Thermal Management Applications Research Articles

(Invited) Near-Field Optics and Its Applications in Nanoscale Materials: A Review

In this paper, we first offer an overview of aperture-type scanning near field optical microscopy –a family of super-resolution imaging techniques based on evanescent waves, which can be combined with atomic force microscopy and are capable of subwavelength resolution nano-optical imaging. In the second part of this review, we will discuss a few applications in which our group capitalized on the super-resolution resolving power of SNOM to design specific nano-optical and nano-photonic systems for light harvesting, resistive memory device applications and nanoscale thermo-optical management. Specific case studies that will be presented include the characterization of weakly photoluminescent and curved carbon dots for memory device applications, the three-dimensional characterization of plasmon-enhanced nanophotonic devices, as well as the development of near-field thermoreflectance imaging for nanophotonic-based thermal management applications. Collectively, our study well represents the versability of SNOM as a unique super-resolution nanophotonic tool for the investigation of light-matter interaction at the nanoscale.

Prestrain Guided Yield of Large Single-Crystal Nickel Foils with High-Index Facets.

Single-crystal metal foils with high-index facets are currently being investigated owing to their potential application in the epitaxial growth of high-quality van der Waals (vdW) film materials, electrochemical catalysis, gas sensing and other fields. However, the controllable synthesis of large single-crystal metal foils with high-index facets remains a great challenge because high-index facets with high surface energy are not preferentially formed thermodynamically and kinetically. Herein, single-crystal nickel foils with a series of high-index facets are efficiently prepared by applying prestrain energy engineering technique, with the largest single-crystal foil exceeding 5×8 cm2 in size. In terms of thermodynamics, the internal mechanism of prestrain regulation on the formation of high-index facets is proposed. Molecular dynamics simulation is utilized to replicate and explain the phenomenon of multiple crystallographic orientations resulting from prestrain regulation. Additionally, large-sized and high-quality graphite films are successfully fabricated on single-crystal Ni(012) foils. Compared to the polycrystalline nickel, the graphite/single-crystal Ni(012) foil composites show more than five-fold increase in thermal conductivity, thereby showing great potential applications in thermal management. This study hence presents a novel approach for the preparation of single-crystal nickel foils with high-index facets, which is beneficial for the epitaxial growth of certain two-dimensional materials. This article is protected by copyright. All rights reserved.

MXene-modified lemon peel-based composite phase change material with excellent photo-thermal conversion efficiency, thermal storage capacity and thermal conductivity for thermal management of electronic components

The preparation of multifunctional composite phase change materials using green technology to achieve an efficient energy storage and conversion remains an issue of concern. In this paper, a lemon peel-based porous carbon (LPC) composite phase change material (CPCM) was prepared by using polyethylene glycol (PEG) 6000 as a phase change medium and MXene nanosheet-modified carbonized lemon peel as a support carrier. MXene nanosheets were bonded to a lemon peel-based porous carbon skeleton to construct an excellent continuous three-dimensional thermally conductive grid system. What makes it noteworthy is that the presence of MXene nanosheets substantially improves the thermal conductivity (0.66 W/mK) and photo-thermal conversion efficiency (θ = 96.4 %) of MXene-modified lemon peel-based porous carbon/polyethylene glycol composite phase change materials (PEG/LPC@M). It is noteworthy that PEG/LPC@M has remarkable thermal stability and still has high enthalpy after 100 cycles, which further proves the recyclability of PEG/LPC@M and PEG/LPC@M embodies great potential in the field of thermal management of electronic components. In conclusion, a novel multifunctional CPCM was prepared by a simple and green process method in this study, which provides a new idea for waste recycling and reuse, and also has a wide range of applications in thermal management of electronic devices.

Enhancing thermal conductance between graphene and epoxy interfaces through non-covalent cation-π interactions

Although graphene has high thermal conductivity, its application in thermal management remains challenging because of the large interfacial thermal resistance between graphene and adjacent materials. This work demonstrates that non-covalent cationic-π interaction can significantly improve the thermal conductance between graphene and substrate interfaces. Cationic polyacrylamide (CPAM) bridges substrate and graphene with hydrogen bonding and cation-π interaction, respectively. The cation-π interaction between graphene and CPAM is confirmed by Raman, UV–Vis and NMR spectroscopy. The results show that CPAM increases the interfacial adhesion of graphene/epoxy from 18.7 ± 2.2 mN to 37.4 ± 7.6 mN (100.0 % improvement) and improves the interfacial thermal conductivity (ITC) from 22 ± 2 MW/m2K to 51 ± 5 MW/m2K (131.8 % improvement). Enhancing the ITC of graphene/epoxy by introducing CPAM assembled layer has advantages over covalent modifications because it provides a similar level of ITC improvement rate, but has little effect on the intrinsic thermal conductivity of graphene. Finally, it is demonstrated that the sample with graphene/cationic polyelectrolyte/substrate structure exhibits great potential for applications in the area of thermal management and printed circuit boards.

