Equivalent Thermal Conductivity Research Articles

Equivalent Thermal Conductivity of Topology-Optimized Composite Structure for Three Typical Conductive Heat Transfer Models

Composite materials and structural optimization are important research topics in heat transfer enhancement. The current evaluation parameter for the conductive heat transfer capability of composites is effective thermal conductivity (ETC); however, this parameter has not been studied or analyzed for its applicability to different heat transfer models and composite structures. In addition, the optimized composite structures of a specific object will vary when different optimization methods and criteria are employed. Therefore, it is necessary to investigate a suitable method and parameter for evaluating the heat transfer capability of optimized composites under different heat transfer models. Therefore, this study analyzes and summarizes three typical conductive heat transfer models: surface-to-surface (S-to-S), volume-to-surface (V-to-S), and volume-to-volume (V-to-V) models. The equivalent thermal conductivity (keq) is proposed to evaluate the conductive heat transfer capability of topology-optimized composite structures under the three models. A validated simulation method is used to obtain the key parameters for calculating keq. The influences of the interfacial thermal resistance and size effect on keq are considered. The results show that the composite structure optimized for the V-to-S and V-to-V models has a keq value of only 79.4 W m−1 K−1 under the S-to-S model. However, the keq values are 233.4 W m−1 K−1 and 240.3 W m−1 K−1 under the V-to-S and V-to-V models, respectively, which are approximately 41% greater than those of the in-parallel structure. It can be demonstrated that keq is more suitable than the ETC for evaluating the V-to-S and V-to-V heat transfer capabilities of composite structures. The proposed keq can serve as a characteristic parameter that is beneficial for heat transfer analysis and composite structural optimization.

Greatly Enhanced Radiative Transfer Enabled by Hyperbolic Phonon Polaritons in α‐MoO3

AbstractOrthorhombic molybdenum trioxide (α‐MoO3) is a highly anisotropic hyperbolic material in nature. Within its wide Reststrahlen bands, α‐MoO3 has hyperboloidal dispersion that supports bulk propagation of high‐k phonon polariton modes. These modes can serve as energy transport channels to greatly enhance radiative heat transfer inside the material. In this work, large radiative transfer enabled by phonon polaritons in α‐MoO3 is demonstrated. The study first determines the temperature‐dependent permittivity of α‐MoO3 from polarized Fourier‐Transform Infrared (FTIR) spectroscopy measurements and then uses a many‐body radiative heat transfer model to predict the equivalent radiative thermal conductivity of hyperbolic phonon polariton. Contribution of radiative transfer to the total thermal transport is experimentally determined from the Time‐Domain Thermoreflectance (TDTR) measurements in a temperature range from −100 to 300 °C. It is found that radiative transfer can account for ≈60% of the total thermal transport at a temperature of 300 °C. That is, conductive thermal transport is enhanced by >100% by radiative transfer, or radiation inside α‐MoO3 is greater than that of conduction. These additional energy pathways will have important implications in thermal management in new materials and devices.

Experimental Investigation on Ultra-Thin Vapor Chamber with Composite Wick for Electronics Thermal Management.

Ultra-thin vapor chambers (UTVCs) are widely used to cool high-power electronics due to their excellent thermal conductivity. In this study, a UTVC of 82 mm × 58 mm × 0.39 mm with composite wick was prepared. The composite wick is composed of two layers of copper mesh and multiple spiral-woven meshes (SWMs), and the composite wick was applied in UTVC to improve liquid replenishment performance and temperature uniformity. Furthermore, the thermal performance of UTVCs with different support column diameters, filling ratios (FRs), and SWM structures was experimentally studied. The results found that the equivalent thermal conductivity (ETC) decreases as the diameter of the support column increases; the UTVC with 0.5 mm support column diameter has the highest ETC, at 3473 W/(m·K). Then, the effect of FR on the heat transfer performance of UTVCs with SWM numbers of 0, 1, 2, and 3 (0 SWMs, 1 SWM, 2 SWMs, 3 SWMs) is consistent, the 30% FR UTVC with 3 SWMs having the highest ETC, at 3837 W/(m·K). Finally, the increased number of SWMs can significantly improve the ultimate power of the UTVCs, the UTVC with 3 SWMs having the highest ultimate power, at 26 W. The above experimental studies indicate that the designed and manufactured UTVCs have great potential advantages in thermal dissipation for electronics.

