‐based insulating materials have attracted considerable attention owing to their tailorable properties. It is known that the thermal conductivity of glass ceramics can be greatly influenced by varying their crystallinity. However, the mechanism of such influence in glass–ceramic foams remains poorly understood. In this study, we demonstrate our new findings regarding the correlation between thermal conductivity and crystallinity in silicate glass–ceramic foams. The foams were produced by mixing ZrO2‐containing soda‐lime glass powder with CaCO3 as foaming agent and foam them using a thermochemical approach. ZrO2 was introduced as a nucleation agent. The crystallinity of the foams was varied by adjusting the heating protocol, i.e., by varying temperature, time, and number of heating cycles. The glass–ceramic foams exhibited relative crystallinities of <30%. The identity of the crystalline phases in the glass–ceramic foams varies with crystallinity. Specifically, cristobalite diminished, but devitrite grew with increasing crystallinity. It was observed that the crystallinity had a nonmonotonic impact on the thermal conductivity of the glass–ceramic foams. The optimum crystallinity for achieving the lowest thermal conductivity was 8–10%, resulting in an approximately 20% lower thermal conductivity compared to noncrystalline. Our findings have implications for the future design of glass–ceramic foams.

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.

Flexible Bridged Thermoelectric Device with an Optimized Heatsink for Personal Thermal Management.

A wearable thermoelectric cooler (TEC) for personal thermal management exhibits significant growth in numerous applications in personal thermal comfort and saving the energy consumed by space cooling. Most TECs provide a large cooling performance with the assistance of rigid heatsinks and electrodes, limiting wearability and practical implementation. Here, we design and propose a flexible bridged personal TEC with a high thermal management heatsink and spray-printed liquid metal electrodes. The system combines a bendable heatsink, a thermally insulative TE layer, and a bottom thermally conductive layer. Especially, the flexible heatsink composed of metal foam, phase change material, and fin structure greatly enhances the thermal conduction, storage, and diffusion capacities. Our TEC exhibits the desired comfortability and obtains an ideal temperature drop of 3 °C on human skin. Also, it could work as a self-generator providing 45 mV with a ΔT of 5 °C, which improves the generation efficiency by more than 3 times due to the stable temperature difference between the two sides. This work provides an effective way to develop wearable TEC devices and paves the way for achieving practical, personalized cooling applications.

Revealing synergistic relationship of thermal conduction and electromagnetic shielding of reduced graphene oxide film

The present work tries to explore the evolution process of electro-magnetic interference shielding effectiveness and thermal conductivity of graphene film. There is an obvious promotion of electrical conductivity (from 3.51×10-3 to 769.20 S m-1) when GO is thermally reduced at 1100°C. Correspondingly, the reduced graphene oxide (rGO) achieves the highest EMI shielding effectiveness (∼54.84 dB) at 1100°C which is an synergetic result of electrical conductivity and porous structure with rich defects. The rGO is furtherly graphitized at 2800°C (G-rGO) to repair the defects and C-C network and then mechanically rolled to a densified film with bulk density of 1.64 g cm-3 (called as DG-rGO). The thermal conductivity of DG-rGO membrane increases to 720.56 W m-1 K-1 after graphitization and rolling. Porous structure and defects are beneficial to higher EMI shielding effectiveness while dense structure without defects lead to higher thermal conductivity. Therefore, the highest EMI shielding effectiveness and thermal conductivity cannot be obtained simultaneously. A reference range is provided to fulfill the request of EMI shielding and thermal conductivity.

Experimental study on the thermal insulation performance of semi-transparent materials based on convection heating method

Radiation heat transfer inside the aerogel materials belongs to medium radiation, so different heating methods have different measurement results of thermal conductivity. For aerogel materials applied in high temperature air flow environment (aerospace field), since the real boundary conditions of aerogel materials during operation can be simulated by convection heating method (CHM), the combustion-gas wind tunnel device based on two-stages atomization, two-stages combustion/mixing mode is constructed, and the performance test is conducted. The operation safety and combustion performance of the device meet the test requirements, so the thermal conductivity test of aerogel materials can be carried out. When the average temperatures are 469 K, 622 K and 763 K respectively, the effective thermal conductivity (ETC) measured by the CHM is smaller than that measured by the thermal conduction heating method (TCHM), which decreases by 2.7 %, 7.84 % and 9.23 % respectively. The CHM solves the limitations of the TCHM, so the ETC of aerogel materials measured by CHM is more valuable for the design of thermal protection system.

