Radial Thermal Conductivity Research Articles

MXene-reduced graphene oxide sponge-based solar evaporators with integrated water-thermal management by anisotropic design

The main issue limiting the performance of the solar evaporators is that water-thermal management is difficult to coordinate. Herein, we achieve integrated water-thermal management by designing hierarchical MXene-reduced graphene oxide sponges with anisotropic thermal conductivity and axial-directional water conveyance channels. The reduced graphene oxide acts as the sponge framework and carbon source for in situ synthesis of MXenes on the surface. The axial-oriented framework supports the structure and provides fast water transmission channels to the air-water interface. Meanwhile, the MXene nanosheets are vertically aligned on the framework surface, making the radial thermal conductivity of the sponges much greater than the axial one, which suppresses heat loss in the axial direction. The material exhibits an evaporation rate of 2.35 kg m−2 h−1 under one sunlight and maintains 85 % energy efficiency under weak sunlight (0.5-sun). Furthermore, the sponge shows a long working life with 96 % evaporation rate retention after a 30-day-sustained operation.

Improved asymptotic expansion method for laminar fluid flow and heat transfer in conical gaps with disks rotating

PurposeThe purpose of this paper was to study laminar fluid flow and convective heat transfer in a conical gap at small conicity angles up to 4° for the case of disk rotation with a fixed cone.Design/methodology/approachIn this paper, the improved asymptotic expansion method developed by the author was applied to the self-similar Navier–Stokes equations. The characteristic Reynolds number ranged from 0.001 to 2.0, and the Prandtl numbers ranged from 0.71 to 10.FindingsCompared to previous approaches, the improved asymptotic expansion method has an accuracy like the self-similar solution in a significantly wider range of Reynolds and Prandtl numbers. Including radial thermal conductivity in the energy equation at small conicity angle leads to insignificant deviations of the Nusselt number (maximum 1.23%).Practical implicationsThis problem has applications in rheometry to experimentally determine viscosity of liquids, as well as in bioengineering and medicine, where cone-and-disk devices serve as an incubator for nurturing endothelial cells.Social implicationsThe study can help design more effective devices to nurture endothelial cells, which regulate exchanges between the bloodstream and the surrounding tissues.Originality/valueTo the best of the authors’ knowledge, for the first time, novel approximate analytical solutions were obtained for the radial, tangential and axial velocity components, flow swirl angle on the disk, tangential stresses on both surfaces, as well as static pressure, which varies not only with the Reynolds number but also across the gap. These solutions are in excellent agreement with the self-similar solution.

Axial and radial thermal conductivity measurement of 18,650 Lithium-ion battery

Thermal conductivities of lithium-ion batteries are critical for the thermal management of battery packs. In this work, a novel method and experimental apparatuses are developed to measure the axial and radial thermal conductivities of the 18,650 LiNiCoAlO2 (NCA) lithium-ion battery. For the axial conductivity measurement, the one-dimensional steady conduction principle considering uniform heat loss is used, while the combined method of experiment and computational fluid dynamics (CFD) simulation is used for the radial conductivity measurement. By measuring the conductivity of the stainless steel cylinder, the errors are estimated to be less than 1.45 % and 1.37 % for the axial and radial measurement methods respectively. The axial and radial conductivities of the battery are measured at different open circuit voltage (OCV) and temperatures. Under the experimental conditions, the axial conductivity of the battery ranges from 10.26 to 14.20 W/m/K, and the axial conductivity generally increases with OCV and temperature. The radial conductivity ranges from 2.14 to 2.87 W/m/K if the battery core and the steel shell are considered as a whole; and the radial conductivity of the core ranges from 1.84 to 2.55 W/m/K if the core and the shell are considered separately. In the normal OCV range, there is no obvious relationship among the radial conductivity, temperature and OCV, whether the core and the shell are treated separately or not. This work may contribute towards improved thermal simulation of Li-ion cells.