General strategy for developing thick-film micro-thermoelectric coolers from material fabrication to device integration

Micro-thermoelectric coolers are emerging as a promising solution for high-density cooling applications in confined spaces. Unlike thin-film micro-thermoelectric coolers with high cooling flux at the expense of cooling temperature difference due to very short thermoelectric legs, thick-film micro-thermoelectric coolers can achieve better comprehensive cooling performance. However, they still face significant challenges in both material preparation and device integration. Herein, we propose a design strategy which combines Bi2Te3-based thick film prepared by powder direct molding with micro-thermoelectric cooler integrated via phase-change batch transfer. Accurate thickness control and relatively high thermoelectric performance can be achieved for the thick film, and the high-density-integrated thick-film micro-thermoelectric cooler exhibits excellent performance with maximum cooling temperature difference of 40.6 K and maximum cooling flux of 56.5 W·cm−2 at room temperature. The micro-thermoelectric cooler also shows high temperature control accuracy (0.01 K) and reliability (over 30000 cooling cycles). Moreover, the device demonstrates remarkable capacity in power generation with normalized power density up to 214.0 μW · cm−2 · K−2. This study provides a general and scalable route for developing high-performance thick-film micro-thermoelectric cooler, benefiting widespread applications in thermal management of microsystems.

Preparation and thermal conductivity of bimodal diamond particles reinforced phenolic resin composites

AbstractThermal conductive polymer composites have broad application prospects in the field of thermal management. However, due to intrinsically low thermal conductivity of polymers, even if fillers with high mass fraction are filled, the thermal conductivity of polymer composites cannot be significantly improved. In this paper, bimodal diamond particles (70 wt.% 150 μm and 22 wt.% 25 μm) were incorporated into phenolic resin to construct continuous heat transfer pathways by close packing, thereby enhancing its thermal conductivity. The results indicated that diamond particles with smaller particle size can effectively bridge the gaps between larger ones, forming a continuous for heat conduction. As a result, a maximum thermal conductivity value of 12.45 W/(m·K) can be achieved, which is 65.5 times, 9.8 times and 8.4 times higher than pure phenolic resin, 25 μm diamond particles reinforced phenolic resin composite and 150 μm diamond particles reinforced phenolic resin composite, respectively. Furthermore, heat dissipation and water cooling experiments also confirm the superior heat dissipation performance of phenolic resin composites reinforced with bimodal diamond particles. When the heating voltage is 10 V and the water cooling rate is 30 mL/min, the upper surface temperature of bimodal diamond composites is 129.2°C lower than that of pure phenolic resin. This investigation provides a new type of polymer composite with high thermal conductivity, which has promising prospects for application in thermal management. It also provides new insights for preparing polymer composites with high thermal conductivity by close packing of bimodal particles.Highlights Surface modification of the filler enhances its combination with resin. The interfacial bonding will be enhanced by D–OH bond on diamond surface. Bimodal diamond particles lead to the formation of a closely packed structure. This special structure can form a three‐dimensional heat conduction network. The highest TC of the DD/PR composite is 12.45 W/(m·K).

