Analysis of thermoelastic dissipation in circular micro-plate resonators using the generalized thermoelasticity theory of dual-phase-lagging model

AbstractThis work aims to study the influence of the rotation on a thermoelastic solid sphere in the context of the hyperbolic two-temperature generalized thermoelasticity theory based on the mechanical damage consideration. Therefore, a mathematical model of thermoelastic, homogenous, and isotropic solid sphere with a rotation based on the mechanical damage definition has been constructed. The governing equations have been written in the context of hyperbolic two-temperature generalized thermoelasticity theory. The bounding surface of the sphere is thermally shocked and without volumetric deformation. The singularities of the studied functions at the center of the sphere have been deleted using L’Hopital’s rule. The numerical results have been represented graphically with various mechanical damage values, two-temperature parameters, and rotation parameter values. The two-temperature parameter has significant effects on all the studied functions. Damage and rotation have a major impact on deformation, displacement, stress, and stress–strain energy, while their effects on conductive and dynamical temperature rise are minimal. The thermal and mechanical waves propagate with finite speeds on the thermoelastic body in the hyperbolic two-temperature theory and the one-temperature theory (Lord-Shulman model).

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Thermoelastic Interactions in a Slim Strip Due to a Moving Heat Source Under Dual-Phase-Lag Heat Transfer

Journal of Heat Transfer ◽

10.1115/1.4044920 ◽

2019 ◽

Vol 141 (12) ◽

Cited By ~ 4

Author(s):

Nantu Sarkar ◽

Sudip Mondal

Keyword(s):

Heat Transfer ◽

Heat Source ◽

Laplace Transform ◽

Time Domain ◽

Generalized Thermoelasticity ◽

Inverse Laplace Transform ◽

Phase Lag ◽

Dual Phase ◽

Moving Heat Source ◽

Transient Phenomena

Abstract Following the link of work of He and Cao (2009, Math. Comput. Modell., 49(7–8), 1719–1720), we employ the theory of generalized thermoelasticity with dual-phase-lag (DPL) to study the transient phenomena in a thin slim strip due to a moving heat source. Both ends of the strip are assumed to be fixed and thermally insulated. Using Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the strip are carried out and presented graphically. The effect of moving heat source speed on temperature, stress, and displacement is studied. The temperature, displacement, and stress in the strip are found to be decreasing at large source speed.

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Thermal shock problem of a three-layered functionally graded zirconia/titanium alloy strip based on a unified generalized thermoelasticity theory

Journal of Thermal Stresses ◽

10.1080/01495739.2016.1237860 ◽

2016 ◽

Vol 40 (5) ◽

pp. 583-602 ◽

Cited By ~ 2

Author(s):

Antonios M. Nikolarakis ◽

Efstathios E. Theotokoglou

Keyword(s):

Titanium Alloy ◽

Thermal Shock ◽

Generalized Thermoelasticity ◽

Functionally Graded ◽

Alloy Strip ◽

Thermoelasticity Theory ◽

Thermal Shock Problem

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Effect of rotation on micropolar generalized thermoelasticity with two temperatures using a dual-phase lag model

Canadian Journal of Physics ◽

10.1139/cjp-2013-0398 ◽

2014 ◽

Vol 92 (2) ◽

pp. 149-158 ◽

Cited By ~ 28

Author(s):

Mohamed I.A. Othman ◽

W.M. Hasona ◽

Elsayed M. Abd-Elaziz

Keyword(s):

Numerical Solutions ◽

Generalized Thermoelasticity ◽

Thermodynamic Temperature ◽

Phase Lag ◽

Dual Phase ◽

Conductive Temperature ◽

Mode Method ◽

Lag Model ◽

Two Temperatures ◽

Physical Quantities

In the present paper, we introduce the dual-phase lag theory to study the effect of the rotation on a two-dimensional problem of micropolar thermoelastic isotropic medium with two temperatures. A normal mode method is proposed to analyze the problem and obtain numerical solutions for the displacement, the conductive temperature, the thermodynamic temperature, the microrotation, and the stresses. The results of the physical quantities have been obtained numerically and illustrated graphically. The results show the effect of phase lag of the heat flux τq, a phase lag of temperature gradient τθ and two-temperature parameter on all the physical quantities.

