Effects of thermal and diffusion phase-lags in a plate with axisymmetric heat supply

2016 ◽  
Vol 12 (2) ◽  
pp. 275-290 ◽  
Author(s):  
Rajneesh Kumar ◽  
Nidhi Sharma ◽  
Parveen Lata
Keyword(s):  
Heat Supply ◽  
Mass Concentration ◽  
Chemical Potential ◽  
Phase Lag ◽  
Dual Phase ◽  
Content Type ◽  
Thermal Phase ◽  
Diffusion Phase ◽  
Phase Lags ◽  
And Diffusion

Purpose – The purpose of this paper is to depict the effect of time and thermal and diffusion phase-lags due to axisymmetric heat supply in a ring. The problem is discussed within the context of dual-phase-lag heat transfer and dual-phase-lag diffusion models. The upper and lower surfaces of the ring are traction free and subjected to an axisymmetric heat supply. Design/methodology/approach – The solution is found by using Laplace and Hankel transform technique and a direct approach without the use of potential functions. The analytical expressions of displacements, stresses and chemical potential, temperature and mass concentration are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect of time and diffusion and thermal phase-lags are shown on the various components. Some particular cases of result are also deduced from the present investigation. Findings – It is observed that change in time changes the behaviour of deformations of the various components of stresses, displacements, chemical potential function, temperature change and mass concentration. The authors find that for t=0.2, trends are oscillatory in all the cases whereas for t=0.1, trends are quite different. A sound impact of diffusion and thermal phase-lags on the various quantities is observed. A lot of difference in the trends of single phase lag and dual phase lag is observed. The use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient. Originality/value – This problem is totally new because dual phase lag is applied in heat conduction and diffusion equation while considering the problem of plate in axisymmetric heat supply.

Plane wave propagation in an anisotropic dual-phase-lag thermoelastic diffusion medium

2014 ◽  
Vol 10 (4) ◽  
pp. 562-592 ◽  
Author(s):  
Rajneesh Kumar ◽  
Vandana Gupta
Keyword(s):  
Mass Flux ◽  
Potential Gradient ◽  
Transversely Isotropic ◽  
Mass Diffusion ◽  
Phase Lag ◽  
Dual Phase ◽  
Thermoelastic Diffusion ◽  
Content Type ◽  
Diffusion Phase ◽  
Phase Lags

Purpose – The purpose of this paper is to depict the effect of thermal and diffusion phase-lags on plane waves propagating in thermoelastic diffusion medium with different material symmetry. A generalized form of mass diffusion equation is introduced instead of classical Fick's diffusion theory by using two diffusion phase-lags, one phase-lag of diffusing mass flux vector, represents the delayed time required for the diffusion of the mass flux and the other phase-lag of chemical potential, represents the delayed time required for the establishment of the potential gradient. The basic equations for the anisotropic thermoelastic diffusion medium in the context of dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models are presented. The governing equations for transversely isotropic and isotropic case are also reduced. The different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically. Numerically computed results are depicted graphically for anisotropic, transversely isotropic and isotropic medium. The effect of diffusion and thermal phase-lags are shown on the different characteristic of waves. Some particular cases of result are also deduced from the present investigation. Design/methodology/approach – The governing equations of thermoelastic diffusion are presented using DPLT model and a new model of DPLD. Effect of phase-lags of thermal and diffusion is presented on different characteristic of waves. Findings – The effect of diffusion and thermal phase-lags on the different characteristic of waves is appreciable. Also the use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient. Originality/value – Introduction of a new model of DPLD in the equation of mass diffusion.

A problem of thick circular plate in modified couple stress thermoelastic diffusion with phase-lags

2016 ◽  
Vol 12 (3) ◽  
pp. 478-494
Author(s):  
Rajneesh Kumar ◽  
Shaloo Devi ◽  
Veena Sharma
Keyword(s):  
Temperature Change ◽  
Couple Stress ◽  
Chemical Potential ◽  
Phase Lag ◽  
Dual Phase ◽  
Field Equations ◽  
Thermoelastic Diffusion ◽  
Content Type ◽  
Lag Model ◽  
Modified Couple Stress

Purpose The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the context of dual-phase-lag model. Design/methodology/approach The Laplace and Hankel transforms have been applied to find the general solution to the field equations. The components of displacement, stresses, temperature change and chemical potential are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Findings The components of normal stress, tangential stress, tangential couple stress, temperature change and chemical potential are obtained numerically and depicted graphically to see the effect of dual-phase-lag diffusion (DLD), dual-phase-lag heat transfer (DLT) and TD models in the absence and presence of couple stress parameter. Originality/value Comparisons are made in the absence and presence of couple stress DLD, DLT and TD models.

