article · International Journal of Applied Mechanics
Theoretical formulations governing heat propagation and elastic interactions under light and thermal excitation are examined through multi-time-derivative phase-lag models. A unified framework for coupled photo-thermoelasticity is established to capture three distinct delay phase-lag times: the temperature gradient, the heat flux, and the thermal displacement gradient. This unified approach consolidates various existing heat conduction formulations found across scientific literature. It incorporates both straightforward and refined versions of Tzou multi-time-derivative single-, dual-, and triple-phase-lag models, alongside established Lord–Shulman, Green–Lindsay, and classical thermoelastic theories. Furthermore, simple and modified formulations are derived for Green–Naghdi type II and type III generalized thermoelasticity models, accounting for conditions both with and without energy dissipation. The work brings disparate mathematical descriptions of photo-thermal interactions into a single comprehensive analytical structure.
Understanding how materials respond simultaneously to light and thermal changes requires accurate mathematical descriptions. By bringing multiple competing phase-lag models into a single unified framework, this theoretical work clarifies how different heat transport assumptions relate to one another. It helps researchers model complex heat conduction behaviours where delay times and energy dissipation play critical roles in coupled thermal and elastic systems.
The abstract does not indicate an application pathway or commercialisation potential for this theoretical work.
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Different subjective developments of the multi-time-derivative (single/dual/triple)-phase-lag heat formulae have been examined in this paper. A unified theory of coupled photo-thermoelasticity is defined to investigate both delay phase-lag times of the temperature gradient and the heat flux as well as the third delay phase-lag time of the thermal displacement gradient. Some unique issues that contain a lot of formulae have been considered to manage all the thoughts about models in the literature. The straightforward and refined Tzou’s multi-time-derivative (single/dual/triple)-phase-lag, Lord–Shulman, Green–Lindsay, and classical theories are all investigated. Moreover, Green–Naghdi of type II, as well as type III models of generalized thermoelasticity with and without energy dissipation, have been attained in simple and modified formulations.
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DOI: 10.1142/s1758825122500053
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