Fractional order triple-phase-lag thermoelasticity in the context of two-temperature theory

Abstract

A new mathematical model is designed through reconstructing the triple-phase-lag model proposed by Roy Choudhuri, where the integer ordered derivatives concerning the time variable are replaced by the Caputo time-fractional derivative of order δ∈(0,1]. Moreover, the three-phase-lag heat conduction equation is derived in the context of two-temperature theories to examine the joint effect of thermodynamical and conductive temperatures. The proposed formulation is applied to the finite dimensional solid slab, whose boundaries are subject to the thermal loading and free from mechanical forces. The integral transform technique is applied to converting the original boundary value problem into an eigenvalue problem. Analytical solutions of the unknown thermal parameters are obtained in the Laplace domain. Time-domain solutions of the analytical results are achieved numerically through the Gaver–Stehfest algorithm. The results are examined graphically for the fixed phase-lag variations admitting various existing thermoelasticity theories.

Keywords

• Generalized coupled thermoelasticity
• Triple-phase-lag
• Two-temperature theory
• The finite speed
• Integral transform