scholarly journals Finite Element Analysis of Thermal-Diffusions Problem for Unbounded Elastic Medium Containing Spherical Cavity under DPL Model

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2782
Author(s):  
Aatef D. Hobiny ◽  
Ibrahim A. Abbas
Keyword(s):  
Finite Element ◽  
Chemical Potential ◽  
Phase Lag ◽  
Dual Phase ◽  
Element Analysis ◽  
Spherical Cavities ◽  
Lag Model ◽  
Phase Lags ◽  
Unbounded Elastic Medium ◽  
Element Technique

In this work, the thermo-diffusions interaction in an unbounded material with spherical cavities in the context dual phase lag model is investigated. The finite element technique has been used to solve the problem. The bounding surface of the inner hole is loaded thermally by external heat flux and is traction-free. The delay times caused in the microstructural interactions, the requirement for thermal physics to take account of hyperbolic effects within the medium, and the phase lags of chemical potential and diffusing mass flux vector are interpreted. A comparison is made in the case of the presence and the absence of mass diffusions between coupled, Lord-Shulman and dual phase lag theories. The numerical results for the displacement, concentration, temperature, chemical potential and stress are presented numerically and graphically.

Thermo-diffusion of solid cylinders based upon refined dual-phase-lag models

2020 ◽  
Vol 16 (6) ◽  
pp. 1417-1434
Author(s):  
Ashraf M. Zenkour
Keyword(s):  
Single Phase ◽  
Chemical Potential ◽  
Thermal Flux ◽  
Closed Form Solution ◽  
Generalized Thermoelasticity ◽  
Phase Lag ◽  
Dual Phase ◽  
Solid Cylinder ◽  
Content Type ◽  
Coupled Equations

PurposeThe thermo-diffusion analysis of an isotropic cylinder under thermal flux and chemical potential impacts has been discussed. Improvements of Green and Naghdi generalized thermoelasticity theory have been proposed.Design/methodology/approachSome models with and without energy dissipation have been presented as well as the simple forms of Green–Naghdi (G–N) theories. These novel multi- and single-/dual-phase-lag models are presented to investigate the thermo-diffusion of the solid cylinder. The closed-form solution of thermo-diffusion governing equations of solid cylinder has been obtained to deduce all field variables.FindingsA comparison study between the simple G–N II and III models and their improved models has been presented. The validations of outcomes are acceptable and so benchmarks are reported to help other investigators in their future comparisons.Originality/valueThe modified Green and Naghdi theories of types II and III are presented to get novel and accurate models of single- and dual-phase-lag of multiterms. The heat of mass diffusion equation as well as the constitutive equations for the stresses and chemical potential of a solid cylinder is added to the present formulation. The system of three differential coupled equations is solved, and all field variables are obtained for the thermal diffusion of the solid cylinder. Some validation examples and applications are presented to compare the simple and modified Green and Naghdi theories of types II and III. Sample plots are illustrated along the radial direction of the solid cylinder. Some results are tabulated to serve as benchmark results for future comparisons with other investigators. The reported and illustrated results show that the simple G–N II and III models yield the largest values of all field quantities. The single-phase-lag models give the smallest values. However, the dual-phase-lag model yields results that are intermediate between those of the simple and single-phase-lag G–N models.

scholarly journals Effects of time and diffusion phase-lags in a thin circular disc with axisymmetric heat supply

2017 ◽  
Vol 4 (1) ◽  
pp. 1369848
Author(s):  
Rajneesh Kumar ◽  
Lajvinder Singh Reen ◽  
S.K. Garg ◽  
Timothy Marchant
Keyword(s):  
Heat Supply ◽  
Circular Disc ◽  
Diffusion Phase ◽  
Phase Lags ◽  
And Diffusion

Effect of phase-lags on Rayleigh wave propagation in thermoelastic medium with mass diffusion

2015 ◽  
Vol 11 (4) ◽  
pp. 474-493 ◽  
Author(s):  
Rajneesh Kumar ◽  
Vandana Gupta
Keyword(s):  
Wave Propagation ◽  
Rayleigh Wave ◽  
Secular Equation ◽  
Mass Diffusion ◽  
Phase Lag ◽  
Dual Phase ◽  
Thermoelastic Medium ◽  
Thermoelastic Diffusion ◽  
Content Type ◽  
Phase Lags

