Heat Conduction Research Articles

Analysis of the dynamic responses of a piezothermoelastic microbeam resonator under dual-phase-lag heat conduction

Thermoelastic vibration responses of a piezothermoelastic (PTE) microbeam resonator have been investigated in the present work under simply supported boundary conditions. The basic governing equations for a transversely isotropic piezothermoelastic solid are formulated by assuming the Euler–Bernoulli beam theory with hyperbolic dual-phase-lag (DPL) heat conduction model. Later on, non-dimensionalization of the variables have been carried out for simplicity to obtain the set of coupled governing equations for thermal deflection, electric field, and thermal moment. Initial and boundary conditions are defined to solve for the non-dimensional thermal deflection and thermal moment by using Laplace transform technique along with the finite Fourier sine transform. Closed-form solutions of the problem are obtained. Moreover, an attempt is made to illustrate the analytical results through numerical simulations by taking a PTE material of Lead Zirconate Titanate (PZT-5A). The influence of the quadratic term of the phase-lag parameter of heal flux in the DPL model is investigated to compare the effects of phase-lags under parabolic and hyperbolic DPL models. In addition, the long-term and short-term vibration responses of thermal moment and thermal deflection are analyzed in detail to observe the impact of different factors which characterize the piezoelectric phenomena and dual-phase-lag effects. Comparative analysis of different well-known models for responses of thermal moment and thermal deflection is also presented for short- and long-time ranges. Some important observations about how piezoelectric parameters, dual-phase-lag parameters, and beam parameters affect the behavior of piezothermoelastic vibrations have been highlighted.

Parameterized level set method based topology optimization of transient heat conduction structures

Parameterized level set method based topology optimization of transient heat conduction structures

In-orbit validation of a ferrofluidic Thermal Switch in ISS microgravity

AbstractFerrofluids offer a wide range of applications by enabling wearless systems for future space missions. As part of the FARGO (Ferrofluid Application Research Goes Orbital) project, an active Thermal Switch using ferrofluid was developed and validated during a 26-day International Space Station (ISS) mission. This experiment was conducted as part of the Überflieger2 competition organized by the Space Agency within the German Aerospace Center (DLR). Thermal management of spacecraft (S/C) and satellites is a universal challenge. In the development of thermal management components, it is therefore essential to minimize or even eliminate stress/strain peaks and potential safety risks for S/C operation and payloads induced by thermal differences. The thermal management system shall be able to keep all components within their acceptable temperature ranges. This shall be achieved under all orbit conditions, for example, when solar irradiance heats one side of the S/C resulting in possibly unwanted temperature gradients toward the cold vacuum of space. An active Thermal Switch allows heat flows to be routed along different paths within the S/C depending on the prevailing conditions. Within project FARGO, an active Thermal Switch was tested during an ISS mission. Tests on the ground already verified a measurable difference in thermal conductivity depending on the state of the switch. Magnetically moving the ferrofluid allows the creation of a thermally isolating and conducting Thermal Switch state. The ferrofluid utilized for the FARGO experiment is EFH-1 with a thermal conductivity of $${0.19\,\mathrm{\text {W}\text {m}^{-1}\text {K}^{-1}}}$$ 0.19 Wm - 1 K - 1 . The Thermal Switch consists of two silver rods in line, acting as heat conductors, separated by an airgap. One side of the switch is heated, and the other one cooled by one thermoelectric cooler (TEC) each. The gap between the conductors can be bridged by ferrofluid moved via magnetic fields. As the EFH-1 has a higher thermal conductivity k than air, thermal conductive change is achieved by switching. The temperature difference between hot and cold side are measured in the ON state as well as the OFF state. From these measurements, the switching ratio as a performance characteristic is calculated. The switch was tested under various heat loads and switching times. Electropermanent magnets (EPMs) are magnets that can be magnetically switched on and off by a current pulse. Compared to conventional electromagnets, heat generation and power generation are significantly reduced. In addition, the switch remains reliably in the selected state, even if a failure of the control electronics occurs, making it bi-stable. Moreover, electric power is only required to switch the state of the EPM, but not to maintain it.

