International Journal of Thermal Sciences最新文献_第2页

Effects of magnetic nanoparticle distribution in cancer therapy through hyperthermia 磁性纳米粒子分布对通过热疗治疗癌症的影响

IF 4.9 2区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Thermal Sciences

Pub Date : 2024-09-27 DOI: 10.1016/j.ijthermalsci.2024.109428

Magnetic hyperthermia (MHT) is a promising cancer treatment that exploits the heating capabilities of magnetic nanoparticles (MNPs) when exposed to alternating magnetic fields. The primary challenge in optimizing MHT lies in understanding the influence of MNP distribution within the tumor microenvironment. This study presents realistic simulations of MNP distribution within a tumor, accounting for diffusion, convection, and internalization dynamics, alongside the presence of a necrotic core. Additionally, a vascular network was modeled based on diagnostic images to assess its impact on nanoparticle behavior and heat generation within the tumor. Our results show that uneven MNP distribution, particularly in areas influenced by the tumor's vasculature and necrotic regions, results in highly variable temperature profiles and irregular thermal damage. By contrast, a more uniform distribution of MNPs leads to a consistent rise in temperature and a broader region of thermal damage, with maximum temperatures reaching 47 °C and 99 % tumor cell death after 60 min of treatment. Key quantitative findings indicate that the tumor's vascular architecture plays a crucial role in determining the heat distribution and treatment efficacy. This study highlights the importance of fine-tuning MNP delivery and distribution to maximize therapeutic outcomes in MHT. The approach offers significant potential for applications in treating deep-seated or inoperable tumors, where precise and localized therapy is critical.

磁性热疗（MHT）是一种很有前景的癌症治疗方法，它利用了磁性纳米粒子（MNPs）在暴露于交变磁场时的加热能力。优化 MHT 的主要挑战在于了解 MNP 在肿瘤微环境中分布的影响。本研究对 MNP 在肿瘤内的分布进行了逼真的模拟，考虑到了扩散、对流和内化动力学以及坏死核心的存在。此外，还根据诊断图像对血管网络进行了建模，以评估其对纳米粒子行为和肿瘤内发热的影响。我们的研究结果表明，不均匀的 MNP 分布，尤其是在受肿瘤血管和坏死区域影响的区域，会导致温度曲线的高度变化和不规则的热损伤。相比之下，分布更均匀的 MNP 会导致温度持续上升，热损伤区域更广，最高温度可达 47 °C，治疗 60 分钟后肿瘤细胞死亡 99%。主要的定量研究结果表明，肿瘤的血管结构在决定热分布和治疗效果方面起着至关重要的作用。这项研究强调了微调 MNP 递送和分布以最大限度地提高 MHT 治疗效果的重要性。这种方法在治疗深部肿瘤或无法手术的肿瘤方面具有巨大的应用潜力，在这些肿瘤中，精确的局部治疗至关重要。

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引用次数: 0

Design and experimental analysis of a novel thermal diode with asymmetric heat transfer inspired by feather 受羽毛启发设计的新型非对称传热二极管及其实验分析

IF 4.9 2区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Thermal Sciences

Pub Date : 2024-09-27 DOI: 10.1016/j.ijthermalsci.2024.109434

To overcome the limitation of isotropic heat transfer of traditional heat pipes, a novel thermal diode with asymmetric flow resistance vapor channel inspired by the goose feather fibers is proposed in this study. The thermal performance of novel thermal diode is experimentally investigated. Results show that under the wide range of operating conditions, the thermal resistance of one end surpasses the thermal resistance of the other end, indicating its excellent thermal rectification capability. Under the filling ratio of 10 % and heating power of 7.5 W, the maximum thermal resistance of the thermal diode is 5.23 times the minimum thermal resistance, demonstrating excellent asymmetric heat transfer performance. Experimental results demonstrate that the novel thermal diode proposed in this study can easily change its unidirectional heat transfer direction by simply adjusting the internal filling ratio, showing significant application potential in the fields of thermal control system.

