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Photothermoelastic survey with memory-dependent response for a rotating solid cylinder under varying heat flux via dual phase lag model

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Abstract

Studying the effects of plasma and heat on semiconductor structures involves simulating a complex system using simultaneous analysis of heat waves, carrier densities and elastic wave equations. Despite the paramount importance of this subject, it still lacks further research and investigation due to the paucity of research work that has been conducted. This paper investigates plasma–photothermoelastic interactions in isotropic and homogeneous semiconductor solids using a novel generalised thermoelasticity model. The model is constructed on the basis of the concept of memory-dependent derivative (MDD) dual-phase lag thermoelasticity and coupled plasma-thermal wave equation. By employing the proposed model, the transient response of a semiconducting solid cylinder rotating axially in an applied magnetic field and subjected to time-dependent heat flux was investigated. The Laplace transform technique was used to solve the derived system of equations and to obtain the different domains, and the numerical results were graphically displayed. The effects of time delay, kernel function and rotation were examined. The obtained numerical results were also compared with different models of thermoelasticity with MDD.

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References

  1. D Y Tzou, J. Heat Transfer 117(1), 8 (1995), https://doi.org/10.1115/1.2822329

    Article  Google Scholar 

  2. L M Jiji, Heat conduction (Springer, New York, 2009), https://doi.org/10.1007/978-3-642-01267-9

    Book  MATH  Google Scholar 

  3. J H Lienhard IV and J H Lienhard V, A heat transfer textbook 3rd Edn (Phlogiston Press, Cambridge, MA, 2008)

    MATH  Google Scholar 

  4. D Y Tzou (CRC Press, Boca Raton, 1996)

  5. D Chandrasekharaiah, Appl. Mech. Rev. 51(12), 705 (1998), https://doi.org/10.1115/1.3098984

    Article  ADS  Google Scholar 

  6. K Zakaria, M A Sirwah, A E Abouelregal and A F Rashid, Int. J. Appl. Mech. 13(07), 2150079 (2021), https://doi.org/10.1142/S1758825121500794

    Article  Google Scholar 

  7. P Antaki, Int. J. Heat Mass Transfer 40, 3247 (1997), https://doi.org/10.1016/S0017-9310(96)00351-1

    Article  Google Scholar 

  8. A E Abouelregal, K Zakaria, M A Sirwah, H Ahmad and A F Rashid, Int. J. Mod. Phys. C., https://doi.org/10.1142/S0129183122500735

  9. C Cattaneo and Sulla Conduzione Del Calore, In: A Pignedoli (eds) Some aspects of diffusion theory (Springer, Berlin, Heidelberg, 2011) Vol. 42, https://doi.org/10.1007/978-3-642-11051-1_5

    Chapter  Google Scholar 

  10. P Vernotte, Comptes Rendus de l 'Academie Bulg. des Sci. 246, 3154 (1958)

  11. D Y Tzou, J. Thermophys. Heat Transfer 9(4), 686 (1995), https://doi.org/10.2514/3.725

    Article  Google Scholar 

  12. M Chester, Phys. Rev. 131, 2013 (1963), https://doi.org/10.1103/PhysRev.131.2013

    Article  ADS  Google Scholar 

  13. H W Lord and Y Shulman, J. Mech. Phys. Solids 15(5), 299 (1967), https://doi.org/10.1016/0022-5096(67)90024-5

    Article  ADS  Google Scholar 

  14. A Green and K Lindsay, J. Elast. 2(1), 1 (1972), https://doi.org/10.1007/BF00045689

    Article  Google Scholar 

  15. A Green and P Naghdi, J. Elast. 31(3), 189 (1993)

    Article  Google Scholar 

  16. S R Choudhuri, J. Therm. Stresses 30(3), 231 (2007), https://doi.org/10.1080/01495730601130919

    Article  Google Scholar 

  17. A Miranville and R Quintanilla, Appl. Math. Optim. 63(1), 133 (2011), https://doi.org/10.1007/s00245-010-9114-9

    Article  MathSciNet  Google Scholar 

  18. A Green and P Naghdi, Proc. R. Soc. London. Ser A: Math. Phys. Sci. 432, 171 (1885), https://doi.org/10.1098/rspa.1991.0012

    Article  ADS  Google Scholar 

  19. M A Ezzat, A S El Karamany and M A Fayik, Arch. Appl. Mech. 82(4), 557 (2012), https://doi.org/10.1007/s00419-011-0572-6

    Article  ADS  Google Scholar 

  20. H Scher and E W Montroll, Phys. Rev. B 12, 2455 (1975), https://doi.org/10.1103/PhysRevB.12.2455

    Article  ADS  Google Scholar 

  21. B Li and J Wang, Phys. Rev. Lett. 91, 044301-1 (2003), https://doi.org/10.1103/PhysRevLett.91.044301

    Article  ADS  Google Scholar 

  22. J L Wang and H F Li, Comput. Math. Appl. 62(3), 1562 (2011), https://doi.org/10.1016/j.camwa.2011.04.028

    Article  MathSciNet  Google Scholar 

  23. Y J Yu, X G Tian and T J Lu, Eur. J. Mech. A/Solids 42, 188 (2013), https://doi.org/10.1016/j.euromechsol.2013.05.006