An approach for topology optimization of heat sinks for two-phase flow boiling: Part 1 – Model formulation and numerical implementation

Two-phase flow boiling in heat sinks and cold plates is attractive for various thermal management applications due to high effective heat capacity rates and high heat transfer coefficients compared to single-phase operation. In addition, multi-physics topology optimization is sought for generation of high performance thermal management components. Yet, the design of heat sinks using topology optimization has been restricted to single-phase flow physics, due to incompatibility between available two-phase flow models and traditional single-phase topology optimization approaches. Interface-capturing two-phase flow models are too computationally expensive for optimization; mixture and two-fluid models that treat the liquid and vapor phases as an interpenetrating continuum with interfacial transport phenomena captured through empirical correlations are computationally tractable for heat-sink-scale optimization. However, the penalization approaches commonly used to define the structures formed during topology optimization results in arbitrary fin and channel geometries for which a universal two-phase flow correlation is not available. To enable coupling with two-phase mixture models, this work leverages a homogenization approach to topology optimization wherein heat sink designs are represented using spatially varying microstructures with optimized dimensions. A predefined microstructure geometry is chosen for which two-phase flow correlations exist and therefore topology optimization can be performed. This work is the first to develop a topology optimization algorithm using a mixture model for simulating two-phase flow boiling to design heat sinks and cold plates. Part 1 of this study develops and implements the algorithm to investigate topology optimized heat sinks at various heat inputs, topology optimization grid sizes, and maximum vapor quality constraints. Topology optimized heat sinks designed for single-phase versus two-phase flow are compared. There are significant differences in hydraulic and thermal responses of the single-phase and two-phase designs due to high effective heat capacity rates and high heat transfer coefficients of flow boiling. A companion paper (Part 2) focuses on manufacturing, model calibration, and experimental validation of the topology optimized heat sinks under two-phase flow boiling. The algorithm demonstrated in this work extends the capabilities of topology optimization to two-phase flow physics, and thereby enables the design of various two-phase flow components such as evaporators, condensers, heat sinks, and cold plates.

Flash soldering of boron nitride nanosheets for all-ceramic films

The assembly of boron nitride nanosheets (BNNSs) into strong, flexible thin films capable of withstanding extreme conditions, such as high/low working temperatures and corrosive environments, holds immense promise for numerous applications. However, BNNSs are difficult to assemble and sinter to achieve the dense thin film structure observed in graphene thin films. We report the rapid fabrication of dense BNNS all-ceramic films (BACFs) in 30 s by combining the fabrication strategies for 2D and ceramic materials. In this process, densely arranged and highly oriented BNNSs are flash soldered into a monolith achieved by precisely controlled ultrafast sintering. This fusion of BNNS leads to an ultrahigh in-plane thermal conductivity of 134.5 W·m−1·K−1, which was among the highest values for BNNS films (mostly ≤ 70 W·m−1·K−1). The as-prepared BACF exhibits the combined advantages of sintered ceramics (durability, stability, acid-alkali resistance) and 2D material films such as flexibility and shock resistance, which is important for practical uses but rarely found in existing ceramics. It also has excellent cooling performance, dielectric properties, and good thermal stability, which is promising for demanding thermal management applications in emerging technologies.

Are Local Heat Transfer Quantities Useful for Predicting the Working Behavior of Different Pulsating Heat Pipe Layouts? A Comparative Study

Despite a continuous effort devoted by the scientific community, a large-scale employment of Pulsating Heat Pipes for thermal management applications is still nowadays undermined by the low reliability of such heat transfer systems. The main reason underlying this critical issue is linked to the strongly chaotic thermofluidic behavior of these devices, which prevents a robust prediction of their working behavior for different geometries and operating conditions, consequently hampering proper industrial design. The present work proposes to thoroughly compare data referring to previous infrared investigations on different Pulsating Heat Pipe layouts, which have focused on the estimation of heat fluxes locally exchanged at the wall–fluid interfaces. The aim is to understand the beneficial contribution of local heat transfer quantities in the prediction of the complex physics underlying such heat transfer systems. The results have highlighted that, regardless of the considered geometry and working conditions, wall-to-fluid heat fluxes are able to provide useful quantities to be employed, to some extent, to generalize Pulsating Heat Pipe operation and to improve their existing numerical models.

A Critical Review on Recent Advancements in Aluminium-Based Metal Matrix Composites

Aluminum matrix composites (AMCs) have garnered significant attention across various industrial sectors owing to their remarkable properties compared to conventional engineering materials. These include low density, high strength-to-weight ratio, excellent corrosion resistance, enhanced wear resistance, and favorable high-temperature properties. These materials find extensive applications in the military, automotive, and aerospace industries. AMCs are manufactured using diverse processing techniques, tailored to their specific classifications. Over three decades of intensive research have yielded numerous scientific revelations regarding the internal and extrinsic influences of ceramic reinforcement on the mechanical, thermomechanical, tribological, and physical characteristics of AMCs. In recent times, AMCs have witnessed a surge in usage across high-tech structural and functional domains, encompassing sports and recreation, automotive, aerospace, defense, and thermal management applications. Notably, studies on particle-reinforced cast AMCs originated in India during the 1970s, attained industrial maturity in developed nations, and are now progressively penetrating the mainstream materials arena. This study provides a comprehensive understanding of AMC material systems, encompassing processing, microstructure, characteristics, and applications, with the latest advancements in the field.