为了克服传统热管各向同性传热的局限性，本研究从鹅毛纤维中汲取灵感，提出了一种具有非对称流阻蒸汽通道的新型热二极管。实验研究了新型导热二极管的热性能。结果表明，在宽范围的工作条件下，一端的热阻超过了另一端的热阻，表明其具有出色的热整流能力。在填充率为 10 %、加热功率为 7.5 W 的条件下，热敏二极管的最大热阻是最小热阻的 5.23 倍，显示出出色的非对称传热性能。实验结果表明，本研究提出的新型导热二极管只需调整内部填充率，就能轻松改变其单向传热方向，在热控制系统领域具有巨大的应用潜力。

引用次数: 0

Optimization and mechanistic analysis of the configurational parameters of a serrated trench for improving film cooling performance 优化锯齿状沟槽的构型参数并对其进行机理分析，以提高薄膜冷却性能

IF 4.9 2区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Thermal Sciences

Pub Date : 2024-09-26 DOI: 10.1016/j.ijthermalsci.2024.109436

Combinations of trench and holes in film cooling design for turbine blades have been suggested recently. In this work, structural optimization is performed for one of our previously proposed serrated trenches. Geometric parameters including serrated angle, width, and height of the trench, which are the key factors affecting the flow and cooling characteristics, are optimized. The relative area-averaged cooling effectiveness, the relative pressure drop coefficient, and the performance evaluation criterion (PEC) are the optimizing objectives. The multi-objective genetic algorithm is employed as the search strategy to achieve PEC maximization at blowing ratios in the range of 0.5–2.0. The individual variations of each parameter are studied by controlling the variables using the response surface method. It shows that the trench height is the most influential factor on flow and heat transfer; while the trench serrated angle mainly affects the heat transfer; and the trench width has a weak effect on both, depending on the blowing ratio. To achieve maximum PEC, the trench height needs to enlarge with the increase in blowing ratio, while contrary to this, the trench width needs to increase under low blowing ratios and decrease under high blowing ratios, and the optimum trench serrated angle is within the range of 80°–85° at all blowing ratios. The optimum geometry reduces the pressure loss while improves the cooling effectiveness by 8.43 %–17.97 % compared to the baseline trench. This work is instructive for the design and application of practical structures for blade cooling.

最近有人建议在涡轮叶片的薄膜冷却设计中结合使用沟槽和孔。在这项工作中，我们对之前提出的一种锯齿沟槽进行了结构优化。优化的几何参数包括锯齿状沟槽的角度、宽度和高度，它们是影响流动和冷却特性的关键因素。相对区域平均冷却效果、相对压降系数和性能评估标准（PEC）是优化目标。采用多目标遗传算法作为搜索策略，在 0.5-2.0 的吹气比范围内实现 PEC 最大化。通过使用响应面法控制变量，研究了各参数的个别变化。结果表明，沟槽高度对流动和传热的影响最大；沟槽锯齿角主要影响传热；沟槽宽度对流动和传热的影响较弱，这取决于吹气比。为了获得最大的 PEC 值，沟槽高度需要随着鼓风比的增大而增大，与此相反，沟槽宽度在低鼓风比时需要增大，而在高鼓风比时则需要减小。与基准沟槽相比，最佳几何形状可减少压力损失，同时提高冷却效果 8.43 %-17.97 %。这项工作对叶片冷却实用结构的设计和应用具有指导意义。

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引用次数: 0

Thermal calculation and experimental study of a double-disk magnetic coupler 双盘磁耦合器的热计算和实验研究

IF 4.9 2区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Thermal Sciences

Pub Date : 2024-09-26 DOI: 10.1016/j.ijthermalsci.2024.109444

Aiming to tackle the difficulties and inaccuracies in calculating the temperature field of double-disk magnetic coupler, a novel thermal calculation method is proposed, integrating the equivalent thermal network method and CFD method. This approach deviates from traditional methods that substitute empirical formulas with rotational speed. An equivalent thermal network model is established to ascertain the temperature rise at each network node. Additionally, a fluid-solid coupling model is constructed, and the impact of uneven air temperature distribution on air density, specific heat capacity, dynamic viscosity, and thermal conductivity is analyzed using the least squares method. The results reveal that after incorporating variable temperature air physical properties, the high-temperature area of the copper conductor decreases, the calculated temperature rise aligns closer to actual values, and air friction loss on the copper surface is reduced by 6.5 %. Experimental verification, conducted on a 55 kW double-disk magnetic coupler, demonstrates maximum errors of 8.86 % and 6.53 % when comparing experimental values to those calculated by the equivalent thermal network method and CFD method, respectively, thereby validating the proposed method. This research provides a theoretical reference for thermal calculations in double-disk magnetic coupler.

