Finite Element Method to Study Elasto-Thermodiffusive Response inside a Hollow Cylinder with Three-Phase-Lag Effect

Authors

  • Bhattacharya D Dept. of Applied Mathematics, University of Calcutta, 92 A. P. C. Road, Kolkata- 700009, West Bengal, India
  • Pal P Dept. of Applied Mathematics, University of Calcutta, 92 A. P. C. Road, Kolkata- 700009, West Bengal, India
  • Kanoria M Dept. of Applied Mathematics, University of Calcutta, 92 A. P. C. Road, Kolkata- 700009, West Bengal, India

DOI:

https://doi.org/10.26438/ijcse/v7i1.148156

Keywords:

Thermoelastic diffusion, Three-phase-lag model, Green-Naghdi model, Lord-Shulman model,, Galerkin finite element method

Abstract

In this article, we deal with a problem of generalized elasto-thermo-diffusion interaction inside an isotropic hollow cylinder in the context of three-phase-lag model. Initially the medium is in rest and undisturbed so that all the state functions are assumed to be zero. Employing Laplace transform as a tool, the governing equations have been expressed in transformed domain, which are then solved by Galerkin finite element technique. The inversion of the transformed solution is carried out by applying a method of Bellman et al. The stresses, temperature, displacement, concentration and chemical potential are computed numerically and presented graphically in a number of figures for copper material. A comparative study for different theories (three-phase-lag model, Green-Naghdi model with energy dissipation and Lord-Shulman model) are presented. The results corresponding to thermoelastic medium (in absence of diffusion) are also carried out in a particular case. The significant points are highlighted.

References

[1] W. Nowacki, “Dynamical problems of thermoelastic diffusion in solids I”, Bulletin of Polish Academy of Science and Technology, Vol.22, pp.55-64, 1974.

[2] W. Nowacki, “Dynamical problems of thermoelastic diffusion in solids II”, Bulletin of Polish Academy of Science and Technology, Vol.22, pp.129-135, 1974.

[3] W. Nowacki, “Dynamical problems of thermoelastic diffusion in solids II”, Bulletin of Polish Academy of Science and Technology, Vol.22, pp.257-266, 1974.

[4] W. Nowacki, “Dynamical problems of thermoelastic diffusion in elastic solids”, Proc Vib Prob, Vol.15, pp.105-128, 1974.

[5] H.W. Lord, Y. Shulman, “A generalized dynamical theory of thermoelasticity”, Journal of Mechanics and Physics of Solid, Vol.15, pp.299-309, 1967.

[6] H.H. Sherief, F.A. Hamza, H.A. Saleh, “The theory of generalized thermoelastic diffusion”,. International Journal of Engineering Science, Vol. 42, pp.591-608, 2004.

[7] H.H. Sherief, H.A. Saleh, “A half-space problem in the theory of generalized thermoelastic diffusion”, International Journal of Solids and Structure, Vol.42, pp.4484-4493, 2005.

[8] M. Aouadi, “Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion”, Journal of Thermal Stresses, Vol.30, pp.665-678, 2007.

[9] M. Aouadi, “A generalized thermoelastic diffusion problem for an infinitely long solid cylinder”, International Journal of Mathematics and mathematical sciences, Vol.2006, pp.1-15, 2006.

[10] M. Aouadi, “A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion”, International Journal of Solids Structure, Vol.44, pp.5711-5722, 2007.

[11] D. Bhattacharya, M. Kanoria, “The influence of two temperature generalized thermoelastic diffusion inside a spherical shell”, International Journal of Engineering and Technical Research, Vo.2, Issue.5, pp.151-159, 2014.

[12]A.A. Allam, K.T. Ramadan, M.A. Omar, “A stochastic thermoelastic diffusion interaction in an infinitely long annular cylinder”, Acta Mechanica, Vol.227, pp.1429-1443, 2016.

[13] M. Aouadi, M. Ciarletta, V. Tibullo, “A thermoelastic diffusion theory with microtemperatures and microconcentrations.” Journal of Thermal Stresses, Vol.40, pp. 486-501, 2017.