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Dual-phase-lag thermoelastic problem in finite cylindrical domain with relaxation time

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-03-2018-0041 ◽

2018 ◽

Vol 14 (5) ◽

pp. 837-856 ◽

Cited By ~ 2

Author(s):

Gaurav Mittal ◽

Vinayak Kulkarni

Keyword(s):

Heat Flux ◽

Relaxation Time ◽

Heat Conduction ◽

Generalized Thermoelasticity ◽

Phase Lag ◽

Dual Phase ◽

Cylindrical Domain ◽

Content Type ◽

Thick Circular Plate ◽

Lag Model

Purpose The purpose of this paper is to frame a dual-phase-lag model using the fractional theory of thermoelasticity with relaxation time. The generalized Fourier law of heat conduction based upon Tzou model that includes temperature gradient, the thermal displacement and two different translations of heat flux vector and temperature gradient has been used to formulate the heat conduction model. The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. Design/methodology/approach The work presented in this manuscript proposes a dual-phase-lag mathematical model of a thick circular plate in a finite cylindrical domain subjected to axis-symmetric heat flux. The model has been designed in the context of fractional thermoelasticity by considering two successive terms in Taylor’s series expansion of fractional Fourier law of heat conduction in the two different translations of heat flux vector and temperature gradient. The analytical results have been obtained in Laplace transform domain by transforming the original problem into eigenvalue problem using Hankel and Laplace transforms. The numerical inversions of Laplace transforms have been achieved using the Gaver−Stehfast algorithm, and convergence criterion has been discussed. For illustrative purpose, the dual-phase-lag model proposed in this manuscript has been applied to a periodically varying heat source. The numerical results have been depicted graphically and compared with classical, fractional and generalized thermoelasticity for various fractional orders under consideration. Findings The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. This model has been applied to study the thermal effects in a thick circular plate subjected to a periodically varying heat source. Practical implications A dual-phase-lag model can effectively be incorporated to study the transient heat conduction problems for an exponentially decaying pulse boundary heat flux and/or for a short-pulse boundary heat flux in long solid tubes and cylinders. This model is also applicable to study the various effects of the thermal lag ratio and the shift time. These dual-phase-lag models are also practically applicable in the problems of modeling of nanoscale heat transport problems of semiconductor devices and accordingly semiconductors can be classified as per their ability of heat conduction. Originality/value To the authors’ knowledge, no one has discussed fractional thermoelastic dual-phase-lag problem associated with relaxation time in a finite cylindrical domain for a thick circular plate subjected to an axis-symmetric heat source. This is the latest and novel contribution to the field of thermal mechanics.

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Thermoelastic Coupling Response of an Unbounded Solid with a Cylindrical Cavity Due to a Moving Heat Source

Mathematics ◽

10.3390/math10010009 ◽

2021 ◽

Vol 10 (1) ◽

pp. 9

Author(s):

Ashraf M. Zenkour ◽

Daoud S. Mashat ◽

Ashraf M. Allehaibi

Keyword(s):

Heat Source ◽

Angular Frequency ◽

Phase Lag ◽

Dual Phase ◽

Moving Heat Source ◽

Thermoelastic Coupling ◽

Thermoelasticity Theory ◽

Current Article ◽

Source Phase ◽

Coupled Solution

The current article introduces the thermoelastic coupled response of an unbounded solid with a cylindrical hole under a traveling heat source and harmonically altering heat. A refined dual-phase-lag thermoelasticity theory is used for this purpose. A generalized thermoelastic coupled solution is developed by using Laplace’s transforms technique. Field quantities are graphically displayed and discussed to illustrate the effects of heat source, phase-lag parameters, and the angular frequency of thermal vibration on the field quantities. Some comparisons are made with and without the inclusion of a moving heat source. The outcomes described here using the refined dual-phase-lag thermoelasticity theory are the most accurate and are provided as benchmarks for other researchers.

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