Gas-compensated thermal flow sensor using an integrated velocity-independent gas properties meter

Abstract A gas-compensated thermal flow sensor is presented that measures the flow rate in real-time, independent of the type of gas, by simultaneously measuring and compensating for the thermal conductivity and volumetric heat capacity of the gas. The thermal flow sensor consists of two free-hanging, heated wires, forming a calorimetric flow meter. The temperature difference between the two wires is a function of the flow rate and the fluid thermal properties. An additional heated wire is integrated on the same chip and used to measure the gas properties. This wire is suspended over a shallow V-groove cavity, and oriented perpendicular to the flow direction, so that it is only affected by the gas properties and not by the flow. DC excitation is used to measure the thermal conductivity, and AC excitation with the 3$\omega$ method is used to determine the volumetric heat capacity. The output of the thermal flow sensor is automatically corrected for the medium using these measured parameters. Measurements were performed with 11 different gases and gas mixtures, and in all cases the deviation between the applied flow rate and measured flow rate is less than 10\%.

Evaluation of thermal parameters with geothermal energy recovery from a cold climate municipal solid waste landfill

This study presents finite element method (FEM) modeling with COMSOL Multiphysics to estimate the thermal properties of a waste landfill through back-analysis of temperature responses from buried thermistors during a full-scale multi-week active thermal response test. Field tests were conducted at the Loraas MSW landfill in Saskatoon, Canada, using instrumented equipment, including a vertical borehole heat exchanger and thermistor strings. The test consisted of two phases: a heat injection test during the summer and a heat extraction test in the winter. The study focused on a landfill 25 m deep, observing temperature changes at various depths over time. The effect of heat generation rate (HGR) on landfill temperature was investigated. Thermal conductivity and volumetric heat capacity increase with depth, with close alignment between summer and winter results, validating the tests. This research enhances the understanding of thermal parameters in MSW landfills by combining field tests and numerical modeling, offering insights into landfill behavior in cold climates. These findings hold significance for optimizing geothermal energy recovery from such landfills, calibrating thermal parameters for coupled models in landfills, and improving waste management practices.

Thermoelastic damping in bi-layered micro/nanobeam resonators using the dual-phase-lag generalized heat conduction model

The existing analytical investigations on thermoelastic damping (TED) in laminated micro/nanobeam resonators have generally neglected the thermal axial force and rarely considered the time lagging in the heat transfer. However, laminated beams will very likely exhibit stretching-bending coupling deformation due to the deviation of the physical neutral surface from the beam mid-surface. Furthermore, the TED in layered beams has been predicted by using the energy rather than the complex frequency approach. In this presentation, TED in bi-layered micro/nanobeams is analyzed based on the Euler-Bernoulli beam theory and the dual-phase-lag (DPL) generalized heat conduction theory by considering the thermal axial force. Analytical solutions for the TED in bi-layered micro/nanobeams are developed by using both the complex frequency approach and the energy method. Numerical results are presented to examine the effects of the thermal axial force and DPL relaxation times on the TED in the laminated beam resonators for different physical and geometrical parameters, vibration modes and mechanical boundary conditions, which reveal that the thermal axial force will increase (decrease) the TED in metal/ceramic (ceramic/ceramic, metal/metal) bi-layered beams. The maximum underestimation for the TED due to neglecting the thermal axial force will reach about 7 % in Ag/Si beam and 15 % in Cu/Si3N4 beam. The DPL effect on the TED is closely related to the material properties of the laminas and their volume fractions. For the Ag/Si beam with the thickness less than 1nm, influence of the DPL relaxation on the TED becomes significant which changes continuously from the negative contribution to the positive one with the increase in the volume fraction of the Si from 0 to 1. However, the DPL effect can be ignored in the bi-layered beams with micrometer size.

Numerical study of plasma and air heating process in single-turn coil discharges

As a kind of destructive pulsed magnet, single-turn coil generates ultra-high magnetic field beyond 100 T by feeding the Mega-Ampère-level discharge current into a coil with the size of several millimeters. Under the effect of high temperature and high electric field, the air around the coil is ionized and exhibits magnetohydrodynamic characteristics. In this study, a numerical model is built to analyze the air heating and sample thermal destruction. This model uses the collision integral method to calculate the physical parameters of the plasma, and considers not only the heat conduction and convection but also the heat sources of Joule heat, electron-heavy particles collision, work done on air by pressure and pressure change, and air viscous dissipation. The results show that heat conduction and heat convection can only significantly heat the air near the surface of the coil. However, the power density of these two heat sources is greater than the other heat sources, resulting in the highest air temperature near the coil. In addition, Joule heat and electron-heavy particles collision have lower power densities but can heat a larger volume of air outside and inside the coil, respectively.