Vertically aligned carbon fiber/polydimethylsiloxane composites prepared by lyophilization with exceptional thermal conductivity and electromagnetic interference shielding performance

Composites with high thermal conductivity and exceptional electromagnetic interference (EMI) shielding properties are crucial for ensuring the long-term stability of electronic devices. One-dimensional carbon fibers (CFs) stand out as promising materials due to their excellent thermal and electrical conductivity. However, the anisotropic nature of CFs limits the overall electrical and thermal conductivity of the composite, thus impeding its practical application. To address this limitation, we investigated the effect of different freezing methods on CF orientation using the ice template method. Subsequently, CF-150/PDMS and CF-250/PDMS composites with varying average lengths of CFs were prepared using the unidirectional freezing technique. We studied the influence of CF content and average length on the anisotropic thermal conductivity and EMI shielding properties of the composites. The CF-250/PDMS composite, with a CF content of 15.71 vol%, exhibits a remarkable thermal conductivity of 9.07 W·m−1·K−1 and a low thermal resistance of 2.61 °C·cm2‧W−1. The thermal conductive mechanism of CF/PDMS composites was simulated by thermal conduction model and finite element analysis. Furthermore, it demonstrates longitudinal electromagnetic interference shielding effectiveness (EMI SE) reaches up to 39.66 dB, while the transverse EMI SE reaches up to 52.55 dB. The vertically aligned CF/PDMS composites exhibit significant potential for a range of applications in thermal management and EMI shielding.

Revisiting lattice thermal conductivity of CsCl: The crucial role of quartic anharmonicity

Thermal conductivity (κL) plays a critical role in thermal management applications. Usually, crystals with simpler structures exhibit higher κL due to fewer phonon scatterings. However, cesium chloride (CsCl) presents an anomaly, demonstrating an unexpectedly low κL of 1.0 W m−1 K−1 at 300 K, as observed in Professor Iversen's experimental measurement despite its simple structure. This prompts a need for understanding anomalous low κL and matching theory with experimental observations. Our study brings forth several findings for CsCl: (i) relying solely on three-phonon scattering inadequately captures κL. (ii) Anharmonic phonon renormalization significantly contributes to increased κL. (iii) Coherent phonons align temperature-dependent κL closely with the experiment. This work not only enhances understanding of anomalous κL in CsCl but also provides an approach to bridge the gap between experiment and theory in other crystals.

Epoxy resin/ aluminium hydroxide/expanded graphite synergistic effects on advancing flame retardancy, mechanical structure and thermal management of octadecanoic acid and octadecanol-based eutectic phase change materials

In the present research, a novel approach wherein a flame-retardant composite phase change material (PCMs) is devised by incorporating eutectic PCMs, epoxy resin (ER), aluminium hydroxide (ATH), and expanded graphite (EG). This innovative formulation capitalizes on the synergistic interaction between ER and ATH, alongside the porous structure of EG, resulting in a triple-layer encapsulation of the eutectic PCMs. The outcome of this formulation is marked by remarkable thermal stability, even under extreme conditions such as exposure to temperatures as high as 800 °C. Notably, one of the representative samples, denoted as S5, showcases impressive attributes with a thermal conductivity of 1.335 W∙m-1K−1 and a substantial phase change latent heat of 150.4 J∙g−1. It was observed an increase in latent heat up to 181.3 J∙g−1 after 100 heating–cooling cycles of composite PCMs. This indicates the good thermal reliability of the form-stable composite PCMs synthesized. Moreover, the composite PCMs exhibit outstanding mechanical properties, especially S5 which showed a 14.69 % and 400.12 % increase in compression strength and compression modulus compared with pure eutectic PCM (S0), respectively. Besides, the ternary composition of ER, ATH, and EG enhances the flame retardancy of the composite PCMs, yielding a substantial reduction of 67.33 % in peak heat release rate and 50.38 % in total heat release. This collaborative effect also establishes a robust defense mechanism against the rapid propagation of flames, as exemplified by the attainment of a V-0 rating in the UL-94 test. As a result, the flame-retardant ER/ATH/EG ternary-based form-stable composite PCM presents itself as a promising candidate for ensuring both safety and efficiency in thermal management applications.

