Dynamic model of generalized thermoelasticity based on thermal mass theory

Abstract

A lagging response in time exists between the propagation of heat flux and the establishment of temperature gradient and it is affected by the space effect during the heat conduction with the micro-scale property. Based on the general heat conduction law of thermal mass, the dynamic model of generalized thermoelasticity is established by Clausius inequality and Helmholtz free energy, where the inertia effect on the time and space of heat flux and temperature is involved. The guiding equations are derived and given for the isotropic and homogeneous materials. By comparison with the existing models of generalized thermoelasticity, the guiding equations can reduce to the L-S, G-L and G-N models when the heat flux is not very high, so that the inertia effect on space of heat flux and temperature can be ignored. For micro-scale heat conduction, the heat flux may be very high and the inertial force due to the spatial velocity variation cannot be ignored, the non-Fourier phenomenon will take place even under steady state condition. In such cases, the thermal conductivity is affected by the inertia effect of the space, which can be explained by the model established in the paper. Meanwhile, the physically impossible phenomenon that thermal conductivity changes with structure size induced by existing generalized model can also be eliminated.