Abouelregal Ahmed E, Marin Marin, Foul Abdelaziz, Askar S S
Department of Mathematics, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt.
Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036, Brasov, Romania.
Sci Rep. 2024 Apr 20;14(1):9122. doi: 10.1038/s41598-024-58866-2.
Accurately characterizing the thermomechanical parameters of nanoscale systems is essential for understanding their performance and building innovative nanoscale technologies due to their distinct behaviours. Fractional thermal transport models are commonly utilized to correctly depict the heat transfer that occurs in these nanoscale systems. The current study presents a novel mathematical thermoelastic model that incorporates a new fractional differential constitutive equation for heat conduction. This heat equation is useful for understanding the effects of thermal memory. An application of a fractional-time Atangana-Baleanu (AB) derivative with a local and non-singular kernel was utilized in the process of developing the mathematical model that was suggested. To deal with effects that depend on size, nonlocal constitutive relations are introduced. Furthermore, in order to take into consideration, the viscoelastic behaviour of the material at the nanoscale, the fractional Kelvin-Voigt model is utilized. The proposed model is highly effective in properly depicting the unusual thermal conductivity phenomena often found in nanoscale devices. The study also considered the mechanical deformation, temperature variations, and viscoelastic characteristics of the functionally graded (FG) nanostructured beams. The consideration was made that the material characteristics exhibit heterogeneity and continuous variation across the thickness of the beam as the nanobeam transitions from a ceramic composition in the lower region to a metallic composition in the upper region. The complicated thermomechanical features of simply supported viscoelastic nanobeams that were exposed to harmonic heat flow were determined by the application of the model that was constructed. Heterogeneity, nonlocality, and fractional operators are some of the important variables that contribute to its success, and this article provides a full study and illustration of the significance of these characteristics. The results that were obtained have the potential to play a significant role in pushing forward the design and development of tools, materials, and nanostructures that have viscoelastic mechanical characteristics and graded functions.
由于纳米级系统具有独特的行为，准确表征其热机械参数对于理解其性能和构建创新的纳米级技术至关重要。分数热传输模型通常用于正确描述这些纳米级系统中发生的热传递。当前的研究提出了一种新颖的数学热弹性模型，该模型纳入了一个用于热传导的新的分数阶微分本构方程。这个热方程有助于理解热记忆效应。在开发所提出的数学模型的过程中，使用了具有局部和非奇异核的分数阶时间阿坦加纳 - 巴莱努（AB）导数。为了处理依赖于尺寸的效应，引入了非局部本构关系。此外，为了考虑纳米级材料的粘弹性行为，采用了分数阶开尔文 - 沃伊特模型。所提出的模型在正确描述纳米级器件中经常发现的异常热导率现象方面非常有效。该研究还考虑了功能梯度（FG）纳米结构梁的机械变形、温度变化和粘弹性特性。考虑到当纳米梁从下部区域的陶瓷成分过渡到上部区域的金属成分时，材料特性在梁的厚度上表现出非均匀性和连续变化。通过应用所构建的模型，确定了承受谐波热流的简支粘弹性纳米梁的复杂热机械特性。非均匀性、非局部性和分数阶算子是促成其成功的一些重要变量，本文对这些特性的重要性进行了全面研究和说明。所获得的结果有可能在推动具有粘弹性机械特性和梯度功能的工具、材料和纳米结构的设计与开发方面发挥重要作用。