Thermohydraulic performance optimization of integrated porous pin fins in microchannel heat sink using shape optimization coupled with NSGA

Micro porous heat sink (MPHS) with enhanced heat transfer performance faces higher pressure drop challenges than conventional heat sinks. Practical applications of MPHS are recently investigated focusing on basic structures. But explorations on complex structures and their performance enhancement are limited. Moreover, the heat conductivity along channel height direction needs further enhancement. To address the problems and extend porous fin designs, we propose a brand-new bionic integrated porous pin fin in MPHS. Procedures of shape optimization coupled with NSGA are applied to the porous fin design. The objective is chosen as figure of merit (FOM) regarding integrated pin fin spacing, solid sub pin fin spacing, and porous zone diameter. This novel method in MPHS investigation helps to find the optimal geometric parameter combination and counter-intuitive design. Then, a detailed performance comparative analysis for the optimized structure is conducted. The results show improvement ratio ranges of FOM are 18.79–––21.65%, 71.84–––108.72%, and 212.7–––231.5%, compared to non-optimized, partially-filled, and fully-filled structures, respectively. This work indicates that the innovative design attains significant energy efficiency improvement, and the novel method is feasible for comprehensive optimization.

A pseudo-density conjugate heat transfer method and its application to simulating the quasi-steady temperature field of a compressor cylinder

The substantial disparity in time scales between heat conduction and convection requires extremely tiny time steps in simulations, leading to significant computational demands when using current-tightly coupled methods to solve the temperature field of cylinders at the quasi-steady stage. A new pseudo-density method is proposed to accelerate the heat conduction rate. The influence of solid density on transient temperature under the periodic third-type boundary conditions is analyzed in a one-dimensional model by analytical methods and verified in a three-dimensional structure by numerical methods. It is found that reducing solid density can accelerate the heat conduction rate and increase the fluctuation amplitude of solid temperature. Therefore, a variable pseudo density is adopted for solids in the simulation of the transient heat transfer characteristics between the compressed gas and the cylinder. The results show that the pseudo-density method provides similar computational accuracy to the current tightly coupled methods, but at significantly lower computational cost. The fluctuation amplitude of the cylinder's temperature decreases rapidly in the wall thickness direction. The distribution of the convective heat transfer coefficient on the inner wall of the cylinder is extremely transient and highly non-uniform, which is consistent with the distribution of gas velocity near the cylinder wall.

Barrier materials integrated with gas regulation function are used to reduce the explosion risk of battery systems

Large-capacity lithium iron phosphate batteries are widely used in energy storage stations and electric vehicles due to their high cost-effectiveness and long lifespan. However, research shows that the gases generated during thermal runaway are mainly combustible, which may lead to fires or even explosions. Nevertheless, within the millimeter-scale confined space of a battery pack, effective solutions are scarce, making it challenging to simultaneously suppress kilowatt-level heat transfer and dilute the accumulated combustible gases. This research has developed a multifunctional fire shield with capabilities of “low-temperature heat conduction, medium-temperature heat absorption, high-temperature thermal insulation, and gas regulation.” The material is composed of hydrogel, aluminum hydroxide, ceramic fiber, and ammonium bicarbonate. In the low-temperature range, it exhibits an excellent thermal conductivity (0.58 W·m−1·K−1), capable of maintaining the battery module’s operating temperature within a reasonable range. In the medium to high-temperature range, its thermal conductivity rapidly decreases (0.04 W·m−1·K−1), and with its high phase change enthalpy (1727 J/g), the material can suppress the thermal propagation of a 100 Ah lithium iron phosphate battery module. This material starts to release CO2 at 90℃. In a confined space, the CO2 mixes uniformly with the gases generated during the thermal runaway process of the battery, reducing the risk of these gases (increasing the lower explosion limit by 44 % and reducing the maximum laminar flame speed by 58 %). Therefore, the multifunctional fire shield demonstrates exceptional heat conduction, heat absorption, thermal insulation, and gas regulation performance. This research provides new insights for the safety design of battery systems.

