Influence of initial stress and gravity on refraction and reflection of SV wave at interface between two viscoelastic liquid under three thermoelastic theories

  • A. A. Khan
  • A. Afzal
Technical Paper


This approach is to examine the impact of magnetic field, viscosity, gravity and initial stress on SV wave while traveling through the interface of two visco-thermoelastic liquid layers. The basic equations in context of three theories have been discussed to drive results for refracted thermal and P waves and reflected thermal, SV and P waves. After using the boundary conditions the amplitude ratios have been computed in matrix form.


Initial stress Viscosity Magnetic field Reflection Refraction 

List of symbols


Initial stress

\(\overrightarrow {\acute\omega }\)

Local rotation


Principal or incremental stress component along x axis


Principal or incremental stress components along y axis


Shear stress component


Normal initial stress component along x axis


Normal initial stress component along y axis


Density of medium


Component of displacement along x axis


Component of displacement along y axis


Lorent’z force along x axis


Lorent’z force along y axis

 \(\gimel\), μ

Lame’s constant


Shear strain component


Principal strain component


Coefficient of linear thermal expansion


Bulk modulus


Absolute temperature


Relaxation time


Specific heat per unit mass


Thermal conductivity


Electric intensity vector


Perturbed magnetic field vector


Magnetic field vector


Electric current density vector


Electric permeability


Magnetic permeability


Magnetic pressure number


Elastic wave velocity


Rotational wave velocity


Initial stress parameter


Circular frequency


Wave number


Thermoelastic coupling constant


Phase lag of gradient of temperature


Strain component


  1. 1.
    Dhaliwal RS, Singh A (1980) Dynamic coupled thermoelasticity Hindustan Publ. Corp, New DelhiGoogle Scholar
  2. 2.
    Lord HW, Shulman Y (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15(5):299–309CrossRefzbMATHGoogle Scholar
  3. 3.
    Green AE, Lindsay KA (1972) Thermoelasticity. J Elast 2(1):1–7CrossRefzbMATHGoogle Scholar
  4. 4.
    RoyChoudhuri SK (2007) One-dimensional thermoelastic waves in elastic half-space with dual phase-lag effects. J Mech Mater Struct 2(3):489–503CrossRefGoogle Scholar
  5. 5.
    Abouelregal Ahmed E, Abo-Dahab SM (2012) Dual phase lag model on magneto-thermoelasticity infinite non-homogeneous solid having a spherical cavity. J Therm Stresses 35(9):820–841CrossRefGoogle Scholar
  6. 6.
    Sheikholeslami Mohsen (2017) Magnetic field influence on nanofluid thermal radiation in a cavity with tilted elliptic inner cylinder. J Mol Liq 229:137–147CrossRefGoogle Scholar
  7. 7.
    Sheikholeslami Mohsen (2017) Numerical simulation of magnetic nanofluid natural convection in porous media. Phys Lett A 381(5):494–503CrossRefGoogle Scholar
  8. 8.
    Sheikholeslami M, Rokni HB (2017) Nanofluid two phase model analysis in existence of induced magnetic field. Int J Heat Mass Transf 107:288–299CrossRefGoogle Scholar
  9. 9.
    Sheikholeslami M (2017) Influence of Coulomb forces on Fe 3 O 4–H 2 O nanofluid thermal improvement. Int J Hydrogen Energy 42(2):821–829CrossRefGoogle Scholar
  10. 10.
    Kandelousi Mohsen Sheikholeslami (2014) Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition. Eur Phys J Plus 11(129):1–12Google Scholar
  11. 11.
    Sheikholeslami M, Hayat T, Alsaedi A (2017) Numerical simulation of nanofluid forced convection heat transfer improvement in existence of magnetic field using lattice Boltzmann method. Int J Heat Mass Transf 108:1870–1883CrossRefGoogle Scholar
  12. 12.
    Sheikholeslami M, Bhatti MM (2017) Forced convection of nanofluid in presence of constant magnetic field considering shape effects of nanoparticles. Int J Heat Mass Transf 111:1039–1049CrossRefGoogle Scholar
  13. 13.
    Sheikholeslami M, Hayat T, Alsaedi A (2017) Numerical study for external magnetic source influence on water based nanofluid convective heat transfer. Int J Heat Mass Transf 106:745–755CrossRefGoogle Scholar
  14. 14.
    Sheikholeslami M, Houman B (2017) Rokni. “Numerical modeling of nanofluid natural convection in a semi annulus in existence of Lorentz force.”. Comput Methods Appl Mech Eng 317:419–430CrossRefGoogle Scholar
  15. 15.
    Abd-Alla AM, Abo-Dahab SM, Kilany AA (2016) SV-waves incidence at interface between solid-liquid media under electromagnetic field and initial stress in the context of three thermoelastic theories. J Therm Stresses 39(8):960–976CrossRefGoogle Scholar
  16. 16.
    Sharma JN, Chauhan RS (1999) On the problems of body forces and heat sources in thermoelasticity without energy dissipation. Indian J Pure Appl Math 30:595–610zbMATHGoogle Scholar
  17. 17.
    Chakraborty N, Singh MC (2011) Reflection and refraction of a plane thermoelastic wave at a solid–solid interface under perfect boundary condition, in presence of normal initial stress. Appl Math Model 35(11):5286–5301MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Deswal S, Tomar SK, Kumar R (2000) Effect of fluid viscosity on wave propagation in a cylindrical bore in micropolar elastic medium. Sadhana 25(5):439–452CrossRefGoogle Scholar
  19. 19.
    Singh MC, Chakraborty N (2016) Reflection and refraction of plane waves at the interface of two visco-thermoelastic liquid layers in presence of magnetic field and compressional stress, with the outer core inside the earth as a model. Int J Appl Comput Math 3(3):2107–2124MathSciNetCrossRefGoogle Scholar
  20. 20.
    De SN, Sen-Gupta PR (1974) Influence of gravity on wave propagation in an elastic layer. J Acoust Soc Am 55(5):919–921CrossRefGoogle Scholar
  21. 21.
    Acharya DP, Roy I, Sengupta S (2009) Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media. Acta Mech 202(1):35–45CrossRefzbMATHGoogle Scholar
  22. 22.
    Biot MA, Drucker DC (1965) Mechanics of incremental deformation. J Appl Mech 32:957CrossRefGoogle Scholar
  23. 23.
    Ewing WM, Jardetzky WS, Press F, Beiser A (1957) Elastic waves in layered media. Phys Today 10:27CrossRefzbMATHGoogle Scholar
  24. 24.
    Dziewonski AM, Anderson DL (1981) Preliminary reference Earth model. Phys Earth Planet Inter 25(4):297–356CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsInternational Islamic UniversityIslamabadPakistan

Personalised recommendations