Thermo-Viscoelastic Interaction Subjected to Fractional Fourier law with Three-Phase-Lag Effects

Authors

  • A Sur Department of Applied Mathematics, University of Calcutta
  • M Kanoria Department of Applied Mathematics, University of Calcutta
  • P Pal Department of Applied Mathematics, University of Calcutta
Abstract:

In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts thermoelasticity without energy dissipation (TEWOED) and with energy dissipation (TEWED)) are employed to study the thermo-mechanical coupling, thermal and mechanical relaxation effects. In the absence of mechanical relaxations (viscous effect), the results for various generalized theories of thermoelasticity may be obtained as particular cases. The governing equations are expressed in Laplace-Fourier double transform domain. The inversion of the Fourier transform is carried out using residual calculus, where the poles of the integrand are obtained numerically in complex domain by using Laguerre's method and the inversion of the Laplace transform is done numerically using a method based on Fourier series expansion technique. Some comparisons have been shown in the form of the graphical representations to estimate the effect of the non-local fractional parameter and the effect of viscosity is also shown.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Rayleigh Surface Wave Propagation in Transversely Isotropic Medium with Three-Phase-Lag Model

The present paper is dealing with the propagation of Rayleigh surface waves in a homogeneous transversely isotropic medium .This thermo-dynamical analysis is carried out in the context of three-phase-lags thermoelasticity model. Three phase lag model is very much useful in the problems of nuclear boiling, exothermic catalytic reactions, phonon-electron interactions, phonon scattering etc. The n...

full text

Slip Effects on Fractional Viscoelastic Fluids

Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions pΨq, by using discrete Laplace transform of the sequential frac...

full text

Effects of Gravitational and Hydrostatic Initial Stress on a Two-Temperature Fiber-Reinforced Thermoelastic Medium for Three-Phase-Lag

The three-phase-lag model and Green–Naghdi theory without energy dissipation are employed to study the deformation of a two-temperature fiber-reinforced medium with an internal heat source that is moving with a constant speed under a hydrostatic initial stress and the gravity field.  The modulus of the elasticity is given as a linear function of the reference temperature. The exact expressions ...

full text

Size-Dependent Forced Vibration Analysis of Three Nonlocal Strain Gradient Beam Models with Surface Effects Subjected to Moving Harmonic Loads

The forced vibration behaviors are examined for nonlocal strain gradient nanobeams with surface effects subjected to a moving harmonic load travelling with a constant velocity in terms of three beam models namely, the Euler-Bernoulli, Timoshenko and modified Timoshenko beam models. The modification for nonlocal strain gradient Timoshenko nanobeams is exerted to the constitutive equations by exc...

full text

Torsional Pile Subjected to Transient Loading in Viscoelastic Poroelastic Medium

Considering viscoelastic saturated soil, The transient dynamic response of an elastic pile is studied. The pile-soil system is divided into thin layers, the control equations of the soil are solved respectively by using Laplace transform. Considering the mixed boundary-value conditions at the interface of pile and soil, expression is derived to describe the relationship between the inner force ...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 7  issue 4

pages  400- 415

publication date 2015-12-30

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023