On energy, uniqueness theorems and variational principle for generalized thermoelasticity with memory-dependent derivative

•The energy theorem for the generalized thermoelasticity under three-phase-lag (TPL) model with memory-dependent derivative (MDD) is stated and proved.•The uniqueness theorem for the present theory is proved from the energy theorem.•The variational principle for the present theory is constructed.•Th...

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Bibliographic Details
Published in:International journal of heat and mass transfer 2020-03, Vol.149, p.119112, Article 119112
Main Authors: Sarkar, Indranil, Mukhopadhyay, Basudeb
Format: Article
Language:English
Subjects:
Computer simulation
Conduction heating
Conduction model
Conductive heat transfer
Energy
Generalized thermoelasticity
Kernel functions
Laplace transforms
Mathematical models
Memory-dependent derivative
Phase lag
Response time
Thermal shock
Thermoelasticity
Three-phase-lag
Time dependence
Time lag
Uniqueness
Uniqueness theorems
Variational principle
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Summary:•The energy theorem for the generalized thermoelasticity under three-phase-lag (TPL) model with memory-dependent derivative (MDD) is stated and proved.•The uniqueness theorem for the present theory is proved from the energy theorem.•The variational principle for the present theory is constructed.•The dissipation function D extended to three-phase-lag (TPL) model is introduced.•The other renowned thermoelasticity theories, such as Lord-Shulman (L-S) model, dual-phase-lag (DPL) model with MDD and the dynamic classical theory are derived from the present model. The research article theoretically deals with the three-phase-lag (TPL) heat conduction model of generalized thermoelasticity, reformulated in terms of the memory-dependent derivative (MDD). The energy theorem and the variational principle of this proposed model are established for an isotropic, homogeneous, thermoelastic continuum. The uniqueness theorem is derived from the energy theorem, and a few special cases are also obtained from the present model. For numerical simulation of the present model, a one-dimensional thermoelastic problem in a semi-infinite medium subjected to a time-dependent thermal shock on its bounding plane is considered. The Laplace transform together with its numerical inversion is adopted to obtain the solutions in the physical domain. The influence of the kernel function and time delay on the variation of the non-dimensional thermophysical quantities are studied graphically and finally some remarkable points are mentioned as conclusions.
ISSN:0017-9310
1879-2189
DOI:10.1016/j.ijheatmasstransfer.2019.119112