Fractional Order Two Temperature Generalized Thermoelasticity in a Symmetric Spherical Shell

Abstract

This paper deals with the determination of thermoelastic stresses, strain and conductive temperature in a spherically symmetric spherical shell in the context of the fractional order two temperature generalized thermoelasticity theory (2TT). The two temperature three-phase-lag thermoelastic model (2T3P) and two temperature Green Naghdi model III (2TGN-III) are combined into a unified formulation. There is no temperature at the outer boundary and thermal load is applied at the inner boundary. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace- transform domain which is then solved by the state-space approach. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The physical quantities have been computed numerically and presented graphically. The effect of the fractional order parameter on the solutions has been studied and the comparisons among different thermoelastic models are made.