Study on the Coupled Heat Transfer of Conduction, Convection, and Radiation in Foam Concrete Based on a Microstructure Numerical Model

Foam concrete is a typical cement-based porous material; its special microstructure endows it with excellent properties, such as light weight, energy efficiency, thermal insulation, and fire resistance. Therefore, it is widely used as a thermal insulation material for buildings. The heat transfer modes of foam concrete include conduction, convection, and radiation. However, previous studies considered conduction to be the dominant mode, often neglecting the effects of convection and radiation. In this study, a stochastic numerical model of the foam concrete microstructure is established based on the statistical parameters of the pore structure. With this model, the heat transfer mechanism of foam concrete is analyzed at the mesoscopic level, and the equivalent thermal conductivity is calculated. By comparing four different working conditions, the influence of conduction, convection, and radiation on the heat transfer of foam concrete is analyzed, and the specific contribution rates of conduction, convection, and radiation are calculated. The results show that the convection effect is weak due to the pore size being smaller than 1 ; so, the influence of convection can be neglected in the heat transfer analysis of foam concrete. The contribution of radiation increases with the decrease in foam concrete density and the increase in temperature difference. When the temperature difference is 40 and the density is 300 , the contribution of radiation exceeds 20. Therefore, for low-density and high-temperature difference situations, the influence of radiation cannot be ignored. The heat transfer in foam concrete is mainly through conduction, but with the decrease in density and the increase in temperature difference, the contribution of conduction shows a downward trend. Nevertheless, the contribution of conduction is still much larger than that of radiation and convection.

Estimating the Thermal Conductivity of Unsaturated Sand

A modified parallel model for estimating the thermal conductivity of unsaturated sand was proposed in this study. The heat conduction in the solid phase of sand depends mainly on the form of contacts between solid particles, while water bridges at the particle contacts increase the contact areas and remarkably enlarge the transfer paths of heat conduction in sandy soils. However, the thermal conductivity of the solid particle itself (λs) cannot describe the influence of the form of contacts and water bridges on heat conduction through the solid phase. In this study, the equivalent thermal conductivity of the solid particle (λes) was presented which reflected the influence of the form of contacts and water bridges between particles under dry conditions or a low degree of saturation, respectively. The relationship between λes and degree of saturation was described by hyperbolic expression. The modified model was calibrated using measured values of the thermal conductivity from published datasets, including those for 41 types of sand from 15 studies. Numerical analyses of the temperature field of the energy pile were performed and validated against laboratory measurements. The results illustrated that the modified model was more applicable than the original model for predictions of sand thermal conductivity.

Influence of Prandtl number on the chaos transition for pure natural and Rayleigh–Bénard convections inside a rectangular cavity

A peculiar flow instability known as multiple chaos transitions was recently reported for the free convection in an enclosure where the direction of the temperature gradient changes continuously; it has been explained to be attributed to the competition for dominance between pure natural and Rayleigh–Bérnard convections. In this study, the chaos transition of free convection is investigated when a horizontal or vertical temperature gradient forms in a rectangular cavity. Analyses are conducted under a laminar flow regime, with Prandtl numbers ranging from 0.01 to 50 and Rayleigh numbers up to 109. In the horizontal temperature gradient, the chaos-transition Rayleigh number increases monotonically with the Prandtl number. However, under vertical temperature gradient conditions, it reaches the maximum value at approximately Pr = 0.5. Contrary to the general knowledge that higher-Prandtl number fluids effectively stabilize natural convection, a free convection in a vertical temperature gradient initiates a new flow instability when the Prandtl number is over 1.0, where momentum and thermal diffusions balance each other. The oscillation pattern, 2D phase trajectory, power spectral density, and Poincaré point of equivalent thermal conductivity are used to assess the free-convection flow instability.

