Nonlocal dual-phase-lag heat conduction and the associated nonlocal thermal-viscoelastic analysis

Abstract

In this paper, the extension of the nonlocal dual-phase-lag (DPL) theory is formulated to account for the heat conduction at nanoscale. Both the temporally and spatially nonlocal effects are considered in heat conduction, which are verified experimentally by the size-dependent thermal conductivity of silicon nanofilms and the transient temperature variation during the femtosecond laser heating of gold films. A generalized uncoupled nonlocal thermoviscoelasticity is hence proposed, which is applied to a one-dimensional analysis of a finite plate under sudden thermal shock. Non-dimensional numerical analyses are performed to illustrate the effects of both nonlocal heat conduction and nonlocal elasticity on thermal propagations and thermoviscoelastic responses.