Two-dimensional problem of two-temperature generalized thermoelasticity using memory-dependent heat transfer: an integral transform approach

  • Nantu Sarkar
  • Sudip MondalEmail author
Original Paper


We investigate the thermoelastic interactions in an isotropic and homogeneous perfectly conducting two-dimensional semi-infinite elastic medium. The bounding surface of the medium is assumed as stress free and subjected to a time-dependent thermal shock. A new two-temperature generalized thermoelasticity theory with memory-dependent derivative is employed for this study. The combined Laplace–Fourier transforms are applied to solve the non-dimensional governing equations to find the solutions for the field variables in the transform domain. An application is considered to enable us to get complete solutions. Numerical results of the field variables are presented graphically to discuss the effect of various parameters of interest.


Thermoelasticity Two-temperature Memory Laplace–Fourier transforms 


44.05. + e 81.40.Jj 62.20.fq 62.20.Dc 62.40. + i 



The authors received no financial support for the research.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. [1]
    R B Hetnarski and J Ignaczak J. Therm. Stresses.22 451 (1999).CrossRefGoogle Scholar
  2. [2]
    H W Lord and Y Shulman J. Mech. Phys. Solids15 299 (1967)ADSCrossRefGoogle Scholar
  3. [3]
    A E Green and K A Lindsay J. Elasticity2 1 (1972)CrossRefGoogle Scholar
  4. [4]
    R S Dhaliwal and H H Sherief Q. Appl. Math.38 1 (1980)Google Scholar
  5. [5]
    D S Chandrasekharaiah Appl. Mech. Rev.39 355 (1986)Google Scholar
  6. [6]
    C C Ackerman, B Bartman, H A Fairbank and R A Guyer Phys. Rev. Lett.16 789 (1966)ADSCrossRefGoogle Scholar
  7. [7]
    R A Guyer and J A Krumhansal Phys. Rev.148 778 (1966)ADSCrossRefGoogle Scholar
  8. [8]
    C C Ackerman and W C Overtone Phys. Rev. Lett.22 764 (1969)ADSCrossRefGoogle Scholar
  9. [9]
    P J Chen, M E Gurtin and W O Williams ZAMP19 969 (1968)Google Scholar
  10. [10]
    P J Chen, M E Gurtin and W O Williams ZAMP20 107 (1969)Google Scholar
  11. [11]
    J K Chen, J E Beraun and C L Tham Int. J. Eng. Sci.42 793 (2004)CrossRefGoogle Scholar
  12. [12]
    T Q Qui and C L Tien Int. J. Heat Mass Transfer115 835 (1993)Google Scholar
  13. [13]
    H M Youssef IMA J. Appl. Math.71 383 (2006)Google Scholar
  14. [14]
    H M Youssef and E A Al-Lehaibi Int. J. Solids Struct.44 1550 (2007)CrossRefGoogle Scholar
  15. [15]
    N Sarkar and A Lahiri Vietnam Journal of Mathematics40 13 (2012)MathSciNetGoogle Scholar
  16. [16]
    M I A Othman and M E M Zidan J. Comput. Theor. Nanosci.12 1687 (2015)CrossRefGoogle Scholar
  17. [17]
    M I A Othman, W M Hasona and E M Abd-Elaziz Can. J. Phys.92 149 (2014)ADSGoogle Scholar
  18. [18]
    S Mondal, A Sur and M Kanoria Acta Mech. 1 (2019)Google Scholar
  19. [19]
    S M Said, Y D Elmaklizi and M I A Othman Chaos Soliton Fract. 97 75 (2017)ADSCrossRefGoogle Scholar
  20. [20]
    M I A Othman and A E Abouelregal Arch. Thermodyn.38 77 (2017)ADSCrossRefGoogle Scholar
  21. [21]
    S Mondal, N Sarkar and N Sarkar J Therm. Stresses, 42 1035 (2019)CrossRefGoogle Scholar
  22. [22]
    I A Abbas J. Comput. Theor. Nanosci.11 987 (2014)Google Scholar
  23. [23]
    I A Abbas Mech. Based Des. Struc.43 501 (2015)Google Scholar
  24. [24]
    M I A Othman and I A Abbas Int. J. Thermophys.33 913 (2012)ADSCrossRefGoogle Scholar
  25. [25]
    I A Abbas and H M Youssef Arch. Appl. Mech.79 917 (2009)ADSCrossRefGoogle Scholar
  26. [26]
    A M Zenkour and I A Abbas Int. J. Mech. Sci.84 54 (2014)CrossRefGoogle Scholar
  27. [27]
    I A Abbas Forsch. Ingenieurwes.71 215 (2007)Google Scholar
  28. [28]
    Y Povstenko Mech. Res. Commun.37 436 (2010)Google Scholar
  29. [29]
    A S El-Karamany and M A Ezzat Math. Mech. Solid.16 334 (2011)CrossRefGoogle Scholar
  30. [30]
    M A Ezzat Physica B: Condensed Matter, 405 4188 (2010)Google Scholar
  31. [31]
    M A Ezzat and A S El-Karaman ZAMP62 937 (2011)ADSGoogle Scholar
  32. [32]
    M A Ezzat and A S El-Karaman Appl. Polym. Sci.124, 2187 (2012)CrossRefGoogle Scholar
  33. [33]
    M Bachher, N Sarkar and A Lahiri Int. J. Mech. Sci.89 84 (2014)CrossRefGoogle Scholar
  34. [34]
    M Bachher, N Sarkar and A Lahiri Meccanica50 2167 (2015)MathSciNetCrossRefGoogle Scholar
  35. [35]
    J Wang and H Li Comput. Math. Appl.62 1562 (2011)MathSciNetCrossRefGoogle Scholar
  36. [36]
    Y-J Yu, W Hu and X-G Tian Int. J. Eng. Sci.81 123 (2014)CrossRefGoogle Scholar
  37. [37]
    M Ezzat, A S El-Karamany and A El-Bary Mech. Adv. Mater. Str.23 545 (2016)CrossRefGoogle Scholar
  38. [38]
    M Ezzat, A S El-Karamany and A. El-Bary Int. J. Mech. Sci.89 470 (2014)CrossRefGoogle Scholar
  39. [39]
    M Ezzat, A S El-Karamany and A. El-Bary Eur. Phys. J. Plus131, 372 (2016)CrossRefGoogle Scholar
  40. [40]
    A Al-Jamel, M F Al-Jamal and A El-Karamany J. Vibration Control, 24 2221 (2016)MathSciNetCrossRefGoogle Scholar
  41. [41]
    N Sarkar J. Math. Models Eng.2 151 (2016)Google Scholar
  42. [42]
    Kh Lotfy and N Sarkar Mech. Time-Depend. Mater.21 15 (2017)CrossRefGoogle Scholar
  43. [43]
    D P Gaver Oper. Res.14 444 (1966).Google Scholar
  44. [44]
    H Stehfest, Commun. ACM13 47 (1970)CrossRefGoogle Scholar

Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of CalcuttaKolkataIndia
  2. 2.Department of MathematicsBasirhat CollegeBasirhatIndia

Personalised recommendations