Modelling effective thermal conductivity in polymer composites: A simple cubic structure approach

In this study, we propose the simple cubic model, a distinctive thermal-conductive mathematics for modelling the effective thermal conductivity in polymer composites, taking both filler size and interface thermal resistance into account. This model is constructed by delineating heat transport paths within simple cubic structural units, leveraging principles involving Fourier's law, minimum thermal resistance, specific equivalent thermal conductivity, and thermal resistance network. Demonstrating broad applicability, the simple cubic model accurately predicts effective thermal conductivity within a 0–40 % volume fraction range of filler in polymer composites, maintaining less than 15 % error. Its robustness is validated across over 100 experimental datasets, encompassing various polymer matrices and granular filler types. This extensive validation underscores the model's efficacy, both with our experimental data and existing literature. The simple cubic model's insightful predictions make it valuable in designing and preparing thermally conductive polymer composites.

Tuning the thermal conductivity of organic-inorganic double-shell thermal storage microcapsules triggered by atomic layer deposition

The regulation of the thermal conductivity of thermal energy storage materials has become a primary challenge to expand the range of utilization for different application scenarios. In this study, organic-shell microcapsule (paraffin@melamine formaldehyde) was initially prepared by in situ polymerization, followed by the deposition of anatase TiO2 on the organic-shell microcapsule using atomic layer deposition (ALD) to form organic-inorganic double-shell microcapsule. The effect of the thickness of the TiO2 shell on the equivalent thermal conductivity of the microcapsules was investigated by utilizing ALD's precise and controllable characteristics for the coating thickness. The obtained double-shell microcapsules indicated a drop in thermal storage capacity, but a substantial boost in thermal stability. Moreover, the thermal conductivity of microcapsules can be tuned in the range between 0.1837 and 0.7529 W m−1 K−1 within 1500 ALD cycle treatment. Furthermore, the parameters of ALD, such as reaction temperature and exposure time, were varied to obtain an amorphous TiO2 shell, and the impacts of different crystal form of TiO2 on the heat transfer properties of microcapsules were concluded by comparison. Double-shell microcapsules exhibited superior mechanical properties compared to single-shell structure. The findings can stimulate significant research interest in broadening the applications of thermal storage microcapsules.

A new winding homogenization method based on thermal resistance concept

PurposeThe aim of this paper is to provide a simple yet accurate and efficient geometric method for thermal homogenization of impregnated and non-impregnated coil winding technologies based on the concept of thermal resistance.Design/methodology/approachFor regular windings, the periodic microscopic cell in the winding space is identified. Also, for irregular windings, the average microscopic cell of the winding is determined. An approximation is used to calculate the thermal resistance of the winding cell. Based on this approximation, the winding insulation is considered as a circular ring around the wire. Mathematical equations are obtained to calculate the equivalent thermal resistance of the cell. The equivalent thermal conductivity of the winding is calculated using equivalent thermal resistance of the cell. Winding thermal homogenization is completed by determining the equivalent thermal properties of the cell.FindingsThe thermal pattern of different windings is simulated and compared with the results of different homogenization methods. The results show that the proposed method is applicable for a wide range of windings in terms of winding scheme, packing factor and winding insulation. Also, the results show that the proposed method is more accurate than other winding homogenization methods in calculating the equivalent thermal conductivity of the winding.Research limitations/implicationsIn this paper, the change of electrical resistance of the winding with temperature and thermal contact between the sub-components are ignored. Also, liquid insulators, such as oils, and rectangular wires were not investigated. Research in these topics is considered as future work.Originality/valueUnlike other homogenization methods, the proposed method can be applied to non-impregnated and irregular windings. Also, compared to other homogenization methods, the proposed method has a simpler formulation that makes it easier to program and implement. All of these indicate the efficiency of the proposed method in the thermal analysis of the winding.