[14]J.J. Tripathi, P.M. Keder, K.C. Deshmukh, “Generalized thermoelastic diffusion in a thick circular plate including heat source”, Alexandria Engineering Journal, Vol.55, pp.2241-2249, 2016.

[15] A.E. Green, P.M. Nagdhi, “A Re-examination of the Basic Postulates of Thermomechanics”, Proceeding of the Royal Society of London. Series A, Vol.432, pp.171-194, 1991.

[16] A.E. Green, P.M. Nagdhi, “On undamped heat waves in an elastic solid”, Journal of Thermal Stresses, Vol.15, pp.252-264, 1992.

[17] A.E. Green, P.M. Nagdhi, “Thermoelasticity without energy dissipation”, Journal of Elasticity, Vol.31, pp.189-208, 1993.

[18] D.S. Chandrasekharaiah, “Hyperbolic thermoelasticity: A review of recent literature”, 1998.

[19] P. Puri, “Plane thermoelastic wave in a rotating medium”, Bulletin of Polish Academy of Science and Technology, Vol.24, pp.137-144, 1974.

[20] R. Singh, V. Kumar, “Eigen value approach to two dimensional problem in generalized magneto micropolar thermoelastic medium with rotation effect”, International Journal of Applied Mechanics and Engineering, Vol.21, Issue.1, pp.205-219, 2016.

[21] S.K. Roychoudhuri, “On a thermoelastic three-phase-lag model”, Journal of Thermal stresses, Vol.30, pp.231-238, 2007.

[22] R. Quintanilla, R. Racke, “A note on stability in three-phase-lag heat conduction”, International Journal of Heat and mass transfer, Vol.51, pp.24-29, 2008.

[23] A. Kar, M. Kanoria, “Analysis of thermoelastic response in a fiber reinforced thin annular disc with three-phase-lag effect”, European Journal of Applied Mathematics, Vol.32, pp.1315-1332, 2011.

[24] P. Das, A. Kar, M. Kanoria, “Analysis of magneto-thermoelastic responce in a transversely isotropic hollow cylinder under thermal shock with three-phase-lag effect”, Journal of Thermal Stresses, Vol.36, pp.239-258, 2013.

[25]P. Pal, M. Kanoria, “Finite element method to study magneto-thermo-elastic wave in a transversely isotropic hollow cylinder”, International Journal of Mathematical Science and Engineering Applications, Vol.10, Issue.1, pp.147-175, 2016.

[26] P. Pal, D. Bhattacharya, M. Kanoria, “Two-temperature elasto-thermo diffusive response inside a spherical shell with three -phase-lag effect,” International Journal of Engineering Research and Application, Vol.5, Issue.8, pp.1-10, 2015.

[27] S.M. Said, “Influence of gravity on generalized magneto-thermoelastic medium for three phase lag effect”, Journal of Computational and Applied Mathematics, Vol.291, pp.142-157, 2016.

[28] S. Biswas, B. Mukhopadhyay, S. Shaw, “Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model”, Journal of Thermal stresses, Vol.40, Issue.4, pp.403-419, 2017.

[29] R. Bellman, R.E. Kolaba, J.A. Lockette, “Numerical inversion of the Laplace transform”, American Elsevier, New York, 1966.

Downloads

Published

2019-01-31
CITATION
DOI: 10.26438/ijcse/v7i1.148156
Published: 2019-01-31

How to Cite

[1]
D. Bhattacharya, P. Pal, and M. Kanoria, “Finite Element Method to Study Elasto-Thermodiffusive Response inside a Hollow Cylinder with Three-Phase-Lag Effect”, Int. J. Comp. Sci. Eng., vol. 7, no. 1, pp. 148–156, Jan. 2019.

Issue

Vol. 7 No. 1 (2019): IJCSE January Edition

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors contributing to this journal agree to publish their articles under the Creative Commons Attribution 4.0 International License, allowing third parties to share their work (copy, distribute, transmit) and to adapt it, under the condition that the authors are given credit and that in the event of reuse or distribution, the terms of this license are made clear.