Series Solutions for Non-Circular Nanoholes With Surface Effects Under Uniform Heat Flux

ZHANG Yu; ZHAO Jieyan; YANG Haibing

doi:10.21656/1000-0887.450308

Volume 47 Issue 1

Jan. 2026

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ZHANG Yu, ZHAO Jieyan, YANG Haibing. Series Solutions for Non-Circular Nanoholes With Surface Effects Under Uniform Heat Flux[J]. Applied Mathematics and Mechanics, 2026, 47(1): 79-89. doi: 10.21656/1000-0887.450308

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Series Solutions for Non-Circular Nanoholes With Surface Effects Under Uniform Heat Flux

doi: 10.21656/1000-0887.450308

1. School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, P.R.China;
2. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China;
3. College of Mechanics and Engineering Science, Hohai University, Nanjing 211100, P.R.China

Funds:

The National Science Foundation of China(11902116)

Received Date: 2024-11-18
Rev Recd Date: 2025-02-26

Available Online: 2026-01-21

Publish Date: 2026-01-01

Abstract

Abstract

The 2D plane problem of non-circular nanoholes under uniform far-field heat flow was investigated. To examine the effects of surface phonon scattering on heat conduction at the microscale, a weakly thermal conductivity model considering temperature jump was introduced, and the complete Gurtin-Murdoch lower-order surface energy model was employed to characterize the surface effects. Based on the theory of complex functions and series expansion, the series solutions for the temperature field and the thermal stress field were obtained corresponding to different hole shapes defined with the conformal mapping techniques. Several numerical examples of non-circular nanoholes were presented to analyze the surface effects on thermal stress fields. The results indicate that, surface effects significantly increase the thermal stresses around the nanohole, and the combined action of surface elasticity and surface tension plays a key role in determining the magnitude of the thermal stress.
- uniform heat flux,
- Gurtin-Murdoch model,
- weakly thermal conductivity model,
- surface effect

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References(29)

References

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