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

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...

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Vydáno v:Multidiscipline modeling in materials and structures Ročník 16; číslo 4; s. 689 - 711
Hlavní autor: Abouelregal, Ahmed E
Médium: Journal Article
Jazyk:angličtina
Vydáno: Bingley Emerald Publishing Limited 06.07.2020
Emerald Group Publishing Limited
Témata:
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
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Shrnutí: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.
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ISSN:1573-6105
1573-6113
DOI:10.1108/MMMS-07-2019-0138