Electromagnetic and Thermal analysis of an Intra-layer no-insulation coil during Quench

The intra-layer no-insulation (LNI) layer-wound REBCO coil has been widely studied for its excellent high thermal stability in the research of nuclear magnetic resonance superconducting magnets. Due to the complex structure of the LNI layer-wound coil and the numerous factors that affect thermal stability, its quench characteristics are not clear. In this paper, a numerical multiphysics coupling model is established to study the transient electromagnetic and thermal behaviors of the LNI layer-wound coil during quench. The results indicate that temperature follows the diffusion law, while the currents evolve through electrical connection and electromagnetic induction. Due to the high contact resistance, the azimuthal current and axial current vary almost in units of the entire coil layer. The direction of the radial current upstream of the turn where a quench occurs is positive due to the bypassing behavior, while the radial current direction is negative downstream. The insulation material inside the LNI layer-wound coil strongly affects the quench propagation. When its thickness decreases, the equivalent radial thermal conductivity increases, thereby increasing the quench propagation velocity and current peak, and shortening the duration of the current response during quench.

Calculation of Equivalent Thermal Conductivity of Motor Winding Based on Conductor Distribution

Abstract To improve the calculation accuracy of motor thermal field, this paper proposes a method for calculating the equivalent thermal conductivity of winding based on conductor distribution, and a 24-slot 26-pole outer-rotor permanent magnet synchronous motor is taken as an example to verify the method. First, the equivalent thermal conductivity of winding is calculated by traditional equivalent methods, namely the equivalent insulation layer method and the area weighting method. Second, the equivalent thermal conductivity of the slot winding and end winding in the three-dimensional (3D) direction is derived using the conductor distribution method. Third, the 3D finite element models corresponding to three equivalent methods are established, and the temperature of the motor under different operating conditions is simulated and compared. Finally, an experimental platform is built to verify the accuracy of the proposed conductor distribution method.

Towards zero-carbon solar heating in severe cold and cold regions of China by building integrated heat pipes

As a climate-responsive building, the building integrated heat pipes (BIHP) can greatly improve the indoor thermal environment during the local heating season, utilizing the thermal diode characteristic and ultrahigh equivalent thermal conductivity of the L-shaped flat gravity heat pipe. The thermophysical properties of the internal envelope greatly influence the heating effect, and the utilization potentiality of BIHP varies in locations with diverse climate resources. In this paper, the utilization effects of BIHP at 61 locations in severe cold and cold regions of China are investigated. Improved backtracking search and particle swarm optimization are used to obtain the optimal heating effect and the corresponding thermophysical properties of the internal envelope at zero-carbon heating locations and non-zero-carbon heating locations, respectively. The relationship between the improvement degree of thermal discomfort and the solar radiation over temperature difference is studied, and the utilization potentiality map and zoning of BIHP are obtained. This study is of great significance for promoting the application of climate-responsive BIHP to effectively and efficiently utilize solar energy to reach zero-carbon heating.

Analytical Calculation and Experimental Validation of Litz Wires Axial Thermal Conductivity

Litz wires are widely used in electrical machines with reduced AC losses, compared to traditional random winding. The reduced AC losses can improve both electrical machines electromagnetic performance, such as efficiency and thermal performance. Thermal aspect is identified as a key enabler for next generation high power density electrical machines, where thermal modelling plays a critical role. Equivalent slot thermal conductivity is one of the most challenging parameters to be determined in the process of thermal model development, due to various components, such as copper, insulation, and impregnation resin. There are extensive literatures where the litz wire thermal conductivity in the radial direction are reported. However, the thermal conductivity in the axial direction is not well studied, which is critical to determine the heat transfer, such as for electrical machines with end winding spray-cooling system. In this paper, the axial thermal conductivity is investigated with analytical calculations and experimental validation. Firstly, 9 litz wire samples are selected with various types, such as rectangular and circular shapes, with varnish process and without. Two different analytical methods are then introduced and presented to calculate the litz wire thermal conductivity in axial direction, based on equivalent length theory and equivalent medium theory, respectively. Finally, experimental tests are conducted, and results are compared to those obtained from the proposed analytical methods. Guidelines are also provided to predict the litz wire axial thermal conductivity in this field.

