Thermoelastic Response of an Infinite Hollow Cylinder under Fractional Order Dual-Phase-Lag Theory

Abstract

With the application of tiny components in scientific research and daily life, heat conduction and structural shape change in solids have attracted the idea of researchers. So further refinement of the theoretical model of thermo-viscoelastic hollow cylinders with fractional-order derivatives is the fundamental purpose of this study and development of fractional-order thermoelasticity theory with fractional-order strains to provide theoretical foundations for some thermodynamic practical applications (e.g., pipeline transport of gases or liquids) and selection of elastic and viscoelastic materials. In this paper, the dynamic response of the inner and outer surfaces of an infinitely sizeable hollow cylinder under the action of thermal shock is examined based on the fractional-order two-phase hysteresis theory and viscoelasticity theory. Convective boundary conditions are imposed on the inner and outer surfaces of the hollow cylinder and there is no traction on the inner and outer surfaces. The governing equations of the problem are established and solved by the Laplace transform method. In the numerical calculations, firstly, the effects of viscoelastic parameters on heat transfer as well as the stability of material structure are examined; secondly, the effects of fractional-order strain parameters on the model and their variations are examined; and finally, the effects brought about by the selection of hysteresis factors are examined. The results show that the introduction of the fractional order strain parameter has an important effect on the generalized thermoelastic model, and the viscoelastic parameter has a significant effect on the physical field of the hollow cylinder, especially the displacement and stress.