Design of Bioinspired Highly Aligned Bamboo-Mimetic Metamaterials With Structural and Functional Anisotropy

Metamaterials have received widespread attention for their unique properties and broad application prospects. With inspiration from bamboo, metamaterials can be rationally designed to achieve anisotropic functionality. Using a combination of 3D printing and subsequent hot pressing of dual-curing composites, we describe a simple method for creating well-aligned SiC whisker (SiCw) composites that mimic bamboo and have achievable anisotropic thermal conductivity (TC), dielectric properties (DP), and flashover performances (FP). The anisotropic structure is proved by scanning electron microscope and X-ray diffraction observations. At the low loading of 8 vol% SiCw, the axial thermal conductivity of the structured composites can reach 0.655 W m-1 K-1, whereas the radial thermal conductivity is only 0.281 W m-1 K-1, with a high anisotropic TC ratio of 2.33. Strong anisotropy in the dielectric constant was also observed with the permittivity of 134 along the axial direction versus that of 65 along the radial direction at 1 kHz, with a high anisotropic DP ratio of 2.06. Notably, metamaterials exhibit significant anisotropy in both their surface conductivity and flashover voltage, with a high conductivity ratio of ~10,000. The flashover voltage in the diametrical direction is 6 times that in the axial direction and 60% higher than that of the neat resin. This study shows that this approach is anticipated to offer a new path for the creation of high-performance functionally anisotropic materials to meet the diversified requirements of modern electronics.

Numerical study of the thermal behavior of a cylindrical fin formed by two orthotropic media

Numerical solutions are constructed and presented for the thermal distribution, the dimensionless heat flux rate, and fin efficiency for a two-dimensional orthotropic fin of cylindrical geometry formed by two media subject to a convection limit condition on the side surface and at the high fin base, and to a uniform temperature imposed on the other base of the fin. The results are presented and discussed according to the study parameters, radial thermal conductivity ratio, radial Biot number, and axial Biot number for each medium. Many specific cases are obtained from the global solution presented in this work, among others, the temperature distribution and the dimensionless heat flux rate at the base of a single orthotropic or isotropic fin as well as the case of a fin formed by an orthotropic and isotropic media. The findings of the present study demonstrate that the newly proposed fin design significantly improves the dimensionless heat flux rate of the fin compared to the conventional design. This improvement is particularly significant when the axial Biot number of the outer medium is high and the axial Biot number of the inner medium is low, regardless of the ratio of radial thermal conductivities. These results suggest that the proposed fin design is better suited for applications where heat transfer is critical, and the external environment has a high thermal resistance. In addition, the proposed design also provides a more compact geometry, which not only improves the mechanical performance of the fin but also reduces the cost of the material used in its fabrication.

Transferring heat accumulated by asphalt pavement from inside to outside through carbon fibers

On the Qinghai-Tibet Plateau, intense solar irradiation will cause serious heat accumulation in asphalt pavement. Downward heat transfer will disturb the permafrost under subgrade, thus leading to a series of subgrade and pavement diseases. This makes construction of asphalt pavement in the permafrost regions of the Qinghai-Tibet Plateau a world-class challenge. This paper proposes for the first time a transversal heat transfer channel in asphalt pavement, which can quickly transfer heat accumulated in pavement to road shoulders. Finite element software ABAQUS was used to simulate the rutting plate with high axial thermal conductivity carbon fibers inserted transversely. Under the constant heat load of 500 W/m2, the heat flux near the carbon fibers showed the characteristic of convergence. The maximum transverse heat flux in the carbon fibers reached 4.97×107W/m2, which was 14 times that in the asphalt mixture. Meanwhile, the maximum vertical heat flux in the carbon fibers reduced to 2.62×106W/m2, which was 12 % less than the asphalt mixture. The effective thermal conductivity of composite specimens with different carbon fiber parameters was studied through control experiments. When the axial thermal conductivity, volume fraction and number of carbon fiber bundles increased to 100 W/m·°C, 10.72 % and 4 bundles respectively, the transverse ETC of composite specimens increased to 4.05 W/m·°C, 7.09 W/m·°C and 16.18 W/m·°C respectively. They were 3.12 times, 5.45 times and 12.45 times of the control group. The radial thermal conductivity of carbon fibers has a significant effect on the vertical ETC. When it decreased to 0.2 W/m·°C, the vertical ETC decreased by 6.15 % compared with the control group. The temperature variation trend of specimens were measured by a laboratory irradiation experiment. The maximum temperature difference between the control group and the experimental group at 0 mm was 5.81 °C, and the average temperature difference within 2 h was 5.14 °C. The maximum temperature difference at 50 mm was 3.84 °C and the average temperature difference within 2 h was 3.24 °C. The results showed that the transverse heat transfer channel can reduce downward heat transfer. The application of the channels will enhance transverse heat release and relieve heat accumulation of asphalt pavement. This can create a low temperature state for pavement structure and has a positive effect on maintaining the stability of the permafrost regions on the Qinghai-Tibet Plateau.