Investigation of thermo-hydrodynamic characteristics in micro-oscillating heat pipe by alternatively-arranged ratchet microchannels

In this study, three flat-plate micro-oscillating heat pipes (FPMOHPs) with different alternatively-arranged ratchet microchannels were designed and fabricated. Then, a combined visualization and thermal experiment was conducted to examine the regulation of thermo-hydrodynamic characteristics in the FPMOHPs by the alternatively-arranged ratchet microchannels, via the comparison with a traditional FPMOHP with completely uniform microchannel. The detailed fluid flow motions and corresponding temperature oscillations as well as thermal performance of the FPMOHPs were illustrated and analyzed to clarify the advantages of this microchannel design. It is indicated that the oscillating frequency and velocity of the fluid are diminished by the ratchet microchannels because of the higher flowing resistance. However, the ratchet microchannels can trigger the stronger flow disturbance, leading to the ascending “wave-like” annular flow broken into the dispersive slugs or bubbles with irregular shape. Among the three different ratchet microchannels, the asymmetric ratchet structure with the larger contraction-expansion ratio near the inlet of the fluid can trigger more intense boiling in the evaporator, which also energizes the downward flow from the condenser. Furthermore, the additional actions on the bubbles/slugs caused by the Laplace pressure jump in three different ratchet microchannels play distinct roles in upward and downward bubble/slug flow, i.e., driving force or resistance force or little role, which determine the most favorable ratchet structure for the fluid flow and heat transfer in the FPMOHPs. In general, the positive effects of the enhanced boiling and the stronger fluid flow disturbance caused by the ratchet microchannel dominates the negative effect of growing flow resistance, leading to the enhanced convective heat transfer. Therefore, the equivalent thermal conductivity can be improved up to 33.8 % on average as compared to the traditional FPMOHP with completely uniform rectangular channel.

Thermal performance of clay bricks with different fillings: a CFD analysis

The thermal conductivity of 15 loadbearing and infill bricks was calculated through a Computational Fluid Dynamic (CFD) analysis. Clay bricks filled with air, expanded polystyrene EPS, and graphitized expanded polystyrene were selected from the catalogue of the manufacturer F.B.M. - Fornaci Briziarelli Marsciano. The company provided the geometric features of each block and the thermal characteristics of the clay mix and the filling. The thermal conductivity value of each air cavity was calculated in compliance with UNI EN ISO 6946. Each volume was discretized in triangular meshes. The equivalent thermal conductivity of each block was calculated starting from the simulation of the isotherms trend inside the sample and from the heat flux passing through it. The obtained results were discussed depending on the filling, the geometry, and the hole percentage. In general, thermal conductivity increases with hole percentage in the bricks with air. Similar geometries have similar thermal behaviour. EPS or graphitized EPS involve better thermal performance as the hole percentage increases. Finally, the influence of the different orientations of the blocks was investigated. Equivalent thermal conductivity values increase for horizontally-brick placed, especially in homogeneous and compact geometries.

Experimental investigation on the heat transfer performance of Galinstan liquid metal driven by electromagnetism

Liquid metals have excellent heat transfer performance and unique electromagnetic characteristics, providing new visions for cooling the high speed motorized spindle shaft. Liquid metal can be driven by the magnetic field of the motor stator to induce current with no dynamic seal problem. In the present study, a shaft cooling structure of a motorized spindle with Galinstan liquid metal as the working fluid was designed and the heat transfer performance of the designed structure was investigated experimentally. The obtained results at the rated speed and rated current show that the induced voltage in the wire installed on the shaft reaches 1.2 V, which can circulate the liquid metal in an 8 mm diameter copper pipe. In this case, its equivalent thermal conductivity reaches 8.1?104 W/m ?C, which can effectively reduce the temperature of the motorized spindle rotor and make the temperature distribution of the motorized spindle more uniform.