Parametric effects of phase change material on solar still productivity: Thermal modeling and selection guides

A solar still utilizes solar energy to produce freshwater by evaporating and condensing saline water, known for its simplicity but limited by low productivity and intermittent solar availability. Phase change materials (PCMs) provide an attractive technique to overcome these drawbacks. In order to investigate the effect of PCM parameters besides providing a clear guide for PCM selection, the current paper presents a thermal modeling on solar sill-PCM behavior for different parameters. The results indicated improved productivity with higher PCM mass, melting point, latent heat of fusion, specific heat, or thermal conductivity. Under extreme conditions, moderate PCM mass or high melting point is optimal, while moderate conditions benefit from high PCM mass or moderate melting point. Long-term use favors high PCM mass or large latent heat of fusion. Combining high mass and melting point mitigates extreme condition challenges. Enhanced thermal conductivity alongside other parameters significantly boosts productivity, though excessive specific heat can reduce output. Improving the heat storage capacity holds significant promise for mitigating the challenges associated with selecting an appropriate melting point. Optimizing PCM selection by prioritizing mass, latent heat of fusion, thermal conductivity, melting point, and specific heat enhances solar still efficiency across diverse environments.

Growth, thermophysical and dielectric properties of undoped and Al-doped CsLiB6O10 crystals

Undoped and Al-doped CsLiB6O10 (CLBO) crystals have been grown by top-seeded solution growth (TSSG) method using Cs2O–Li2O–MoO3 flux system. The thermophysical properties of undoped and Al-doped CLBO were systematically studied, including thermal expansion, specific heat, thermal diffusion and thermal conductivity. The measured thermal expansion coefficients of undoped and Al-doped CLBO in the temperature range of 30–500 °C are αa=1.81×10-5/°C, αc=-2.98×10-5/°C and αa=1.10×10-5/°C, αc=-2.56×10-5/°C, respectively, displaying much weaker anisotropy than those of widely used nonlinear optical crystals, such as β-BaB2O4 and CsB3O5. CLBO exhibits specific heat of 0.86–1.03 Jg-1K-1 in the temperature range from 30 to 500 °C. The thermal conductivities of undoped and Al-doped CLBO at 30 °C are respectively calculated to be κa=1.73 Wm-1K-1, κc=1.69 Wm-1K-1 and κa=1.74 Wm-1K-1, κc=1.49 Wm-1K-1, which are larger than those of β-BaB2O4. Dielectric properties were investigated in the temperature range of 20–400 °C within the frequency range of 100 Hz–1 MHz. The measured dielectric constants of undoped and Al-doped CLBO at 1 MHz and 25 °C are εa=5.27, εc=5.92 and εa=4.96 , εc=5.49, respectively. Additionally, undoped and Al-doped CLBO exhibit significantly low dielectric losses (0.005–0.016 at 1 MHz and 25 °C) and superior dielectric temperature stability (20–300 °C). These results indicate that undoped and Al-doped CLBO possess excellent thermophysical performance and could be two promising dielectric material candidates for high frequency device applications.

Effects of thermal desorption temperature up to 500°C on the thermophysical properties and fertility of soil in organic-contaminated sites

High-temperature thermal desorption is effective for remediating organic-contaminated sites, but its damage to soil functions and high energy consumption raise concerns. In this work, the variation of fertility indicators of two soils with thermal treatment temperature was investigated experimentally. To overcome the difficulties in measuring soil thermophysical properties under sealing and high-temperature conditions, two apparatus matching with the Hot Disk device were established and by which massive data were measured. The results show that, as temperature rises up to 500°C, the combustion and decomposition of organic components and soil minerals gradually enhance, leading to a decrease in most fertility indicators, but an increase in grain size and pH. Available phosphorus and exchangeable potassium decrease with temperature rise first, but increase over 400°C. Soil thermal conductivity and specific heat are positively correlated with temperature and water content. Water diffusion will intensify over 40∼60°C, leading to an intense increase in soil thermal conductivity. The results are expected to provide data basis and theoretical guidance for the comprehensive consideration of remediation effects, land reuse, and energy consumption in practical applications of thermal desorption remediation.

