Skip to main content
SpringerLink
Log in

Novel model of thermo-magneto-viscoelastic medium with variable thermal conductivity under effect of gravity

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the Green- Lindsay (G-L) theory, the coupled (CD) theory, and the Lord-Shulman (L-S) theory. The variable thermal conductivity is considered as a linear function of the temperature. Using suitable non-dimensional variables, these basic equations are solved via the eigenvalue approach. The medium is initially assumed to be stress-free and subject to a thermal shock. The numerical results reveal that the viscosity, the two-temperature parameter, the gravity term, and the magnetic field significantly influence the distribution of the physical quantities of the thermoelastic medium.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. GROSS, B. Mathematical Structure of the Theories of Viscoelasticity, Hemann, Paris (1953)

    MATH  Google Scholar 

  2. STAVERMAN, A. J. and SCHWARZL, F. Linear Deformation Behaviour of High Polymers, Die Physik der Hochpolymeren, Springer, Berlin (1956)

    Google Scholar 

  3. ATKINSON, C. and CRASTER, R. Theoretical aspects of fracture mechanics. Progress in Aerospace Sciences, 31, 1–83 (1995)

    Article  Google Scholar 

  4. KOLTUNOV, M. Creeping and Relaxation, Vysshaya Shkola, Moscow (1976)

    Google Scholar 

  5. BLAND, D. R. The Theory of Linear Viscoelasticity, Pergamon Press, New York (1960)

    MATH  Google Scholar 

  6. ACHARYA, D. P., ROY, I., and BISWAS, P. K. Vibration of an infinite inhomogeneous transversely isotropic viscoelastic medium with cylindrical hole. Applied Mathematics and Mechanics (English Edition), 29(3), 367–378 (2008) https://doi.org/10.1007/s10483-008-0308-z

    Article  Google Scholar 

  7. SINGH, P., CHATTOPADHYAY, A., and SINGH, A. K. Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress. Applied Mathematics and Mechanics (English Edition), 39(3), 317–334 (2018) https://doi.org/10.1007/s10483-018-2306-9

    Article  MathSciNet  Google Scholar 

  8. KUMAR, R., CHAWLA, V., and ABBAS, I. A. Effect of viscosity on wave propagation in anisotropic thermoelastic medium with three-phase-lag model. Theoretical and Applied Mechanics, 39, 313–341 (2012)

    Article  MathSciNet  Google Scholar 

  9. ELLAHI, R. The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: analytical solutions. Applied Mathematical Modelling, 37, 1451–1467 (2013)

    Article  MathSciNet  Google Scholar 

  10. DESWAL, S., PUNIA, B. S., and KALKAL, K. K. Thermodynamical interactions in a twotemperature dual-phase-lag micropolar thermoelasticity with gravity. Multidiscipline Modeling in Materials and Structures, 14, 102–124 (2018)

    Article  Google Scholar 

  11. SHEORAN, S. S., KALKAL, K. K., and DESWAL, S. Fractional order thermo-viscoelastic problem with temperature dependent modulus of elasticity. Mechanics of Advance Material and Structures, 23, 407–414 (2016)

    Article  Google Scholar 

  12. ABO-DAHAB, S. M., JAHANGIR, A., MUHAMMAD, N., FARWA, S., BASHIR, Y., and USMAN, M. Propagation phenomena in a visco-thermo-micropolar elastic medium under the effect of micro-temperature. Results in Physics, 8, 793–798 (2018)

    Article  Google Scholar 

  13. HENDY, M. H., AMIN, M. M., and EZZAT, M. A. Two-dimensional problem for thermoviscoelastic materials with fractional order heat transfer. Journal of Thermal Stresses, 42, 1–18 (2019)

    Article  Google Scholar 

  14. YOUSSEF, H. Dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity. Applied Mathematics and Mechanics (English Edition), 26(4), 470–475 (2005) https://doi.org/10.1007/BF02465386

    Article  Google Scholar 

  15. YOUSSEF, H. and EL-BARY, A. A. Two-temperature generalized thermoelasticity with variable thermal conductivity. Journal of Thermal Stresses, 33, 187–201 (2010)

    Article  Google Scholar 

  16. ZENKOUR, A. M., MASHAT, D. S., and ABOULREGAL, A. E. The effect of dual-phase-lag model on reflection of thermoelastic waves in a solid half space with variable material properties. Acta Mechenica Solida Sinica, 26, 659–670 (2013)