Improved multiphysics model of the High Temperature Engineering Test Reactor for the simulation of loss-of-forced-cooling experiments

We present a multiphysics model of the High Temperature Engineering Test Reactor for comparison with past and predict future loss-of-forced-cooling (LOFC) experiments. The approach selected combines (1) 3-D full-core superhomogenization-corrected neutronics, (2) 3-D full-core homogenized or semi-heterogeneous heat transfer (macroscale), (3) 2-D axisymmetric fuel rod heat transfer (pin-scale), and (4) 1-D thermal-hydraulics channels. Although large uncertainties remain, the time and magnitude of the first power peak after re-criticality is predicted within 1.5 h and 175 kW, respectively. The novelty of our work includes (1) a new macroscale/pin-scale heat transfer coupling approach relying on gap conductance to drastically speed up numerical convergence by two orders of magnitude, (2) determination of a radial effective thermal conductivity, reproducing the semi-heterogeneous re-criticality time within one hour using a homogenized macroscale model, and (3) a preliminary study of the reactor’s early behavior following a LOFC event, enabling further assessment of numerical models against fission power measurements.

Comparative study of thermal management systems with different cooling structures for cylindrical battery modules: Side-cooling vs. terminal-cooling

Indirect-cooling through cooling plate is a common way in the design of liquid-based battery thermal management system (BTMS), which can be divided into side-cooling and terminal-cooling according to the position arrangement of the cooling plates. In this work, comparative investigations are performed to analyze the specific merits and demerits between these two cooling structures and further understandings are provided for the heat dissipation mechanisms of BTMSs for the cylindrical battery modules. It is found that the side-cooling BTMS exhibits a better ability in the temperature rise control with a maximum temperature (Tmax) of 30.84 °C at the end of 1 C discharge compared with the terminal-cooling one where corresponding Tmax rises to 35.48 °C. But meanwhile, it encounters an inherent drawback on the temperature uniformity with a maximum temperature difference (ΔTmax) of 5.76 °C after 1 h discharging due to the low radial thermal conductivity of the batteries, which forms a significant thermal gradient along its thermal transport paths. In contrast, corresponding ΔTmax in the terminal-cooling case is only 2.86 °C. Effects of coolant velocity and channel number on the heat dissipation performances of the side-cooling and terminal-cooling BTMSs are examined and further, different strategies are proposed and tested for these two cooling structures respectively to ameliorate their heat dissipation performances based on their different characteristics in the heat transport paths and thermal field distributions. The results could provide useful guidance for the future design of BTMS for the cylindrical battery modules.

Method to Measure Radial Thermal Conductivity for Cylindrical Samples.

Anisotropy is a prevailing property in most substances in the real world. The thermal conductivity characteristic of anisotropy must be determined for utilizing geothermal resources and assessing battery performances. Most core samples were primarily obtained by drilling and intended to be cylindrical in shape, with the cores resembling quantities of familiar batteries. Although Fourier's law could be used to measure the axial thermal conductivity of square or cylindrical samples, there is still a need to develop a new method to measure the radial thermal conductivity of cylindrical samples and evaluate their anisotropy. Thus, we established a testing method for cylindrical samples using the theory of complex variable functions following the heat conduction equation and implemented a numerical simulation to determine the difference between this method and typical ones via a finite element model for various samples. Results show that the method could perfectly gauge the radial thermal conductivity of cylindrical samples with more powerful availability.