Heat conduction applied in ‘River Pollutant Diffusion’

Environment problems are a highly valued topic in today’s society, where water pollution issue is one of the most significant that could threaten human’s safety. Sources such as industrial wastewater and agricultural runoff are affecting the water quality. Rivers around the world suffer from varying degrees of pollution. In this paper, we investigate river heat pollution and employ a numerical model to investigate its evolution and impacts downstream by adapting the heat advection-diffusion equation. We explore the stability of our numerical solutions using von Neumann stability analysis of the forward and backward differencing method of discretization of the analytical equations. We further consider a setting where there are multiple sources of pollutant in the river to explore interaction of the two pollution sources. We use python to develop the model and plot temperature diffusion in the river as a function of time and location. Our model reflects the relationship between the speed of diffusion and thermal diffusivity, and how advection enhances pollutant. Our results show that heat pollution is very quickly transported to other locations and can affect water and food quality in many locations along the river. Additionally, pollution in rivers with fast currents will be more readily transported downstream, therefore both proximity to cities and speed of river water needs to be taken into account when addressing the problem of heat pollution in rivers near cities.

A merging approach for hole identification with the NMM and WOA-BP cooperative neural network in heat conduction problem

Defect identification is an important issue in structural health monitoring. Herein, originated from inverse techniques, a merging approach is established by the numerical manifold method (NMM) and whale optimization algorithm-back propagation (WOA-BP) cooperative neural network to identify hole defects in heat conduction problems. On the one hand, the NMM can simulate varying hole configurations on a fixed mathematical cover, which eases the generation of “big data” for the training of neural network to a large extent. On the other hand, the WOA, a global optimization algorithm, is adopted to optimize the initial weights and thresholds of the BP neural network to alleviate its frequently encountered local optimum phenomenon. The boundary temperatures of sampling points by the NMM and the associated hole geometries are used for the learning of WOA-BP neural network, which is then applied to predict the hole defects. Numerical examples concerning the detection of circular/ elliptical holes demonstrate that the proposed method possesses higher accuracy and satisfying robustness in holes prediction compared with standard BP network under the same condition. The present work provides a convenient pathway and great potential in application of structural health monitoring.

Conservative numerical algorithm for simulating thermoelectrical semiconductor device with unconditional optimal convergence analysis

We propose conservative type numerical method to simulate thermoelectrical semiconductor device problem, in which mixed finite element method used for electric potential equation, conservative characteristic finite element method for electron and hole concentration equations, and standard finite element method for heat conduction equation. By temporal-spatial error splitting argument, the optimal error estimates without certain time step restriction are derived, and low order convergence rate of electrostatic potential and electric field intensity will not affect the accuracy of the electron, hole density and temperature. Numerical tests are performed to validate the theoretical results and application performance of the given method.

Comparison of microwave and roasting pretreatments on peony seed oil: Compositions, physicochemical properties and emulsification characteristics

Peony seeds, as a valuable emerging oil resource, are rich in unsaturated fatty acids (UFAs), tocopherols, phytosterols and sterols. Based on the different heating conduction methods, this study investigates the effects of the microwave and roasting pretreatments on the quality, compositions, physicochemical properties and emulsification characteristics of peony seed oil (PSO). Peony seeds were pretreated by microwave at 700W for 0.5, 1.0, 1.5, 2.0min, pretreated by roasting at 120 ℃ for 10, 20, 30, 40min, respectively. The nanoemulsions of PSO were prepared with Tween-20 by the ultrasound technology. The results showed that microwave increased the oil yield, SV, p-AV, TOV, TBARS and BI, but decreased AV of PSO. Roasting increased the oil yield, AV, SV, PV, p-AV, TOV and BI; but decreased the TBARS level of PSO. Microwave pretreatment decreased the γ-tocopherol, and β-carotene levels of PSO. However, roasting increased the γ-tocopherol and β-carotene levels. Total phytosterol level gradually decreased with the prolong of heating time. α-linolenic, linoleic and oleic acids were the dominated fatty acids in the PSO. Microwave and roasting slightly decreased the UFAs level. Microwave and roasting increased the particle size and Ke value of PSO nanoemulsion. The longer storage time or higher incubation temperature could increase the particle size, PDI, zeta-potential and Ke of PSO nanoemulsion.

High-performance electromagnetic absorbing Ni/C composites derived from Ni-MOF materials: Effects of organic ligands and pyrolysis temperatures

Magnetic carbon-based materials derived from nickel organic framework (Ni-MOF) are considered to be a kind of electromagnetic wave (EMW) absorbing materials with great potential and application value. However, the precise design of Ni-MOF-derived magnetic carbon-based materials remains a huge challenge. In the present work, through the modulation of organic ligand and pyrolysis temperature, Ni/C composites with excellent electromagnetic absorption properties are obtained due to their improved multiple loss and optimized impedance matching. Specifically, the organic ligand and pyrolysis temperature affect the degree of graphitization of the carbon frame and the specific surface area of the Ni/C composites, thus changing the conductivity, magnetic properties and electromagnetic parameters. In particular, the sample Ni/C-2-500 using H2BPDC as the organic ligand and calcined at 500 °C gives an RLmin of –50.37 dB and an EAB of 6.0 GHz at a packing rate of 30 wt% and a thickness of 2.5 mm, which covers the entire Ku band. In addition, Ni/C-2-500 exhibits good thermal conductivity. Therefore, this study provides an idea for exploring MOF materials and their derivatives with tunable EMW absorbing properties and heat conduction advantages prepared by different organic ligands.

Enhancement of battery thermal management effect by a novel MOF based composite phase change material

The introduction of phase change materials (PCMs) into battery thermal management systems (BTMS) can effectively enhance the cooling performance, safety and practical thermal management applications of lithium-ion batteries (LIBs). However, further study is needed to address the low heat conductivity and rapid phase change leakage of PCMs. This study proposed a metal–organic framework based shape-stabilized composite PCM (MOF/expanded graphite (EG) /multi-walled carbon nanotube (MWCNT) /paraffin wax (PW)) to construe battery cooling system, and its effect of battery thermal management is experimentally tested under various conditions. The results show the CPCM reveals a superior thermal management effect under varying ambient temperatures and discharge multipliers and outperforms natural convection. Even in the harsh environment of 40 °C and 3 C, the maximum temperature (Tmax) and Tmax difference (ΔTmax) of the CPCM-cooled module are 61.38 and 2.67 °C, which are 22 and 9 °C below the natural air-cooled module. Remarkably, the ΔTmax of the CPCM-cooled battery module in discharge decreases with the temperature rise at the discharge rate of 3 C, which is the exact opposite to the case of the air-cooled module. Moreover, the ΔTmax of CPCM-cooled module is 1.69, 1.84, 2.67 °C, all below the safe 5 °C at high temperatures (40 °C) as the discharge rate increases. The designed MOF-CPCM cooling system can effectively improve the temperature uniformity and thermal safety of the battery in harsh environments. Therefore, this novel MOF-based CPCM shows great promise in BTM.

Thermal performance analysis of a deep coaxial borehole heat exchanger with a horizontal well based on a novel semi-analytical model

This study introduces a novel semi-analytical model for deep coaxial borehole heat exchanger with a horizontal well(H-DBHE), which incorporates the effects of formation stratification and transient heat conduction within the pipe walls. Initially, the model's validity was checked through a comparison with the results derived from the published numerical models. This semi-analytical approach significantly reduces computational time while ensuring calculation accuracy. Subsequently, the study quantitatively examined the influence of the operation parameters, structural characteristics and the thermal capacity within the borehole on the dynamic heat extraction of H-DBHE. The numerical results demonstrate that the thermal capacity within the borehole significantly influences the heat extraction performance during intermittent operations of H-DBHE. Based on this finding, the study further investigated the effects of intermittent operation and heating time on the heat recovery performance of the system. Additionally, the study compared the long-term operational performance and thermal attenuation between H-DBHE and deep coaxial borehole heat exchanger (DBHE) over a ten-year simulation period. This research introduces a novel semi-analytical model for H-DBHE, which is of significant theoretical guidance for accurately predicting the heat extraction performance of H-DBHE and scientifically designing geothermal utilization systems.