    Article  Google Scholar 

  17. WANG, Y., LIU, D., WANG, Q., and ZHOU, J. Asymptotic solutions for generalized thermoelasticity with variable thermal material properties. Archives of Mechanics, 68, 181–202 (2016)

    MathSciNet  MATH  Google Scholar 

  18. XIONG, C., YU, L., and NIU, Y. Effect of variable thermal conductivity on the generalized thermoelasticity problems in a fiber-reinforced anisotropic half-space. Advances in Materials Science and Engineering, 2019, 8625371 (2019)

    Google Scholar 

  19. ELLAHI, R., ZEESHAN, A., SHEHZAD, N., and ALAMRI, S. Z. Structural impact of Kerosene- Al2O3 nanoliquid on MHD Poiseuille flow with variable thermal conductivity: application of cooling process. Journal of Molecular Liquids, 264, 607–615 (2018)

    Article  Google Scholar 

  20. AKBAR, N. S., RAZA, M., and ELLAHI, R. Peristaltic flow with thermal conductivity of H2O + Cu nanofluid and entropy generation. Results in Physics, 5, 115–124 (2015)

    Article  Google Scholar 

  21. ELLAHI, R., ZEESHAN, A., HUSSAIN, F., and ABBAS, T. Two-phase Couette flow of couple stress fluid with temperature dependent viscosity thermally affected by magnetized moving surface. Symmetry, 11, 647 (2019)

    Article  Google Scholar 

  22. AILAWALIA, P. P. and NARAH, N. S. Effect of rotation in generalized thermoelastic solid under the influence of gravity with an overlying infinite thermoelastic fluid. Applied Mathematics and Mechanics (English Edition), 30(12), 1505–1518 (2009) https://doi.org/10.1007/s10483-009-1203-6

    Article  MathSciNet  Google Scholar 

  23. ABO-DAHAB, S. M., ABD-ALLA, A. M., and KILANY, A. A. Effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids by using the Lord-Shulman and dual-phase-lag models. Applied Mathematics and Mechanics (English Edition), 40(8), 1135–1154 (2019) https://doi.org/10.1007/s10483-019-2504-6

    Article  Google Scholar 

  24. SUR, A., PAL, P., and KANORIA, M. Modeling of memory-dependent derivative in a fiberreinforced plate under gravitational effect. Journal of Thermal Stresses, 41, 973–992 (2018)

    Article  Google Scholar 

  25. SETHI, M., GUPTA, K. C., GUPTA, D., and MANISH, G. Surface waves in fibre-reinforced anisotropic solid elastic media under the influence of gravity. International Journal of Applied Mechanics and Engineering, 18, 177–188 (2013)

    Article  Google Scholar 

  26. SHAW, S. and MUKHOPADHYAY, B. Moving heat source response in micropolar half-space with two-temperature theory. Continuum Mechanics and Thermodynamics, 25, 523–535 (2013)

    Article  MathSciNet  Google Scholar 

  27. SAID, S. M. Influence of gravity on generalized magneto-thermoelastic medium for three-phase-lag model. Journal of Computational and Applied Mathematics, 291, 142–157 (2016)

    Article  MathSciNet  Google Scholar 

  28. YOUSSEF, H. M. State-space approach on generalized thermoelasticity for an infinite material with a spherical cavity and variable thermal conductivity subjected to ramp type heating. Canadian Applied Mathematics Quarterly, 13, 369–390 (2015)

    MathSciNet  MATH  Google Scholar 

  29. HETNARSKI, R. B. Thermal Stresses I, 2nd series, Vol. 1, Taylor & Francis Group, LLC, North-Holland (1986)

  30. DAS, N. C. and BHAKATA, P. C. Eigenfunction expansion method to the solution of simultaneous equations and its application in mechanics. Mechanics Research Communications, 12, 19–29 (1985)

    Article  MathSciNet  Google Scholar 

  31. GHOSH, M. K. and KANORIA, M. Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock. Applied Mathematics and Mechanics (English Edition), 29(10), 1263–1278 (2008) https://doi.org/10.1007/s10483-008-1002-2

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt

    S. M. Said

  2. Department of Mathematics, Faculty of Science and Arts, Qassim University, Buridah, 51931, Al-mithnab, Saudi Arabia

    S. M. Said

Authors
  1. S. M. Said
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. M. Said.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Said, S.M. Novel model of thermo-magneto-viscoelastic medium with variable thermal conductivity under effect of gravity. Appl. Math. Mech.-Engl. Ed. 41, 819–832 (2020). https://doi.org/10.1007/s10483-020-2603-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-020-2603-9

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation