Closed-Form Solution for a Circular Nanohole with Surface Effects Under Uniform Heat Flux

Abstract

This paper investigates the steady-state thermoelastic problem of a circular nanohole embedded in an infinitely large elastic plane subjected to a uniform far-field heat flux. A lowly conductive surface model is used to account for the effects of surface phonon scattering, while the complete Gurtin–Murdoch model is utilized to characterize the effects of surface tension and surface elasticity. The closed-form solution to the temperature and stress field surrounding the hole is derived in the context of complex variable methods. Several numerical examples are presented to analyze the influence of surface effects on thermal stress fields. It is shown that surface effects induce notable increases in normal and shear stresses around the hole. Specifically, all three stress components (hoop, normal, and shear) in the vicinity of the hole exhibit substantial augmentation with increasing surface tension and surface modulus. In particular, it is found that the presence of surface effects amplifies the variation in stress gradients and intensifies stress concentration around the hole.