针对双盘磁耦合器温度场计算中的困难和不准确性，提出了一种新型热计算方法，将等效热网络方法和 CFD 方法融为一体。这种方法不同于用转速替代经验公式的传统方法。建立了一个等效热网络模型，以确定每个网络节点的温升。此外，还构建了流固耦合模型，并使用最小二乘法分析了空气温度分布不均对空气密度、比热容、动态粘度和热导率的影响。结果表明，在考虑了变温空气的物理特性后，铜导体的高温面积减小，计算出的温升更接近实际值，铜表面的空气摩擦损耗降低了 6.5%。在 55 kW 双盘磁耦合器上进行的实验验证表明，实验值与等效热网络法和 CFD 法计算值的最大误差分别为 8.86 % 和 6.53 %，从而验证了所提出的方法。这项研究为双盘磁耦合器的热计算提供了理论参考。

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引用次数: 0

Thermal characterisation of isotopic heat sources for enhanced thermophotovoltaic systems 用于增强型热光电系统的同位素热源的热特性分析

IF 4.9 2区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Thermal Sciences

Pub Date : 2024-09-25 DOI: 10.1016/j.ijthermalsci.2024.109443

Radioisotope thermophotovoltaics (RTPVs) are playing an increasingly important role in the energy supply for deep space exploration. The output performance of RTPVs can be significantly improved by increasing the surface temperature of isotopic heat sources and reducing the high-temperature degradation effect of the thermophotovoltaic cells. This work proposes methods such as selective emission coating and adjusting heat source structure to improve heat source temperature and optimize heat distribution. Results showed that the surface temperature of the heat source could generally reach more than 1000 K by using the selective coating when the thermal power of the isotopic heat source was 500 W. The use of selective coatings can also make the thermophotovoltaic cells closer to the heat source, and the volume of RTPVs could be reduced from 1.23 × 10⁻³ m³ to 0.49 × 10⁻³ m³, with a reduction of ∼60 %. Under the condition of W@SiO₂ selective coating and 500 W heat source, RTPVs could produce the maximum output power of 22 mW/cm² when the distance between the InGaAs cell and the heat source is 2 cm. The results provided effective guidance for the design of the heat source and miniaturization of RTPVs in space applications.

放射性同位素热光电（RTPV）在深空探测的能源供应中发挥着越来越重要的作用。通过提高同位素热源的表面温度，降低热光电池的高温衰减效应，可以显著提高 RTPV 的输出性能。本研究提出了选择性发射涂层和调整热源结构等方法来提高热源温度和优化热量分布。结果表明，当同位素热源的热功率为 500 W 时，通过使用选择性涂层，热源表面温度一般可达到 1000 K 以上；使用选择性涂层还可使热光伏电池更靠近热源，RTPV 的体积可从 1.23 × 10-3 m3 减小到 0.49 × 10-3 m3，减小了 ∼ 60 %。在 W@SiO2 选择性涂层和 500 W 热源条件下，当 InGaAs 电池与热源之间的距离为 2 cm 时，RTPV 可产生 22 mW/cm2 的最大输出功率。这些结果为空间应用中的热源设计和 RTPV 微型化提供了有效指导。

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引用次数: 0

Innovative-serpentine cooling method of batteries: Both thermal and statistical method approach 创新的蛇形电池冷却方法：热方法和统计方法

IF 4.9 2区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Thermal Sciences

Pub Date : 2024-09-25 DOI: 10.1016/j.ijthermalsci.2024.109437

Renewable energy, in particular, is critical for a sustainable world. Effective storage of energy is at the heart of all systems. While energy storage allows us to preserve the beauties offered by nature, it also requires innovative solutions that push the limits of technology. The most important factor affecting the performance of batteries is their temperature. For this reason, the serpentine cooling model, which is an innovative battery cooling method, was evaluated in this study. Generally, in the literature, batteries are considered as heat masses and given a certain heat flux and their temperature distributions are examined. In this study, batteries were connected to each other with busbars as in reality and thermal analyses were performed. In addition, a serpentine cooling method, which has never been used before, was tried as a cooling method in batteries. While all these evaluations were made, statistical analyses were performed for the priority order of the parameters used. All of these situations show how innovative the study is. The NTGK model was used in CFD analyses. 5 different parameters were considered. These are the discharge rate (0.5C, 1C, 1.5C, 2C and 2.5C), the type of refrigerant (air and water), the speed at which the refrigerant enters the model (0.01 m/s, 0.03 m/s and 0.05 m/s), the ambient temperature (293K, 298K and 300K), and the SOH value (50 %, 65 %, 75 %).Water has been shown to be a better refrigerant than air. As the inlet speed of the refrigerant was increased, the discharge rate was reduced, and the SOH value decreased, the temperature values obtained by the model were lower. The temperature values of the batteries according to their location in the model were also examined. 5-factor, 2-level experiments were conducted to examine statistically. It was checked whether the created values fit the distributions and it was seen that the most effective parameter used in the model was the type of refrigerant. In addition, the most statistically effective working conditions were also determined.

