A control volume finite element method for the thermoelastic problem in functional graded material with one relaxation time

Liu, Qi; Qian, Peng; Ming, Pingjian

doi:10.1177/0954406220979022

Cited by 7 publications

(3 citation statements)

References 32 publications

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“…( 4 and 5 ) to known physical quantities, it is sufficient to compare these two equations to the well-known standard forms of the evolution equations for the heat flux (C.f. 10 , 21 ): where , are the thermal relaxation times for the x - and y -directions respectively, and , are the thermal conductivities in these two directions. Direct comparison of these last two equations with ( 4 ) and ( 5 ) reveals that The above governing equations need to be cast in a convenient form for later work.…”

Section: The Linear System Of Equationsmentioning

confidence: 99%

On a two-dimensional model of generalized thermoelasticity with application

Ahmed

El-Dhaba

Abou-Dina

et al. 2022

Sci Rep

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A 2D first order linear system of partial differential equations of plane strain thermoelasticity within the frame of extended thermodynamics is presented and analyzed. The system is composed of the equations of classical thermoelasticity in which displacements are replaced with velocities, complemented with Cattaneo evolution equation for heat flux. For a particular choice of the characteristic quantities and for positive thermal conductivity, it is shown that this system may be cast in a form that is symmetric t-hyperbolic without further recurrence to entropy principle. While hyperbolicity means a finite speed of propagation of heat waves, it is known that symmetric hyperbolic systems have the desirable property of well-posedness of Cauchy problems. A study of the characteristics of this system is carried out, and an energy integral is derived, that can be used to prove uniqueness of solution under some boundary conditions. A numerical application for a finite slab is considered and the numerical results are plotted and discussed. In particular, the wave propagation nature of the solution is put in evidence.

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Section: The Linear System Of Equationsmentioning

confidence: 99%

On a two-dimensional model of generalized thermoelasticity with application

Ahmed

El-Dhaba

Abou-Dina

et al. 2022

Sci Rep

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“…To address this shortcoming that contradicts the physical phenomena, different non-Fourier theories such as the Cattaneo-Vernotte heat wave model [42,43], dual-phase lag (DPL) theory [44] and three-phase lag models suggested by Choudhuri [45] have emerged. Among the most well-known generalized thermoelastic theories, the Lord and Shulman (LS) model [46], the Green and Lindsey model (G-L) [47], in addition to the Green and Naghdi (GN) [48,49] theories becomes more popular in the field.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic characteristics of moving viscoelastic nanobeams based on the nonlocal couple stress theory and dual-phase lag model

Abouelregal¹,

Sedighi²

2022

Phys. Scr.

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Thermal behavior of a moving viscoelastic nanobeam under the influence of periodic thermal load is considered in the ‎framework of Kelvin-Voigt viscoelastic model with fractional operators. The equation of motion for axially moving ‎nanobeam is modeled by employing the Eringen's nonlocal elastic theory in conjunction with the couple stress ‎hypothesis and the conventional Euler-Bernoulli beam model. The thermoelastic features is then established by ‎employing the generalized dual phase-lag heat conduction model. After utilizing the Laplace transform, the ‎thermomechanical equations are coupled and solved. The current results are validated by presenting numerical ‎examples and comparing with previous solutions obtained by traditional theories in the literature. According to the ‎provided numerical simulations, the deflection of the axially moving nanobeam as well as its temperature change ‎reduce with the axial velocity and the influences of small scale and nonlocal parameters are also revealed and ‎discussed.‎

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“…Qi Liu et al. , 3 indeed, in their paper have developed a new direct vertex-centred finite volume method for the thermoelastic problem in functional graded material based on Lord-Shulman theory. Some benchmark examples are used to demonstrate the capability of the present method for hyperbolic heat conduction and thermoelastic coupled problems.…”

mentioning

confidence: 99%