Heat transport regimes in structured reactors: CFD analysis and influence of reactor diameter and length

Temperature control in catalytic reactors is critical to ensure high yields and a stable process for highly exothermic reactions. To better understand the processes within structured reactors, it has already been shown that heat source based Computational Fluid Dynamics (CFD) is a simple and valid way to mimic the heat intake of catalytic surface reactions and to capture general heat transport properties. In case of structured reactors, the heat transport is highly dominated by thermal conduction. Building on these achievements, this work systematically investigates the influence of the reactor diameter and length on heat transfer and temperature distribution in a Periodic Open Cell Structure (POCS) reactor. It is found that the typically high percentage of thermal conductivity is reduced by up to 50% if the reactor diameter changes from 20 mm to 50 mm. Furthermore, heat transport regimes are introduced along the reactor axis separating reactor parts with different predominant heat transfer mechanisms. This provides a fundamental comprehension of heat transfer in structured reactors and highlights the necessity to consider a sufficient reactor length. Lastly, the influence of thermal radiation is isolated. In addition to lowering the temperature increase significantly (from 1,300 K to 500 K in a specific case), it can also enhance the heat conduction through the solid by increasing the solid's temperature close to the reactor wall. Although the heat source simulations are a simplification, they are ideal to understand the reactor systems from a heat transport perspective.

A simplified procedure for evaluation of damage-depth in concrete exposed to high temperature using the impact-echo method

Concrete is widely recognized as a material capable of withstanding the intrusion of high temperatures during fires. However, under different high-temperature conditions, concrete can still experience strength reduction, cracking, or spalling, which can significantly impact the safety and durability of concrete structures. Conventionally, the wave refraction technique was used to detect the depth of this damage layer. However, the wave refraction technique is a time-consuming point-by-point detection method. In order to increase detection efficiency, this paper proposes a simplified method based on a single-point test. Numerical analysis of the thermal conduction of a concrete slab exposed to elevated temperature was performed first to investigate the temperature distribution within the concrete slab. Subsequently, the wave refraction technique was numerically simulated to evaluate the damage depth of the concrete slab. According to the refracted wave propagation path, a simplified procedure is proposed for the detection of the damage depth of concrete under high temperature. In the simplified procedure, a receiver is placed at an adequate distance from the impact source so that the first arrival wave at the receiver will be a wave refracted from the interface between the damaged layer and the sound layer inside the concrete. To verify the applicability of the proposed simplified procedure, concrete slab specimens subjected to an elevated temperature of 600 °C were tested in this study. The experimental results indicate that the simplified method proposed in this paper can indeed be used to detect the depth of high-temperature damage in concrete. In addition, the experimental results show that under the same high-temperature exposure conditions, the depth of fire damage increases with a decrease in the water-cement ratio. This can be attributed to the higher thermal conductivity coefficient of concrete with a lower water-cement ratio.

Rubber-lignin-ammonium polyphosphate bio-composite foams: Fabrication, thermomechanical properties and flame retardancy

Bio-composite foams based on Epoxidized Natural Rubber (ENR) filled with lignin (LG) and ammonium polyphosphate (APP) were fabricated via batch foaming. The addition of APP accelerated the foaming process at lower temperatures. Pre-mixing induced ionic and hydrogen bonding between the LG and the APP particles, which reduced crosslinking between LG and ENR. The resulting ENR bio-composite foams with LG/APP exhibited a significant increase in compressive strength (up to 700 %) and modulus (up to 600 %) compared to the ENR foam baseline. Furthermore, the LG/APP foams demonstrated lower thermal conductivity than both the ENR foam baseline and foams containing only LG or APP, attributed to optimal thermal conduction in the solid phase and convection within the pore cells. The combination of APP and LG produced synergistic effects, with phosphorus (from APP) and high carbon content (from LG) enhancing flame-retardant efficiency. This study highlights the potential of these sustainable bio-composite foams for applications requiring enhanced thermal insulation and flame retardancy attributes for insulation and other practical applications.

Exploring the mechanisms of thermal insulation and heat conduction properties of composite materials based on simulation models

Exploring the mechanisms of thermal insulation and heat conduction properties of composite materials based on simulation models

Transport coefficient sensitivities in a semi-analytic model for magnetized liner inertial fusion

Performance of magnetized liner inertial fusion (MagLIF) experiments is highly dependent on transport processes including magnetized heat flows and magnetic flux losses. Magnetohydrodynamic simulations used to model these experiments require a choice of model for the transport coefficients, which are the constants of proportionality relating driving terms, such as temperature gradients and currents, to the associated heat and magnetic field transport. The coefficients have been the subject of repeated recalculation using various methods throughout the years. Using a semi-analytic MagLIF model [McBride and Slutz, Phys. Plasmas 22, 052708 (2015)], we compare models for the transport coefficients provided by Braginskii [Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 205], Epperlein and Haines [Phys. Fluids 29, 1029 (1986)], Ji and Held [Phys. Plasmas 20, 042114 (2013)], Davies et al. [Phys. Plasmas 28, 012305 (2021)], and Sadler et al. [Phys. Rev. Lett. 126, 075001 (2021)]. The choice of model modifies magnetic-flux losses caused by the Nernst thermoelectric effect and thermal conduction losses. We present simulated results from parameter scans conducted in order to compare the effects of the different models on parameters of interest in MagLIF. In some regions of parameter space, discrepancies of up to 38% are found in integrated quantities like the fusion yield. These results may serve as a guide for experimental validation of the various models, particularly as laser preheat energies and initial axial field strengths are increased on MagLIF experiments.