可再生能源对于可持续发展的世界尤为重要。有效的能源储存是所有系统的核心。储能可以让我们保护大自然的美景，但同时也需要突破技术极限的创新解决方案。影响电池性能的最重要因素是其温度。因此，本研究评估了蛇形冷却模型，这是一种创新的电池冷却方法。一般来说，文献中将电池视为热块，并给予一定的热通量，然后研究其温度分布。在本研究中，电池之间用母线连接，就像现实中一样，并进行了热分析。此外，还尝试了一种以前从未使用过的蛇形冷却方法，作为电池的冷却方法。在进行所有这些评估的同时，还对所用参数的优先顺序进行了统计分析。所有这些情况都表明了这项研究的创新性。在 CFD 分析中使用了 NTGK 模型。考虑了 5 个不同的参数。这些参数包括排气速率（0.5C、1C、1.5C、2C 和 2.5C）、制冷剂类型（空气和水）、制冷剂进入模型的速度（0.01 m/s、0.03 m/s 和 0.05 m/s）、环境温度（293K、298K 和 300K）以及 SOH 值（50%、65% 和 75%）。随着制冷剂入口速度的增加、排放速率的降低以及 SOH 值的降低，模型得到的温度值也随之降低。此外，还根据电池在模型中的位置对其温度值进行了研究。进行了 5 因子、2 级实验，以进行统计检验。检查了所创建的值是否符合分布，发现模型中使用的最有效参数是制冷剂类型。此外，还确定了统计上最有效的工作条件。

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引用次数: 0

Effects of transverse divider wall within the squealer cavity on the performance of a novel squealer tip with rail crown holes for the gas turbine blade 尖叫器空腔内的横向分隔墙对燃气轮机叶片上带有轨道冠孔的新型尖叫器尖端性能的影响

IF 4.9 2区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Thermal Sciences

Pub Date : 2024-09-24 DOI: 10.1016/j.ijthermalsci.2024.109432

The squealer tip with rail crown holes is a novel design that offers superior overall performance, effectively enhancing tip cooling and controlling leakage flow in turbine blades. In this study, the transverse divider wall is added to the squealer cavity further to explore the potential advantages of this novel blade tip structure. This study aims to investigate the influence of the position and number of the divider walls on the blade tip performance. Numerical results show that the hindrance effect of the divider wall significantly enlarges the range of the cavity coolant, which enhances the coolant reattachment on the cavity floor and reduces the leading-edge high heat transfer coefficient (h). After cavity flow strides over the divider wall, it inclinedly impacts the rear cavity floor, forming a reattachment line (RL), which increases both the film cooling efficiency (η) and h behind the divider wall. As the divider wall shifts backward, the h near the leading-edge RL gradually increases, and the low-η region of the suction-side corner is expanded. As the divider wall number increases, the second utilization of the coolant within the cavity is improved, compared with Baseline, the

\overline{η}

in case with three divider walls is improved by about 59.13 %. The flow structure near each divider wall is similar, simultaneously, the downstream divider wall can promote coolant attachment near the adjacent upstream divider wall. In aerodynamic aspect, the position and number of the divider walls minimally influence the total leakage flow rate (LFR), but they exert a notable effect on the LFR distribution along streamwise. In general, upstream of the divider wall, the LFR is significantly diminished, but the reduced leakage is compensated downstream of the divider wall, resulting in an overall constant total leakage.

