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Visco-thermodiffusive elastic interactions in plate within the framework of two-temperature fractional thermoelastic models

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Abstract

Extensive advancement in the field of geotechnology, hypersonic transport mediums and design of new materials have attracted researchers to make in-depth study of thermoelastic materials considering diffusion and viscosity effects. Fractional calculus produces more rational results in such studies. In this view, considering two-temperature generalized visco-thermoelastic diffusion with fractional order theory of generalized thermoelasticity, a model is formulated in the context of Lord Shulman (LS) and Green Lindsay (GL) theories of thermoelasticity. The medium considered for study is thermoelastic plate which is kept traction free initially at uniform temperature and is isoconcentrated. The constitutive relations and governing equations are non-dimensionalized and transformed to ordinary differential equation using Laplace transformation with respect to time ‘t’ and Fourier transformation with respect to space variable ‘x’. Mechanical and thermal loads are applied on both surfaces of the plate. Solutions in transformed domain are obtained from resulting system of differential equations. Various quantities like stress, temperature field, mass concentration and chemical potential are obtained for copper material in physical domain by numerical inversion of Laplace and Fourier transforms. The numeric results of LS model are presented graphically. The outcome of this work underlines that disturbances in field quantities can be reduced by increasing two-temperature parameter or decreasing fractional order parameter. Also viscosity parameters have significant influence on field quantities.