Modifications of SPH towards three-dimensional simulations of an icy moon with internal ocean

There are some traces of the existence of internal ocean in some icy moons, such as the vapor plumes of Europa and Enceladus. This implies a region of liquid water beneath the surface ice shell. Since liquid water would be essential for the origin of life, it is important to understand the development of these internal oceans, particularly their temperature distribution and evolution. The balance between tidal heating and radiative cooling is believed to sustain liquid water beneath an icy moon’s surface. We aim to simulate the tidal heating of an internal ocean in an icy moon using 3-dimensional numerical fluid calculations with the Smoothed Particle Hydrodynamics (SPH) method. We incorporated viscosity and thermal conduction terms into the governing equations of SPH. However, we encountered two issues while calculating rigid body rotation using SPH with a viscous term: (1) conventional viscosity formulations generated unphysical forces that hindered rotation, and (2) there was artificial internal energy partitioning within the layered structure, which was due to the standard SPH formulations. To address the first issue, we modified the viscosity formulation. For the second, we adopted Density Independent SPH (DISPH) developed in previous studies to improve behavior at discontinuous surfaces. Additionally, we implemented radiative cooling using an algorithm to define fluid surfaces via the particle method. We also introduced an equation of state accounting for phase transitions. With these modifications, we have refined the SPH method to encompass all necessary physical processes for simulating the evolution of icy moons with internal oceans.

Comprehensive enhancement of melting-solidifying process in latent heat storage based on eccentric fin-foam combination

A novel fin-foam combination, applying upward fins to accelerate natural convection and downward foams to dominate thermal conduction, was established to comprehensively enhance the melting and solidifying performance of horizontal shell-and-tube latent heat storage devices. Enhancement mechanisms of the current design were numerically investigated and compared with the typical eccentric and concentric design the whole melting-solidifying process. Among investigated enhancement designs, the fin-foam combination achieved the best results, reducing the melting time and the solidifying time by 47.9% and 55.4% respectively. Meanwhile, the relative difference between the melting and solidifying time was reduced to 12%, indicating a significant mitigation of the buckets effect of solidifying caused by eccentric designs. Further, the effect of the total enhancement material usage was investigated. Results showed that the marginal effect of the heat transfer enhancement started at 9 fins and 0.91 porosity, but the relative difference between melting and solidifying time then dropped below 0.61%. The economic assessment showed that increasing the amount of enhancement material can significantly improve the storage capacity per unit cost when the price ratio of the enhancement material to PCM is less than 10, indicating a considerable applicability and cost performance of fin-foam combination under different power density demands.

On thermal conduction in the solar atmosphere: An analytical solution for nonlinear diffusivity without compact support

Context. The scientific community employs complicated multiphysics simulations to understand the physics in solar, stellar, and interstellar media. These must be tested against known solutions to ensure their validity. Several well-known tests exist, such as the Sod shock tube test. However, a test for nonlinear diffusivity is missing. This problem is highly relevant in the solar atmosphere, where various events release energy that subsequently diffuses by Spitzer thermal conductivity. Aims. The aim is to derive an analytical solution for nonlinear diffusivity in 1D, 2D, and 3D, which allows for a nonzero background value. The solution is used to design a test for numerical solvers and study Spitzer conductivity in the solar atmosphere. Methods. There exists an ideal solution assuming zero background value. We performed an analytical first-order perturbation of this solution. The first-order solution was first tested against a dedicated nonlinear diffusion solver, whereupon it was used to benchmark the single- and multifluid radiative magnetohydrodynamics code Ebysus, used to study the Sun. The theory and numerical modeling were used to investigate the role of Spitzer conductivity in the transport of energy released in a nanoflare. Results. The derived analytical solution models nonlinear diffusivity accurately within its region of validity and approximately beyond. Various numerical schemes implemented in the Ebysus code is found to model Spitzer conductivity correctly. The energy from a representative nanoflare is found to diffuse 9 Mm within the first second of its lifetime due to Spitzer conductivity alone, strongly dependent on the electron density. Conclusions. The analytical first-order solution is a step forward in ensuring the physical validity of intricate simulations of the Sun. Additionally, since the derivation and argumentation are general, they can easily be followed to treat other nonlinear diffusion problems.