Dual-polarization small-angle strong nonreciprocal thermal radiator with Weyl semimetal

The development of dual-polarization irreversible radiators that can operate without external magnetic field is an arduous task. To avoid the need of strong magnetic field, a dual-polarization nonreciprocal thermal radiator with the introduction of Weyl semimetal is demonstrated. It consists of cross-shaped silicon nanopores, Weyl semimetal, and Ag reflective layer. The simulation results show that the proposed radiator offers both TE- and TM-polarized strong irreversible radiation with an incident angle of 1.6°. The TE-polarized absorptivity and TM-polarized emissivity are 98.8% and 97.6%, respectively. The dual-polarization nonreciprocity exceeds 80%. The physical principle is explained by the electric field energy distribution and impedance matching theory. The demonstrated scheme and radiator have potential application in dual-polarization multi-band irreversible radiation and thermal management.

Anisotropic Lattice Thermal Conductivity in Highly Ordered PEDOT Fibers

AbstractWhen it comes to sustainable and efficient energy solutions, organic semiconductors can play an important role in thermoelectric applications, since they are non‐toxic, cheap, made of abundant chemical species, and show intrinsically low thermal conductivities. Their electrical conductivity can be optimized via doping. Yet, thermal conduction should be as low as possible and, to this end, the atomic scale mechanisms behind heat transport –e.g. the correlation between morphology and thermal conductivity or the role of doping– should be understood in detail. Fully atomistic molecular dynamics calculations of the lattice thermal conductivity of doped poly(3,4‐ethylenedioxythiophene) (PEDOT) highly ordered, quasi‐crystalline nanofibers are presented here. It is found that the conductivity along the backbone direction is not necessarily the highest, but it depends on the length of the PEDOT chains, thus the degree of anisotropy depends on the the aspect ratio of the nanofiber. Indeed, transport along the lamellar direction can be of the same order or higher than that of the backbone if their lengths are comparable. These results challenge the usual expectation that thermal conduction along the backbone largely exceeds those along the lamellar and π − π direction and have the important consequence that the anisotropy could be leveraged in thermal management applications.

Stable and reliable PEG/TiO2 phase change composite with enhanced thermal conductivity based on a facile sol-gel method without deionized water

Some shortcomings exist in organic phase change materials, including leakage susceptibility, low thermal conductivity, and preparation complexity. Herein, polyethylene glycol/titanium dioxide shape-stabilized composite phase change material (PEG/TiO2 ss-CPCM) was fabricated by facile sol-gel method without deionized water using tetrabutyl titanate (TBOT) as precursor. In this composite, not adding deionized water prolonged the gelation time, allowing PEG to bind as much TiO2 as possible and enhancing energy storage capability; TiO2 acted as the supporting framework to maintain the material's shape stability and enhance thermal conductivity. The melting and crystallization phase change enthalpies of prepared PEG/TiO2 ss-CPCM were 128.3 J/g and 113.1 J/g with an encapsulation efficiency of 74.14 % when PEG: TBOT = 1.5: 1. After repeating 300 thermal cycles, the phase change enthalpy remained almost constant. Besides, the thermal conductivity of PEG/TiO2 ss-CPCM was 1.22 times that of PEG, and the potential for thermal management applications. The advantages (energy storage capability, shape stability in thermal environments, thermal reliability, and thermal management) of the PEG/TiO2 ss-CPCM prepared by facile synthesis, not only propose a phase change material with excellent thermal properties and shape stabilization but provide a green and feasible strategy for the fabrication of PEG/TiO2 composite phase change materials utilizing the sol-gel method.

A PAM hydrogel surface-coated hydroponic bamboo evaporator with efficient thermal utilization for solar evaporation

Solar-driven interfacial water purification emerges as a sustainable technology for seawater desalination and wastewater treatment to address the challenge of water scarcity. Currently, the energy losses via radiation and convection to surrounding environment minimize its energy efficiency. Therefore, it is necessary to develop strategies to minimize the heat losses for efficient water purification. Here, a novel evaporator was developed through the in situ gelation of PAM hydrogel on the surface carbonized hydroponic bamboo (PSC) to promote energy efficiency. The inherent porous and layered network structures of bamboo, in synergy with the functional hydration capacity of PAM hydrogel, facilitated adequate water transportation, while reducing evaporation enthalpy. The PAM hydrogel firmly covered on the photothermal layer surface effectively minimized the radiation and convection heat losses, while further harvesting those thermal energy that would otherwise dissipate into the surrounding environment. The reduced thermal conductivity of PSC served as a thermal insulator as well, obstructing heat transfer to bulk water and thus diminishing conduction losses. Consequently, the rational designed PSC could efficiently convert solar energy to purified water, leading to the evaporation of 2.09 kg m−2 h−1, the energy efficiency of 87.6 % under one sun irradiation, and yielding 9.6 kg m−2 fresh water over 11 h outdoor operation. Moreover, the PSC also performs excellent salt rejection, and long-term stability at outdoor experiment. These results demonstrated high and stable solar evaporation performance could be achieved if turning heat losses into a way of extra energy extraction to further enhance the evaporation performance. This strategy appears to be a promising strategy for effective thermal energy management and practical application.

A Review of β-Ga2O3 Power Diodes.

As the most stable phase of gallium oxide, β-Ga2O3 can enable high-quality, large-size, low-cost, and controllably doped wafers by the melt method. It also features a bandgap of 4.7-4.9 eV, a critical electric field strength of 8 MV/cm, and a Baliga's figure of merit (BFOM) of up to 3444, which is 10 and 4 times higher than that of SiC and GaN, respectively, showing great potential for application in power devices. However, the lack of effective p-type Ga2O3 limits the development of bipolar devices. Most research has focused on unipolar devices, with breakthroughs in recent years. This review mainly summarizes the research progress fora different structures of β-Ga2O3 power diodes and gives a brief introduction to their thermal management and circuit applications.

Corner- and edge-mode enhancement of near-field radiative heat transfer.

It is well established that near-field radiative heat transfer (NFRHT) can exceed Planck's blackbody limit1 by orders of magnitude owing to the tunnelling of evanescent electromagnetic frustrated and surface modes2-4, as has been demonstrated experimentally for NFRHT between two large parallel surfaces5-7 and between two subwavelength membranes8,9. However, although nanostructures can also sustain a much richer variety of localized electromagnetic modes at their corners and edges10,11, the contributions of such additional modes to further enhancing NFRHT remain unexplored. Here we demonstrate both theoretically and experimentally a physical mechanism of NFRHT mediated by the corner and edge modes, and show that it can dominate the NFRHT in the 'dual nanoscale regime' in which both the thickness of the emitter and receiver, and their gap spacing, are much smaller than the thermal photon wavelengths. For two coplanar 20-nm-thick silicon carbide membranes separated by a 100-nm vacuum gap, the NFRHT coefficient at room temperature is both predicted and measured to be 830W m-2 K-1, which is 5.5 times larger than that for two infinite silicon carbide surfaces separated by the same gap, and 1,400 times larger than the corresponding blackbody limit accounting for the geometric view factor between two coplanar membranes. This enhancement is dominated by the electromagnetic corner and edge modes, which account for 81% of the NFRHT between the silicon carbide membranes. These findings are important for future NFRHT applications in thermal management and energy conversion.

On the effective thermal conductivity of gallium-based liquid metal filled elastomers

Gallium based alloys are liquid at ambient temperature, combining both metal-like high thermal conductivity and fluidity characteristics, which contributes to their applications in thermal management, soft robotics, stretchable electronics and etc. A great number of experimental researches have been performed in preparing Ga-based liquid metal filled elastomers (LMFEs) with various constituent systems, processing techniques, droplet morphology and filler sizes in attempt to obtain the best thermal conductive efficiency. The thermal conductive mechanisms in these LMFEs are still lacking a comprehensive understanding up to date, and therefore the present work aimed to conduct a thorough analysis on this topic using both theoretical models and finite element method (FEM) simulations. The predictability of four classic micromechanics models was compared with the experiments and FEM simulations, and their relevant thermal conductive principles were identified from the simulated thermal flux evolution. Some deficiencies of these analytical models are identified and amended by reconsidering their special architectures. This work is favorable for establishing a general and quantitative relationship between the effective thermal conductivity and microstructures for most of the synthesized LMFEs available in the literatures.