Strong, Shape-Memory Lignocellulosic Aerogel via Wood Cell Wall Nanoscale Reassembly.

Polymer shape-memory aerogels (PSMAs) are prospects in various fields of application ranging from aerospace to biomedicine, as advanced thermal insulators, actuators, or sensors. However, the fabrication of PSMAs with good mechanical performance is challenging and is currently dominated by fossil-based polymers. In this work, strong, shape-memory bio-aerogels with high specific surface areas (up to 220 m2/g) and low radial thermal conductivity (0.042 W/mK) were prepared through a one-step treatment of native wood using an ionic liquid mixture of [MTBD]+[MMP]-/DMSO. The aerogel showed similar chemical composition similar to native wood. Nanoscale spatial rearrangement of wood biopolymers in the cell wall and lumen was achieved, resulting in flexible hydrogels, offering design freedom for subsequent aerogels with intricate geometries. Shape-memory function under stimuli of water was reported. The chemical composition and distribution, morphology, and mechanical performance of the aerogel were carefully studied using confocal Raman spectroscopy, AFM, SAXS/WAXS, NMR, digital image correlation, etc. With its simplicity, sustainability, and the broad range of applicability, the methodology developed for nanoscale reassembly of wood is an advancement for the design of biobased shape-memory aerogels.

Study on Polypropylene Composites with High Thermal Conductivity and Its Preparation

Polypropylene (PP) composite materials were prepared through two molding methods of injection and compression molding, taking PP, FG as the matrix and thermal conductive filler. The effects of molding methods and FG content on the thermal conductivity of composite materials were studied, and the SEM, XRD, and thermal expansion properties of the materials were further analyzed. Results showed that thermal conductivity of the composite material increases with increasing of the FG content. When the FG content was 75 wt%, the average thermal conductivity of the composite materials prepared by injection molding and compression molding is 9.88 W·m-1·K-1 and 6.03 W·m-1·K-1, respectively. The axial thermal conductivity is 16.6 W·m-1·K-1 and 1.35 W·m-1·K-1, and the radial thermal conductivity is 5.88 W·m-1·K-1 and 26.9 W·m-1·K-1, respectively. In composite materials formed by injection molding, the flaky FG is mainly oriented vertically, while in compression molding, the flaky FG is mainly oriented horizontally.

A pseudo-local heat transfer approach in a low tube to particle diameter ratio packed bed catalytic reactor: Oxidative dehydrogenation of ethane as a case study

A generalized approach to model heat transfer in an industrial-scale wall-cooled packed bed reactor with a low tube-to-particle diameter ratio (<8) is proposed and assessed in this work. The modeling approach rests on the realization of experiments carried out in absence of reaction in bench-scale as well as in industrial-scale packed beds. The approximation overcomes historical limitations identified when modeling radial heat transfer mechanisms by applying conventional approaches. The methodology leads to the reliable determination of the external wall heat transfer coefficient and pseudo-local radial effective thermal conductivity. The approach allows the quantification of heat transfer resistances through the core, the internal and the external wall of the bed indicating that approximately 30 % of the resistances are located along the internal side of the packed bed when it was operated at Particle Reynolds numbers ranging from 700 to 1400. Because of its complex impact on heat transfer, fluid dynamics is accounted for by implementing a methodology that uses pressure drop data and the mass conservation criterion to describe velocity profiles, including the determination of the viscous and inertial resistances caused by solid surfaces at the core and near the wall. Finally, the heat transfer information is transferred to a pseudo-heterogenous model to simulate the performance of an industrial-scale wall-cooled packed bed reactor for the highly exothermic oxidative dehydrogenation of ethane. Simulations demonstrate both the reliability of the proposed heat transfer approach and the limitations of the conventional approximations when describing temperature profiles in a packed bed reactor.

A high-efficient anisotropic continuum model for the optimization of heat transfer and chemical reaction in a packed-bed water gas shift reactor

The packed bed reactor with the high-temperature shift reaction has been a competitive industrial device for the production of hydrogen fuel. While the temperature distribution in the packed bed plays an important role in improving the reaction efficiency, and numerical simulation is a powerful way to recover the heat transfer inside the reactor. Nevertheless, the current simulation methods are either high computational cost or low accuracy for the high-temperature shift. To accomplish the effective computational cost and accuracy simultaneously, we developed a two-dimensional anisotropic continuum model with modified space-dependent effectiveness factor and anisotropic thermal conduction based on the pseudo continuum model. Meanwhile, the simulation results were compared with those by the particle-resolved 3D computational fluid dynamics to validate the model accuracy. Due to the overestimation of the radial thermal conductivity by the pseudo continuum model, the axial temperature rise in the packed bed was only 10 K, but a significant temperature rise of 50 K was presented by the other two methods, suggesting the coordinate computational accuracy of the anisotropic continuum model. However, the computational time consumed by the particle-resolved 3D computational fluid dynamics was up to 1320 min, which exceeds a thousand times more than that in current advanced model. All the comparisons indicate the anisotropic continuum model can predict the heat transfer through the packed bed with sufficient computational accuracy and efficiency, making a powerful and time-saving method to conduct the effective heat management in packed bed reactors for actual industrial applications.

Anisotropic and Lightweight Carbon/Graphene Composite Aerogels for Efficient Thermal Insulation and Electromagnetic Interference Shielding.

High-performance and lightweight carbon aerogels (CAs) have attracted considerable attention in various fields such as electrochemistry, catalysis, adsorption, energy storage, and so on. However, finding an environmentally friendly and efficient preparation method and achieving a controllable performance of CAs are still a challenge. Herein, a series of anisotropic carbon/graphene composite aerogels were synthesized by unidirectional freezing of polyamic acid ammonium salt/graphene oxide (PAS/GO) suspension followed by lyophilization, thermal imidization, and carbonization. The prepared aerogels presented a tubular pore structure oriented along the freezing direction. The GO dispersed in the polymer matrix reinforced the skeleton of aerogels, which significantly inhibited the volume shrinkage during the preparation process, thus giving low densities of 0.074-0.185 g cm-3. In addition, the oriented pore structure endowed the composite aerogels with obviously anisotropic heat insulation performance. The radial thermal conductivity was as low as 0.038 W m-1 K-1 at the density of 0.074 g cm-3. When the initial content of GO rose to 20 phr, the resultant aerogels exhibited a high electrical conductivity of about 0.77 S cm-1 in the radial direction and the electromagnetic interference shielding effectiveness (EMI SE) reached 54.6 dB at the same time. Therefore, this study provided a facile and environmentally friendly method to prepare lightweight and anisotropic carbon aerogels.

Numerical investigation on the thermal behavior of cylindrical lithium-ion batteries based on the electrochemical-thermal coupling model

• HET model and LET model are proposed. • Radial temperature gradient of cylindrical LIB is non-negligible. • Inhomogeneous discharge due to non-uniform temperature distribution inside cylindrical LIB is investigated. • This work provides insights to choose appropriate electrochemical-thermal coupling models. In this paper, a one-dimensional electrochemical model and a three-dimensional axisymmetric heat transfer model are coupled to simulate the electrochemical and thermal behavior of cylindrical lithium-ion batteries (LIBs). The model is verified against the experimental data of discharge voltage and surface temperature of LIBs under different discharge rates. First, the holistic electrochemical-thermal coupling (HET) model and the layered electrochemical-thermal coupling (LET) model are established. In contrast to the traditional HET model, the advantage of the LET model is that it can realize the investigation on the inhomogeneous discharge and aging induced by the non-uniform temperature distribution inside the battery. We demonstrate the radially inhomogeneous discharge of cylindrical LIBs with a 4-layer LET model in this work. It is also found that the HET model can provide desirable simulation accuracy in temperature with less computational cost. This provides insights for researchers to choose more appropriate electrochemical-thermal coupling models in accordance with the different scenarios. Second, the thermal behavior of cylindrical LIBs at different discharge rates is studied by analyzing the heat generation rate and heat dissipation characteristics during the discharge process. The study reveals that, unlike pouch LIBs, there is a significant temperature gradient in the radial direction of cylindrical LIBs. Finally, the factors that affect the temperature uniformity of the battery, such as cooling conditions, ambient temperature, discharge rate, radial dimension, and radial thermal conductivity are analyzed in detail. Meanwhile, some suggestions are provided to improve the temperature uniformity. The findings in this work are of benefit to obtain profound understading of thermal behavior in cylindrical LIBs. Besides, they also have potential applications in improving the prediction accuracy of the temperature signal in the battery thermal management system of LIBs.

Theoretical and experimental study on the anisotropic thermal conductivity of composite phase change materials prepared by hot-pressing method

A convenient and efficient anisotropic thermal conductivity prediction model of composite phase change materials (CPCMs) prepared by hot-pressing method was proposed. This model quantitatively calculates the angular distribution of thermal conductivity particles in CPCMs. The predicted value of anisotropic thermal conductivity is in good agreement with the experimental value. The distribution of ellipsoidal thermal conductivity particles in the CPCMs tends to be horizontal with increasing compression ratio, which makes the anisotropy of the thermal conductivity of CPCMs obvious. By decreasing the particle thickness, increasing the particle length and reducing the boundary thermal resistance of the particles, the radial thermal conductivity of the CPCMs can be improved.

Radial heat transport in a fixed-bed reactor made of metallic foam pellets: Experiment and particle-resolved computational fluid dynamics

Open-cell metallic foams in the shape of pelletized catalysts are regarded as potential catalyst substrates for the application in fixed-bed reactors. This work reports an experimental study and a detailed Computational Fluid Dynamics (CFD) model to investigate the heat transfer performance of a fixed-bed reactor made of open-cell metallic foam pellets. The steady-state heat transfer behavior of a hot gas flowing through such a packed bed under wall-cooled conditions was examined. The proposed CFD model is in line with the particle-resolved CFD (PRCFD) approach that accounts explicitly for the random packing structure, so that the transport processes in the interstitial regions are fully resolved. The momentum and energy transports inside the highly porous foam particles are considered by closure equations based on the porous-media model. The Rigid Body Dynamics (RBD) method is adopted to create the packing geometry. The axial temperature and the pressure drop obtained by the CFD simulations show good agreement with experimental data. To evaluate the thermal performance, effective heat transport parameters in a packed bed such as the effective radial thermal conductivity and the apparent wall-fluid heat transfer coefficient are determined, with the aid of a 2D pseudo-homogenous plug-flow reactor model. The correlations for heat transport characteristics as a function of particle Reynolds number for the metallic foam packed bed are also presented.

In-situ copper ion reduction and micro encapsulation of wood-based composite PCM with effective anisotropic thermal conductivity and energy storage

This work develops metallic wood-based phase change materials (MWPCM) with high-performance anisotropic thermal conductivity by impregnating wood with phase change microcapsules and subsequent in situ chemical deposition of copper inside the wood cell lumen. Phase change material (PCM) is encapsulated by polymer to form phase change microcapsules, which solve the leakage problem effectively. Benefited with the well-aligned and hierarchical porous structure of wood, phase change microcapsules coated with copper layer are orderly confined inside wood vessels and fibers, developing a continuous and anisotropic heat transfer network along the highly oriented transport tissues of wood. The morphology, chemical structure and crystallization of microcapsules and MWPCM are investigated using scanning electronic microscope (SEM), flourier transformation infrared spectroscopy (FTIR) and X-ray diffractometer (XRD), and the thermal storage capacity, thermal stability and thermal conductivity of the developed PCM composites are examined using differential scanning calorimetry (DSC), thermal gravimetric analysis (TGA) and laser flash diffusivity apparatus (LFA) respectively. The results show that PCM capsules were effectively accommodated in orderly porous wood as a carrier; the radial and longitudinal thermal conductivity of MWPCM reached 0.37 W/(m*K) and 0.53 W/(m*K), which increased by 362% and 211% compared to pure wood, respectively. The anisotropic thermal conductivity of MWPCM enabled an efficient heat transfer along the longitudinal direction and reduced the heat loss in the transverse direction. MWPCM exhibited good thermal energy storage capacity (92.9 J/g and 94.6 J/g) and suitable phase change temperature (11.4 °C and 29.4 °C) for indoor thermal energy management. MWPCM also displayed outstanding shape-stability, excellent thermal stability and temperature regulation, which has a great potential for building energy collecting, storage and management.