Purpose – The purpose of this paper is to study the propagation of Rayleigh waves in thermoelastic medium with mass diffusion. Design/methodology/approach – The field equations for the linear theory of homogeneous isotropic thermoelastic diffusion medium are taken into consideration by using dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obtained. After developing mathematical formulation, the dispersion equation is obtained, which results to be complex and irrational. This equation is converted into a polynomial form of higher degree. Findings – From the polynomial equation, Rayleigh wave root is found. The secular equation is resolved into a polynomial form to find the roots and therefore to find the existence and propagation of Rayleigh wave. The existence of Rayleigh wave in the assumed model depends on the values of various parameters involved in the secular equation. These roots are resolved for phase velocity and attenuation of the inhomogeneous propagation of Rayleigh wave. Behavior of particle motion of these waves inside and at the surface of the thermoelastic medium with mass diffusion is studied. Particular cases of the interest are also deduced from the present investigation. Originality/value – Governing equations corresponding to DPLT and DPLD models of thermoelastic diffusion are formulated to study the wave propagation and their dependence on various material parameters. In this paper effects of thermal and diffusion phase lags on the phase velocity, attenuation and on particle paths are observed and depicted graphically.

A study of plane wave and fundamental solution in the theory of microstretch thermoelastic diffusion solid with phase-lag models

2015 ◽  
Vol 11 (2) ◽  
pp. 160-185 ◽  
Author(s):  
Rajneesh Kumar ◽  
Sanjeev Ahuja ◽  
S.K. Garg
Keyword(s):  
Fundamental Solution ◽  
Plane Wave ◽  
Phase Lag ◽  
Dual Phase ◽  
Elementary Functions ◽  
Thermoelastic Diffusion ◽  
Content Type ◽  
Propagation Technique ◽  
Steady Oscillations ◽  
Phase Velocity And Attenuation

Purpose – The purpose of this paper is to study of propagation of plane wave and the fundamental solution of the system of differential equations in the theory of a microstretch thermoelastic diffusion medium in phase-lag models for the case of steady oscillations in terms of elementary functions. Design/methodology/approach – Wave propagation technique along with the numerical methods for computation using MATLAB software has been applied to investigate the problem. Findings – Characteristics of waves like phase velocity and attenuation coefficient are computed numerically and depicted graphically. It is found that due to the presence of diffusion effect, these characteristics get influenced significantly. However, due to decoupling of CD-I and CD-II waves from rest of other, no effect on these characteristics can be perceived. Originality/value – Basic properties of the fundamental solution are established by introducing the dual-phase-lag diffusion (DPLD) and dual-phase-lag heat transfer (DPLT) models.

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

2018 ◽  
Vol 14 (5) ◽  
pp. 837-856 ◽  
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.

The Reflection of Magneto-Thermoelastic P and SV Waves at a Solid Half Space Using Dual-Phase-Lag Model

2011 ◽  
Vol 3 (6) ◽  
pp. 745-758
Author(s):  
Ahmed E. Abouelregal
Keyword(s):  
Reflection Coefficients ◽  
Transfer Model ◽  
Phase Lag ◽  
Dual Phase ◽  
Angle Of Incidence ◽  
Lag Model ◽  
Phase Lags ◽  
Energy Ratios ◽  
Thermoelastic Solid ◽  
P And Sv Waves

AbstractThe dual-phase-lag heat transfer model is employed to study the reflection phenomena of P and SV waves from a surface of a semi-infinite magneto-thermoelastic solid. The ratios of reflection coefficients to that of incident coefficients are obtained for P- and SV-wave cases. The results for partition of the energy for various values of the angle of incidence are computed numerically under the stress-free and rigidly fixed thermally insulated boundaries. The reflection coefficients are depending on the angle of incidence, magnetic field, phase lags and other material constants. Results show that the sum of energy ratios is unity at the interface. The results are discussed and depicted graphically.

Effect of gravity on generalized thermoelastic diffusion due to laser pulse using dual-phase-lag model

2018 ◽  
Vol 14 (3) ◽  
pp. 457-481 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
Ebtesam E.M. Eraki
Keyword(s):  
Plane Surface ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Graphical Form ◽  
Phase Lag ◽  
Dual Phase ◽  
Field Equations ◽  
Gaussian Laser Beam ◽  
Content Type ◽  
Non Gaussian

Purpose The purpose of this paper is to obtain a general solution to the field equations of generalized thermo-diffusion in an infinite thermoelastic body under the effect of gravity in the context of the dual-phase-lag (DPL) model. The half space is considered made of an isotropic homogeneous thermoelastic material. The boundary plane surface is heated by a non-Gaussian laser beam. Design/methodology/approach An exact solution to the problem is obtained using the normal mode analysis. Findings The derived expressions are computed numerically for copper and the results are presented in graphical form. Originality/value Comparisons are made with the results predicted by Lord-Shulman theory and DPL model for different values of time and in the presence and absence of gravity as well as diffusion.

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