Transient heat conduction in the cracked medium by Guyer–Krumhansl model

• Published in: International journal of fracture Vol. 246; no. 2-3; pp. 145 - 160
• Main Authors: Yang, Wenzhi, Gao, Ruchao, Liu, Zhijun, Cui, Yi, Pourasghar, Amin, Chen, Zengtao
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2024; Springer Nature B.V
• Subjects: Automotive Engineering; Boundary conditions; Bounding surface; Characterization and Evaluation of Materials; Civil Engineering; Classical Mechanics; Conduction heating; Conductive heat transfer; Cyclic loads; Engineering; Fourier transforms; Laplace transforms; Mechanical Engineering; Partial differential equations; Singular integral equations; Transient heat conduction; Fourier transform; Laplace transform; Guyer–Krumhansl model; Crack
• ISSN: 0376-9429; 1573-2673
• DOI: 10.1007/s10704-023-00727-6

In this article, the nonclassical transient heat propagation process in a cracked strip is investigated by Guyer–Krumhansl (G–K) model, which incorporates both the time lagging behavior and the spatially nonlocal effect. The impulsive thermal loading as well as cyclic loading exerted on the top bounding surface are examined to explore the non-Fourier thermal characteristics. By means of the Laplace transform and Fourier transform, the governing partial differential equations subjected to mixed boundary conditions are converted to a group of singular integral equations. With the aid of numerical Laplace inversion, the transient temperatures are calculated to make comparisons of thermal responses determined by Fourier’s law, Cattaneo–Vernotte (C–V) equation, and G–K model. The numerical results display the specific thermal behaviors of G–K model in the cracked medium and demonstrate the G–K model’s capabilities in eliminating the unrealistic phenomena accompanied by C–V equation. Our research would contribute to achieving a better understanding of the transient heat conduction in small-sized systems or composites at the macroscopic scale.