High-strength and superamphiphobic chitosan-based aerogels for thermal insulation and flame retardant applications

In recent years, aerogel has been reported as a good thermal insulation material. However, it has remained a great challenge to realize high mechanical property and excellent anti-fouling performance concurrently of aerogel in practical applications. Here, a composite aerogel was developed via directional freezing and chemical vapor deposition (CVD) modification using chitosan (CS) and montmorillonite (MMT) as heat-resistant raw materials and cellulose nanofibrillated fiber (CNF) as reinforcing filler. The intercalation between the CS molecular chain and MMT endows the aerogel with excellent mechanical properties. Due to the anisotropic structure, the axial Young's modulus is high up to 630 KPa, and the radial thermal conductivity is as low as 31 mW m−1 K−1. Meanwhile, the aerogel shows a high limiting oxygen index (LOI) value of 43%. Furthermore, CVD treatment increases the contact angles to water and various oils higher than 150°, which portects the aerogle from being contaminated by common liquids. Compared to conventional insulation materials, this aerogel can maintain excellent insulation performance in extreme environments such as heavy rain or oil leakage. The composite aerogel is expected to play an important role in the fields of house warmth, vehicle interior, aviation, and etc.

Concerning the effect of radial thermal conductivity in a self-similar solution for rotating cone-disk systems

PurposeThus, the purposes of this study are to study the limits of applicability of the self-similar solution to the problem of fluid flow, heat and mass transfer in conical gaps with small conicity angles, to substantiate the impossibility of using a self-similar formulation of the problem in the case of large conicity angles and to substantiate the absence of the need to take into account the radial thermal conductivity in the energy equation in its self-similar formulation for the conicity angles up to 4°.Design/methodology/approachIn the present work, an in-depth and extended analysis of the features of fluid flow and heat transfer in a conical gap at small angles of conicity up to 4° is performed. The Couette-type flow arising, in this case, was modeled using a self-similar formulation of the problem. A detailed analysis of fluid flow calculations using a self-similar system of equations showed that they provide the best agreement with experiments than other known approaches. It is confirmed that the self-similar system of flow and heat transfer equations is applicable only to small angles of conicity up to 4°, whereas, at large angles of conicity, this approach becomes unreasonable and leads to significantly inaccurate results. The heat transfer process in a conical gap with small angles of conicity can be modeled using the self-similar energy equation in the boundary layer approximation. It was shown that taking into account the radial thermal conductivity in the self-similar energy equation at small conicity angles up to 4° leads to maximum deviations of the Nusselt number up to 1.5% compared with the energy equation in the boundary layer approximation without taking into account the radial thermal conductivity.FindingsIt is confirmed that the self-similar system of fluid flow equations is applicable only for small conicity angles up to 4°. The inclusion of radial thermal conductivity in the model unnecessarily complicates the mathematical formulation of the problem and at small conicity angles up to 4° leads to insignificant deviations of the Nusselt number (maximum 1.5%). Heat transfer in a conical gap with small conicity angles up to 4° can be modeled using the self-similar energy equation in the boundary layer approximation.Originality/valueThis paper investigates the question of the validity of taking into account the radial heat conduction in the energy equation.