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References

  1. P J Chen, M E Gurtin, J. Appl. Math. Phys. 19 614 (1968)

    Google Scholar 

  2. P J Chen, M E Gurtin and W O Williams, J. Appl. Math. Phys. 20 107 (1969)

    Google Scholar 

  3. H M Youssef, E A Al-Lehaibi, Int. J. Solids. Struct. 44 1550 (2007)

    Article  Google Scholar 

  4. R Quintanilla, Acta Mech. 168 61 (2004)

    Article  Google Scholar 

  5. H M Youssef, A H Al-Harby, Arch. Appl. Mech. 77 675 (2007)

    Article  ADS  Google Scholar 

  6. E A Al-Lehaibi, Int. J. Acoust. Vib. 21 222 (2016)

    Google Scholar 

  7. A Sur, M Kanoria, Int. J. Comput. Methods 14 1750030 (2017)

    Article  MathSciNet  Google Scholar 

  8. H M Youssef, A A El-Bary, Mater. Phys. Mech. 40 158 (2018)

    Google Scholar 

  9. S Deswal, S Kumar and K Jain, Waves Random Complex Media 32 43 (2022)

  10. A K Khamis, A A El-Bary, H M Youssef and A M Nasr, Microsyst. Technol. 25 4731 (2019)

    Article  Google Scholar 

  11. Z N Xue, Y J Yu and X G Tian, Waves Random Complex Media 27 440 (2017)

    Article  ADS  Google Scholar 

  12. S Deswal, K K Kalkal, App. Math. Model. 39 7093 (2015)

    Article  Google Scholar 

  13. Z Hashin, NASA CR-1974. (1972)

  14. A M Freudenthal, J. Appl. Phys. 25 1110 (1954)

    Article  ADS  Google Scholar 

  15. A A Ilioushin, B E Pobedria, Russian, Nauka, Moscow 45 (1970)

    Google Scholar 

  16. M A Ezzat, A S El-Karamany, Can. J. Phys. 81 823 (2003)

    Article  ADS  Google Scholar 

  17. H H Sherief, M N Allam and M A El-Hagary, Int. J. Thermophys. 32 1271 (2011)

    Article  ADS  Google Scholar 

  18. M Kanoria, S H Mallik, Euro. J. Mech. A/Solids 29 695 (2010)

    Article  ADS  Google Scholar 

  19. Y Xu, Z D Xu, Y Q Guo, Y Dong and X Huang, J. Heat Transfer, 141 082002–1 (2019)

    Article  Google Scholar 

  20. C Li, X Tian and T He, Mech. Adv. Mater. Struct. 28 1797 (2021)

  21. M A K Molla, N Mondal and S H Mallik, J. Therm. Stress. 43 784 (2020)

    Article  Google Scholar 

  22. W Peng, Y Ma, C Li and T He, J. Therm. Stress. 43 38 (2020)

    Article  Google Scholar 

  23. W Nowacki, Proc. Vib. Prob. 15 105 (1974)

    Google Scholar 

  24. H H Sherief, F A Hamza and H A Saleh, Int. J. Eng. Sci. 42 591 (2004)

    Article  Google Scholar 

  25. M I Othman, S M Said, Arch. Thermodyn. 39 (2018)

  26. A E Abouelregal, Eur. Phys. J. Plus 135 263 (2020)

    Article  Google Scholar 

  27. I A Abbas, M Marin, Iran. J. Sci. Technol. Trans. Mech. Eng. 42 57 (2018)

    Article  Google Scholar 

  28. K Paul, B Mukhopadhyay, J. Solid Mech. 12 263 (2020)

    Google Scholar 

  29. E M Hussein, J. Therm. Stress. 43 1150 (2020)

    Article  Google Scholar 

  30. D K Sharma, D Thakur, V Walia and N Sarkar, J. Therm. Stress. 43 981 (2020)

    Article  Google Scholar 

  31. H Guo, T He, X Tian and F Shang, Waves Random Complex Media 31 2355 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  32. D K Sharma, D Thakur and N Sarkar, Waves Random Complex Media (2020). https://doi.org/10.1080/17455030.2020.1831100

    Article  Google Scholar 

  33. A M Zenkour, J. Ocean. Eng. Sci. 5 214 (2020)

    Article  Google Scholar 

  34. G Gilhotra, P K Sharma, Waves Random Complex Media (2021). https://doi.org/10.1080/17455030.2021.1976436

    Article  Google Scholar 

  35. N Abel, Oeuvres 1 11 (1881)

    Google Scholar 

  36. L Debnath, Int. J. Math. Edu. Sci. Tech. 35 487 (2004)

    Article  Google Scholar 

  37. M Caputo, J. Acoust. Soc. Am. 56 897 (1974)

    Article  ADS  Google Scholar 

  38. M Caputo, Geophys. J. Int. 13 529 (1967)

    Article  ADS  Google Scholar 

  39. Y Z Povstenko, Mech. Res. Commun. 37 436 (2010)

    Article  Google Scholar 

  40. H H Sherief, A M A El-Sayed and A M Abd El-Latief, Int. J. Solids Struct. 47 269 (2010)

  41. H M Youssef, J. Heat Transfer 132 061301-1 (2010)

    Google Scholar 

  42. M A Ezzat, M A Fayik, J. Therm. Stress. 31 851 (2011)

    Article  Google Scholar 

  43. S Choudhary, S Kumar and J S Sikka, Microsyst. Technol. 23 5435 (2017)

    Article  Google Scholar 

  44. H H Sherief, M A El-Hagary, Mech. Time. Depend. Mater. 24 179 (2019)

    Article  ADS  Google Scholar 

  45. S Deswal, K K Kalkal and S S Sheoran, Physica B Condens. Matter. 496 57 (2016)

    Article  ADS  Google Scholar 

  46. H H Sherief, E M Hussein, J. Therm. Stress. 43 440 (2020)

    Article  Google Scholar 

  47. D S Mashat, A M Zenkour and A E Abouelregal, Mech. Adv. Mater. Struct. 22 925 (2015)

    Article  Google Scholar 

  48. S Deswal, K K Kalkal and R Yadav, Appl. Math. Model. 49 144 (2017)

    Article  MathSciNet  Google Scholar 

  49. K K Kalkal, S Deswal, J. Mech. 30 383 (2014)

    Article  Google Scholar 

  50. H W Lord, Y Shulman, J. Mech. Phys. Solids. 15 299 (1967)

    Article  ADS  Google Scholar 

  51. A E Green, K A Lindsay, J. Elast. 2 1 (1972)

    Article  Google Scholar 

  52. R B Hetnarski, Encyclopedia of Thermal Stresses (Netherlands: Springer Reference) Ch[], p 567 (2014)

  53. H M Youssef, IMA J. Appl. Math. 71 383 (2006)

  54. D V Strunin, J. Appl. Mech. 68 816 (2001)

    Article  ADS  Google Scholar 

  55. A Bajpai, P K Sharma and R Kumar, J. Appl. Math. Mech. e202000321 (2021)

  56. H H Sherief, K A Helmy, Int. J. Eng. Sci. 40 587 (2002)

    Article  Google Scholar 

  57. R Yadav, K K Kalkal and S Deswal, J. Math. 2015 1 (2015)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics & Scientific Computing, National Institute of Technology, Hamirpur, Himachal Pradesh, 177005, India

    G Gilhotra & P K Sharma

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  1. G Gilhotra
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  2. P K Sharma
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Gilhotra, G., Sharma, P.K. Visco-thermodiffusive elastic interactions in plate within the framework of two-temperature fractional thermoelastic models. Indian J Phys 96, 3867–3879 (2022). https://doi.org/10.1007/s12648-022-02313-3

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  • DOI: https://doi.org/10.1007/s12648-022-02313-3

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