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

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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Numerical analysis of a dual‐phase‐lag model involving two temperatures

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.6082 ◽

2019 ◽

Vol 43 (5) ◽

pp. 2759-2771

Author(s):

Noelia Bazarra ◽

José R. Fernández ◽

Antonio Magaña ◽

Ramón Quintanilla

Keyword(s):

Numerical Analysis ◽

Phase Lag ◽

Dual Phase ◽

Lag Model ◽

Two Temperatures

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Three-Dimensional Thermoelastic Problem Under Two-Temperature Theory

International Journal of Computational Methods ◽

10.1142/s021987621750030x ◽

2017 ◽

Vol 14 (03) ◽

pp. 1750030 ◽

Cited By ~ 21

Author(s):

Abhik Sur ◽

M. Kanoria

Keyword(s):

Thermal Loading ◽

Normal Mode Analysis ◽

Three Dimensional ◽

Thermodynamic Temperature ◽

Mode Analysis ◽

Phase Lag ◽

Field Equations ◽

Conductive Temperature ◽

Lag Model ◽

Two Temperature

The present paper deals with the problem of thermoelastic interactions in a homogeneous, isotropic three-dimensional medium whose surface suffers a time dependent thermal loading. The problem is treated on the basis of three-phase-lag model and dual-phase-lag model with two temperatures. The medium is assumed to be unstressed initially and has uniform temperature. Normal mode analysis technique is employed onto the non-dimensional field equations to derive the exact expressions for displacement component, conductive temperature, thermodynamic temperature, stress and strain. The problem is illustrated by computing the numerical values of the field variables for a copper material. Finally, all the physical fields are represented graphically to analyze the difference between the two models. The effect of the two temperature parameter is also discussed.

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Generalized Two Temperatures Thermoelasticity of Micropolar Porous Circular Plate with Three Phase Lag Model

Journal of Mechanics ◽

10.1017/jmech.2017.69 ◽

2017 ◽

Vol 34 (6) ◽

pp. 779-789 ◽

Cited By ~ 2

Author(s):

R. Kumar ◽

A. Miglani ◽

R. Rani

Keyword(s):

Circular Plate ◽

Volume Fraction ◽

Generalized Thermoelasticity ◽

Thermal Source ◽

Phase Lag ◽

Three Phase ◽

Lag Model ◽

Phase Lags ◽

Two Temperatures ◽

Inversion Techniques

AbstractThe present study is to focus on the two dimensional problem of micropolar porous circular plate with three phase lag model within the context of two temperatures generalized thermoelasticity theory. The problem is solved by applying Laplace and Hankel transforms after using potential functions. The expressions of displacements, microrotation, volume fraction field, temperature distribution and stresses are obtained in the transformed domain. To show the utility of the approach, normal force and thermal source are taken. The numerical inversion techniques of transforms have been carried out in order to evaluate the resulting quantities in the physical domain. Finally, the resulting quantities are depicted graphically to show the effect of porosity, two temperatures and phase lags.

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