Generalized solution of the thermoelastic problem for the axisymmetric structure with temperature-dependent properties

The purpose of this paper is to seek the generalized solutions of the thermo-elastic problem with variable material properties. The governing equations with temperature-dependent properties are proposed firstly by means of general C-T theory, where the dual-phase-lag heat conduction equation (DPL equation) is introduced to describe the micro-scale effect in time and space, induced in the rapid transient heat conduction. An analytical method, based on the partial expansion techniques along with a linearization approach, is then used to solve these nonlinear equations analytically. The thermo-elastic response of the axisymmetric structure with variable material properties and its boundary subjected to a sudden thermal shock, which is a typical problem commonly encountered in some extraordinary heat process, is solved by this method. The short-time solutions with variable material properties, described the heat transport and associated thermo-elastic response in micro-scale, are obtained. Utilizing these analytical solutions, the propagation of thermo-elastic wave and thermal wave, as long as the distributions of each physical field, is illustrated to qualitatively evaluate the effect of variable material properties on the heat transport and associated thermo-elastic behavior in micro-scale.