Modified fractional thermoelasticity model with multi-relaxation times of higher order: application to spherical cavity exposed to a harmonic varying heat

Abstract

Several researchers have introduced different models of fractional order thermoelasticity theory depending on fractional calculus. In this research, a new modified model of generalized thermoelasticity with multi-relaxation times is derived based on fractional calculus and Taylor series expansion of time-fractional order. The models of Green and Lindsay two relaxation times [1] and coupled thermoelasticity [2] as well as fractional thermoelasticity with two relaxation times proposed by Hamza et al. [3] follow as limiting cases. The model is then adopted to study thermoelastic interactions in an infinite body with a spherical cavity whose boundary is subjected to harmonic varying heat and traction free. The basic equations governing the problem were solved using Laplace transformations. To find the analytical formulas of the physical quantities and to find inverse Laplace transforms, a numerical method was used. Detailed analysis of the effects of the fractional order parameter and the angular frequency of thermal vibration on the absolute temperature, stresses and displacement are studied.