Yang Xujiao, Gai Jinlei, Zheng Xinliang, Xie Yi, Yu Xiaomiao, Gong Ruizhi, Meng Zhongqing, Zhai Shuo, Zhao Xunlong
School of Civil Engineering and Transportation, Beihua University, Jilin, 132013, China.
Forestry College, Beihua University, Jilin, 132013, China.
Sci Rep. 2025 Jul 1;15(1):22381. doi: 10.1038/s41598-025-06196-2.
Traditional building materials have significant limitations in function and performance: insulation materials are easy to peel and age, waterproof materials have a short life, and fireproof materials have degraded flame retardancy. These shortcomings cannot meet the needs of modern buildings for energy efficiency, safety and durability. Therefore, it is imperative to study gradient building materials that integrate function and structure. In this study, based on the non-Fourier heat conduction law, a heat wave propagation model is established to derive a complete analytical solution for the heat wave scattering field of a subsurface circular defect in an exponentially gradient material. The effects of thermal diffusion length (µ/a), wave number (ka), non-uniformity coefficient (σ₁a), and defect embedding ratio (b/a) on the surface temperature distribution are systematically analysed by the wavefunction expansion method and the virtual mirror technique combined with the independently developed numerical procedure. The results show that: the peak temperature amplitude occurs in the region directly in front of the scatterer; the thermal fluctuation effect is significantly enhanced with the increase of the thermal diffusion length or the decrease of the defect size; the temperature fluctuation response is strengthened by the high modulation frequency (large ka) and the shallow burial depth of the defects; and the increase of the non-uniformity parameter of the material σ₁a results in the increase of the surface temperature. The study confirms the limitations of traditional Fourier's law in short-pulse heat conduction scenarios, and the results provide theoretical basis and data support for the design of functional gradient materials and nondestructive inspection by infrared thermography.
保温材料易剥落和老化，防水材料寿命短，防火材料阻燃性下降。这些缺点无法满足现代建筑对能源效率、安全性和耐久性的需求。因此，研究功能与结构一体化的梯度建筑材料势在必行。在本研究中，基于非傅里叶热传导定律，建立了热波传播模型，以推导指数梯度材料中地下圆形缺陷热波散射场的完整解析解。通过波函数展开法和虚拟镜像技术结合自主开发的数值程序，系统分析了热扩散长度（µ/a）、波数（ka）、非均匀系数（σ₁a）和缺陷埋深比（b/a）对表面温度分布的影响。结果表明：峰值温度幅值出现在散射体正前方区域；随着热扩散长度的增加或缺陷尺寸的减小，热波动效应显著增强；高调制频率（大ka）和缺陷浅埋深会增强温度波动响应；材料非均匀参数σ₁a的增加导致表面温度升高。该研究证实了传统傅里叶定律在短脉冲热传导场景中的局限性，研究结果为功能梯度材料的设计和红外热成像无损检测提供了理论依据和数据支持。