FIELD EXPERIMENTAL INVESTIGATION OF THE INSULATION DETERIORATION CHARACTERISTICS OF OVERHEAD PIPELINE FOR STEAM HEATING NETWORK

The thermal insulation performance of pipeline is significant for the safety and economical operation of vapor steam network. In order to investigate the long-time insulation performance of pipeline, a field test was carried out in pipelines of 12 different heating networks with the operating time ranging from 1 to 11 years. Two different types of insulation coating layer were included. The total heat flux and surface heat flux in a pipeline were measured to obtain the equivalent thermal conductivity of the insulation coating layer, and a deterioration coefficient was applied to analyze the insulation deterioration characteristics. The results show that the one-dimensional thermal conduction method is feasible to calculate the heat flux of the pre-manufactured pipeline with hard insulation materials, and an error less than 2% for pipeline 1 was obtained. Further, a proper size of slip in the insulation coating layer has improved the insulation performance by 13.6% in pipeline 2. For the soft type insulation coating, the structure has been changed under the long-term effect of gravity. Accordingly, a single thermal conductivity cannot accurately characterize the heat transfer process within the insulation layer. The surface heat flux accounts for less than 30% of the total heat loss. The insulation deterioration trend with operating time cannot exactly be obtained by the surface heat flux. In addition to the thickness reduction at the top and hollow at the bottom, the convection heat leakage from the gaps should also be a concern for long time operation.

Modeling Method of C/C-ZrC Composites and Prediction of Equivalent Thermal Conductivity Tensor Based on Asymptotic Homogenization

Modeling Method of C/C-ZrC Composites and Prediction of Equivalent Thermal Conductivity Tensor Based on Asymptotic Homogenization

Study on heat transfer characteristics of pulsating heat pipe heat exchanger with asymmetric structure

The Pulsating Heat Pipe (PHP), lauded for its efficacy in heat transfer, is distinguished by its uncomplicated architecture, economical production, diminutive form, and robust adaptability to environmental conditions. This study delineates the design of an asymmetric PHP heat transfer apparatus, achieved through the alteration of select conduit lengths within the comprehensive circulation system. The thermal transfer efficacy of this apparatus was empirically scrutinized under dual dissipation modalities: natural and forced convection. It was observed that the asymmetric PHP, when devoid of oscillatory activity, maintained a heat source temperature of 25∘C, whereas the temperature escalated to 26∘C upon the initiation of pipe vibration. Under the regime of forced convection, the asymmetric PHP demonstrated expedited activation, reduced initiation temperature, and heightened oscillatory behavior compared to its natural convection counterpart, thereby facilitating the phase change condensation within the condensation segment and ensuring efficient, sustained heat dissipation. Consequently, this bolstered the PHP’s heat transfer capabilities. The thermal resistance exhibited a declining trajectory under both dissipation strategies, with forced convection consistently yielding lower thermal resistance than natural convection. Nonetheless, the decrement in thermal resistance was gradual near the critical startup juncture and throughout the initiation phase. The PHP’s equivalent thermal conductivity displayed an upward trend in tandem with the escalation of the heat source’s temperature under both dissipation methods. Despite the superior heat transfer performance at elevated heat source temperatures, the efficiency of natural convection dissipation remained suboptimal, necessitating the application of forced convection to the condensation segment to further enhance the PHP’s thermal transfer proficiency and the overall device performance.

An equivalent thermal conductivity model of TSV arrays for thermal analysis in 3-D integrated circuits

An equivalent thermal conductivity model of TSV arrays for thermal analysis in 3-D integrated circuits