Analysis of thermal wave scattering and temperature distribution in sub-surface, defects of gradient construction materials

Abstract 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 building...

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Main Authors: Xujiao Yang, Jinlei Gai, Xinliang Zheng, Yi Xie, Xiaomiao Yu, Ruizhi Gong, Zhongqing Meng, Shuo Zhai, Xunlong Zhao
Format: Article
Language:English
Published: Nature Portfolio 2025-07-01
Series:Scientific Reports
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Online Access:https://doi.org/10.1038/s41598-025-06196-2
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author Xujiao Yang
Jinlei Gai
Xinliang Zheng
Yi Xie
Xiaomiao Yu
Ruizhi Gong
Zhongqing Meng
Shuo Zhai
Xunlong Zhao
author_facet Xujiao Yang
Jinlei Gai
Xinliang Zheng
Yi Xie
Xiaomiao Yu
Ruizhi Gong
Zhongqing Meng
Shuo Zhai
Xunlong Zhao
author_sort Xujiao Yang
collection DOAJ
description Abstract 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.
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issn 2045-2322
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publishDate 2025-07-01
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spelling doaj-art-8010d9e3b3984d50ba621c39c78e0f912025-08-20T04:01:24ZengNature PortfolioScientific Reports2045-23222025-07-011511910.1038/s41598-025-06196-2Analysis of thermal wave scattering and temperature distribution in sub-surface, defects of gradient construction materialsXujiao Yang0Jinlei Gai1Xinliang Zheng2Yi Xie3Xiaomiao Yu4Ruizhi Gong5Zhongqing Meng6Shuo Zhai7Xunlong Zhao8School of Civil Engineering and Transportation, Beihua UniversityForestry College, Beihua UniversitySchool of Civil Engineering and Transportation, Beihua UniversitySchool of Civil Engineering and Transportation, Beihua UniversityForestry College, Beihua UniversitySchool of Civil Engineering and Transportation, Beihua UniversitySchool of Civil Engineering and Transportation, Beihua UniversitySchool of Civil Engineering and Transportation, Beihua UniversitySchool of Civil Engineering and Transportation, Beihua UniversityAbstract 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.https://doi.org/10.1038/s41598-025-06196-2Gradient Building materialsNon-Fourier lawThermal wave scatteringTemperature distributionSubsurface defects
spellingShingle Xujiao Yang
Jinlei Gai
Xinliang Zheng
Yi Xie
Xiaomiao Yu
Ruizhi Gong
Zhongqing Meng
Shuo Zhai
Xunlong Zhao
Analysis of thermal wave scattering and temperature distribution in sub-surface, defects of gradient construction materials
Scientific Reports
Gradient Building materials
Non-Fourier law
Thermal wave scattering
Temperature distribution
Subsurface defects
title Analysis of thermal wave scattering and temperature distribution in sub-surface, defects of gradient construction materials
title_full Analysis of thermal wave scattering and temperature distribution in sub-surface, defects of gradient construction materials
title_fullStr Analysis of thermal wave scattering and temperature distribution in sub-surface, defects of gradient construction materials
title_full_unstemmed Analysis of thermal wave scattering and temperature distribution in sub-surface, defects of gradient construction materials
title_short Analysis of thermal wave scattering and temperature distribution in sub-surface, defects of gradient construction materials
title_sort analysis of thermal wave scattering and temperature distribution in sub surface defects of gradient construction materials
topic Gradient Building materials
Non-Fourier law
Thermal wave scattering
Temperature distribution
Subsurface defects
url https://doi.org/10.1038/s41598-025-06196-2
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