A novel generalized thermoelasticity with higher-order time-derivatives and three-phase lags

• Published in: Multidiscipline modeling in materials and structures Vol. 16; no. 4; pp. 689 - 711
• Main Author: Abouelregal, Ahmed E
• Format: Journal Article
• Language: English
• Published: Bingley Emerald Publishing Limited 06.07.2020; Emerald Group Publishing Limited
• Subjects: Conduction; Conduction heating; Conduction model; Conductive heat transfer; Displacement; Energy dissipation; Fourier law; Heat; Heat flux; Mathematical analysis; Mathematical models; Phase lag; Propagation; Series expansion; Taylor series; Thermoelasticity; Higher order; Annular cylinder; Three-phase lags; Modified thermoelasticity model
• ISSN: 1573-6105; 1573-6113
• DOI: 10.1108/MMMS-07-2019-0138

Purpose In this work, a modified thermoelastic model of heat conduction, including higher order of time derivative, is constructed by extending the Roychoudhuri model (TPL) (Choudhuri, 2007). In this new model, Fourier’s law of heat conduction is replaced by using Taylor series expansions, including three different phase lags for the heat flux, the thermal displacement and the temperature gradient. The generalized thermoelasticity models of Lord–Shulman (Lord and Shulman, 1967), Green and Naghdi (1991), dual-phase lag (Tzou, 1996) and three-phase lag (TPL) (Choudhuri, 2007) are obtained as special cases. The paper aims to discuss these issues. Design/methodology/approach The aim of this work is to establish a new generalized mathematical model of thermoelasticity that includes TPL in the vector of heat flux, and in the thermal displacement and temperature gradients extending TPL model (Li et al., 2019e). In this model, Fourier law of heat conduction is replaced by using Taylor series expansions to a modification of the Fourier law with introducing three different phase lags for the heat flux vector, the temperature gradient, and the thermal displacement gradient and keeping terms up with suitable higher orders. Findings The established high-order three-phase-lag heat conduction model reduces to the previous models of thermoelasticity as special cases. Originality/value In this paper, a TPL thermoelastic model is developed by extending the Roychoudhuri (Sherief and Raslan, 2017) model (TPL) considering the Taylor series approximation of the equation of heat conduction. This model is an alternative construction to the TPL model. The new model includes high order of TPL in the vector of heat flux, and in the thermal displacement and temperature gradients.