带轨冠孔的涡轮叶尖是一种新颖的设计，具有卓越的整体性能，可有效提高叶尖冷却效果并控制涡轮叶片的泄漏流。在本研究中，为进一步探索这种新型叶尖结构的潜在优势，在尖叫器空腔中增加了横向分隔墙。本研究旨在探讨分隔壁的位置和数量对叶尖性能的影响。数值结果表明，分隔壁的阻碍效应显著扩大了空腔冷却剂的范围，从而增强了冷却剂在空腔底部的再附着，降低了前缘高传热系数（h）。空腔流跨过分隔墙后，倾斜地冲击后空腔底板，形成重新附着线（RL），从而提高了分隔墙后的薄膜冷却效率（η）和传热系数（h）。随着分流壁的后移，前缘 RL 附近的 h 逐渐增大，吸气侧转角的低η区域也随之扩大。随着分流壁数的增加，空腔内冷却剂的二次利用率得到提高，与基线相比，三分流壁情况下的η‾提高了约 59.13%。各分流壁附近的流动结构相似，同时，下游分流壁可促进冷却剂附着在相邻的上游分流壁附近。在空气动力学方面，分流壁的位置和数量对总泄漏流速（LFR）的影响很小，但对沿流向的泄漏流速分布有显著影响。一般来说，在分流壁的上游，泄漏流速会显著降低，但在分流壁的下游，降低的泄漏量会得到补偿，从而使总泄漏量保持不变。

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引用次数: 0

Numerical analysis of thermal-hydraulic characteristics of the whole LFR core under blockage conditions 堵塞条件下整个低温冷冻机堆芯热液压特性的数值分析

IF 4.9 2区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Thermal Sciences

Pub Date : 2024-09-23 DOI: 10.1016/j.ijthermalsci.2024.109435

Blockage accidents are critical scenarios in the design and safety analysis of lead-bismuth cooled fast reactor (LFR) core. Traditional analysis of blockage accidents in LFR focuses on localized, fine-scale computational fluid dynamics (CFD) simulations of single or three assemblies, but the analysis of the whole core scale impact caused by blockage accidents is insufficient. Therefore, this paper uses CorTAF-LBE, a three-dimensional thermal-hydraulic analysis code developed by XJTU-NuTHeL, to analyze the impact of blockage accidents on the whole core of the LFR. The reliability of the code in calculating thermal-hydraulic parameters under blockage accidents was validated based on the KALLA-THEADES and KALLA-IWF experiments. Taking the MYRRHA-FASTEF core as the object, simulations and analyses are conducted for various blockage scenarios with different lengths and positions. The results indicate that blockage accidents lead to an enlarged coolant temperature gradient at the core outlet. Lengthening the blockage results in an elevation of the peak temperature in the cladding. Under 2.06 % blockage at the center of the assembly, blockage in the middle of the heating segment poses the greatest threat to cladding integrity, with the maximum temperature reaching 1336.9K, an increase of 635.4K compared to normal operating conditions. Under 4.59 % blockage at the edge of the assembly, the maximum cladding temperature reaches 1381.8K, and the heat transfer rate of the inter-wrapper flow (IWF) adjacent to the blockage area is 24.2 % higher than under normal operation. Additionally, severe degradation in heat transfer downstream was not observed in several simulated blockage scenarios.

堵塞事故是铅铋冷却快堆（LFR）堆芯设计和安全分析中的关键情景。传统的快堆堆芯堵塞事故分析侧重于单个或三个组件的局部、精细尺度计算流体动力学（CFD）模拟，但对堵塞事故造成的整个堆芯尺度的影响分析不足。因此，本文采用西安交大-核动力院开发的三维热工水力分析代码 CorTAF-LBE 来分析堵塞事故对长征四号乙运载火箭整个堆芯的影响。在KALLA-THEADES和KALLA-IWF试验的基础上，验证了该代码在堵塞事故下计算热液参数的可靠性。以 MYRRHA-FASTEF 堆芯为对象，对不同长度和位置的各种堵塞情况进行了模拟和分析。结果表明，堵塞事故会导致堆芯出口处的冷却剂温度梯度增大。加长堵塞会导致包壳的峰值温度升高。在组件中心堵塞率为 2.06% 的情况下，加热段中部的堵塞对堆芯完整性的威胁最大，最高温度达到 1336.9K，比正常运行条件下增加了 635.4K。在组件边缘 4.59% 的阻塞情况下，包层最高温度达到 1381.8K，阻塞区域附近的包层间流 (IWF) 热传导率比正常运行条件下高 24.2%。此外，在几种模拟堵塞情况下都没有观察到下游传热的严重退化。

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引用次数: 0

Thermal modeling and analysis of multi-mover motors considering mover quantity and dynamic states 多电机热建模与分析（考虑电机数量和动态状态

