应用数学和力学2026，Vol.47Issue(1)：79-89,11.DOI:10.21656/1000-0887.450308
均匀热流作用下考虑表面效应的非圆形纳米孔的级数解
Series Solutions for Non-Circular Nanoholes With Surface Effects Under Uniform Heat Flux
摘要
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-or-der 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 numer-ical 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.关键词
均匀热流/Gurtin-Murdoch模型/弱热传导模型/表面效应Key words
uniform heat flux/Gurtin-Murdoch model/weakly thermal conductivity model/surface effect分类
数理科学引用本文复制引用
张雨,赵婕燕,杨海兵..均匀热流作用下考虑表面效应的非圆形纳米孔的级数解[J].应用数学和力学,2026,47(1):79-89,11.基金项目
国家自然科学基金(11902116) （11902116）
广东省自然科学基金(2022A1515011773) （2022A1515011773）