IF 4.9 2区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Thermal Sciences

Pub Date : 2024-09-21 DOI: 10.1016/j.ijthermalsci.2024.109429

—Multi-mover motors are widely used in logistics transportation systems. However, the unique number of movers and variations in motion states complicate the distribution of loss and thermal characteristics, thereby increasing the difficulty of calculating temperature rise. In this paper, a winding loss calculation method that considers the multi-condition and dynamic characteristics of multi-mover motors is proposed. The convective heat transfer coefficient (CHTC) is calculated using computational fluid dynamics (CFD) and response surface methodology (RSM), with a detailed analysis of velocity distribution characteristics. The interactive effects of mover speed, acceleration, mover quantity, and the distance between adjacent movers on the CHTC are investigated. A simplified yet accurate thermal modeling is developed, reducing the required time for a single operating condition from 4 h to 0.5 h, with an error of only 4 %. Through both single variable and multivariable analyses, the thermal characteristics of multi-mover motors under different conditions are revealed. Finally, a prototype is created and tested under various operating conditions. The discrepancies between the experimental and calculated values are within 5 %, validating the accuracy of the proposed model and analysis.

-多电机广泛应用于物流运输系统。然而，独特的动子数量和运动状态的变化使损耗和热特性的分布变得复杂，从而增加了温升计算的难度。本文提出了一种绕组损耗计算方法，该方法考虑了多电机的多工况和动态特性。利用计算流体动力学（CFD）和响应面方法（RSM）计算了对流传热系数（CHTC），并详细分析了速度分布特征。研究了移动器速度、加速度、移动器数量和相邻移动器之间的距离对 CHTC 的交互影响。建立了一个简化但精确的热建模，将单一运行条件所需的时间从 4 小时减少到 0.5 小时，误差仅为 4%。通过单变量和多变量分析，揭示了多电机在不同条件下的热特性。最后，创建了一个原型，并在各种运行条件下进行了测试。实验值和计算值之间的误差在 5 % 以内，验证了所提出模型和分析的准确性。

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引用次数: 0

Nonlinear static behaviors of nonlocal nanobeams incorporating longitudinal linear temperature gradient 含有纵向线性温度梯度的非局部纳米梁的非线性静态行为

IF 4.9 2区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Thermal Sciences

Pub Date : 2024-09-21 DOI: 10.1016/j.ijthermalsci.2024.109421

The elastic parameters and the coefficient of thermal expansion (CTE) of nanomaterials change with temperature. If the elastic modulus, the CTE, and the longitudinal linear temperature gradient are coupled, the longitudinal symmetry of the mechanical properties of nanobeams is broken. However, researchers have not yet to examine how this symmetry breaking affects the mechanical properties of nanobeams. This paper provides a new analysis of the modified thermoelastic beam model established by the nonlocal stress gradient theory. The present analysis incorporates the coupling of the longitudinal linear temperature gradient, elastic modulus, thermal expansion, and scale effect. Afterward, we apply the Galerkin method to explore the buckling, post-buckling, and transverse bending of a $(10, 10)$ single-walled carbon nanotube (SWCNT). The results show that the linear temperature gradient induces the breaking of the nanobeam's longitudinal symmetry and then results in the coupling of the symmetrical and antisymmetrical weight functions of the deformations. While the linear temperature gradient marginally affects the symmetry of nanobeams, it significantly raises the buckling temperature and introduces the complexity of the post-buckling and transverse force bending. In addition, the integration of the linear longitudinal temperature gradient, elastic modulus, and nonlocal effect more significantly affects nanobeams' mechanical properties than individual factors.

纳米材料的弹性参数和热膨胀系数（CTE）会随温度变化。如果将弹性模量、热膨胀系数和纵向线性温度梯度耦合在一起，纳米梁力学性能的纵向对称性就会被打破。然而，研究人员尚未研究这种对称性的破坏如何影响纳米梁的力学性能。本文对非局部应力梯度理论建立的修正热弹性梁模型进行了新的分析。本分析结合了纵向线性温度梯度、弹性模量、热膨胀和尺度效应的耦合。随后，我们应用 Galerkin 方法探讨了 (10,10) 单壁碳纳米管 (SWCNT) 的屈曲、后屈曲和横向弯曲。结果表明，线性温度梯度导致纳米梁的纵向对称性被打破，然后导致变形的对称和非对称权重函数耦合。虽然线性温度梯度对纳米梁的对称性影响不大，但它会显著提高屈曲温度，并带来屈曲后和横向力弯曲的复杂性。此外，线性纵向温度梯度、弹性模量和非局部效应的综合影响比单个因素对纳米梁力学性能的影响更大。

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