    Article  ADS  MathSciNet  Google Scholar 

  24. A Soleiman, A E Abouelregal and H Ahmad, Phys. Scr. (2020), https://doi.org/10.1088/1402-4896/abbfcb

    Article  Google Scholar 

  25. P Chadwick, Progress in solid mechanics (North Holland, Amsterdam, 1960)

  26. S Kaliski and W Nowacki, Bull. Acad. Pol. Sci. (Sci. Technol.), 1, l0 (1962), https://doi.org/10.1016/0020-7225(63)90031-4

    Article  Google Scholar 

  27. S Mondal, Int. J. Comput. Methods 17, 1950072 (2020), https://doi.org/10.1142/S0219876219500725

    Article  MathSciNet  Google Scholar 

  28. J N Sharma and D Chand, Int. J. Eng. Sci. 26, 951 (1988), https://doi.org/10.1016/0020-7225(90)90057-P

    Article  Google Scholar 

  29. M A Ezzat, M I A Othman and A A Smaan, Int. J. Eng. Sci. 39, 1383 (2001), https://doi.org/10.1016/j.ijsolstr.2006.06.035

    Article  Google Scholar 

  30. A E Abouelregal and H Ahmad, Phys. Scr. 95, 125501 (2020), https://doi.org/10.1088/1402-4896/abc03d

    Article  ADS  Google Scholar 

  31. A C Tam, Rev. Mod. Phys. 58, 381 (1986), https://doi.org/10.1103/RevModPhys.58.381

    Article  ADS  Google Scholar 

  32. B Busse and A Rosencwaig, Appl. Phys. Lett. 36, 815 (1980), https://doi.org/10.1063/1.91327

    Article  ADS  Google Scholar 

  33. J Baumann and R Tilgner, J. Appl. Phys. 58, 1982 (1985), https://doi.org/10.1063/1.336006

    Article  ADS  Google Scholar 

  34. F Lepoutre, D Fournier and A C Boccara, J. Appl. Phys. 57, 1009 (1985), https://doi.org/10.1063/1.334540

    Article  ADS  Google Scholar 

  35. Y Song, D M Todorovic, B Cretin and P Vairac, Int. J. Solids Struct. 47(14), 1871 (2010), https://doi.org/10.1016/j.ijsolstr.2010.03.020

    Article  Google Scholar 

  36. Y Song, D M Todorovic, B Cretin, P Vairac, J Xu and J Bai, Int. J. Thermophys. 35(2), 305 (2014), https://doi.org/10.1007/s10765-014-1572-x

    Article  ADS  Google Scholar 

  37. D M Todorovic, Rev. Sci. Instrum. 74, 582 (2003), https://doi.org/10.1063/1.1523133

    Article  ADS  Google Scholar 

  38. A E Abouelregal, Silicon 12, 2837 (2020), https://doi.org/10.1007/s12633-020-00380-x

    Article  Google Scholar 

  39. A D Hobiny and I A Abbas, Phys. Mesomech. 23, 167 (2020), https://doi.org/10.1134/S1029959920020083

    Article  Google Scholar 

  40. K Z Elsherbeny, A E Abouelregal, S M Abo-Dahab and A F Rashid, J. Comput. Theor. Nanosci. 13(7), 4493 (2016), https://doi.org/10.1166/jctn.2016.5309

    Article  Google Scholar 

  41. M Biot, J. Appl. Phys. 27, 240 (1956), https://doi.org/10.1063/1.1722351

    Article  ADS  MathSciNet  Google Scholar 

  42. M Caputo, J. Acoust. Soc. Am. 56, 897 (1974), https://doi.org/10.1121/1.1903344

    Article  ADS  Google Scholar 

  43. K Diethelm, The analysis of fractional differential equations. Lecture notes in mathematics (Springer-Verlag, Berlin, 2010), https://doi.org/10.1007/978-3-642-14574-2

    Book  MATH  Google Scholar 

  44. T Saeed and I A Abbas, Appl. Math. Mech. 41, 927 (2020), https://doi.org/10.1007/s10483-020-2612-8

    Article  Google Scholar 

  45. A Mandelis, M Nestoros and C Christofides, Opt. Eng. 36, 459 (1997), https://doi.org/10.1117/1.601217

    Article  ADS  Google Scholar 

  46. K Zakaria, M A Sirwah, A E Abouelregal and A F Rashid, Silicon 13, 573 (2021), https://doi.org/10.1007/s12633-020-00451-z

    Article  Google Scholar 

  47. M A Ezzat, A S El-Karamany and A A El-Bary, Mech. Adv. Mater. Struct. (2016), https://doi.org/10.1080/15376494.2016.1196793

    Article  Google Scholar 

  48. R E Wagner and A Mandelis, Semicond. Sci. Technol. 11, 289 (1996), https://doi.org/10.1088/0268-1242/11/3/006

    Article  ADS  Google Scholar 

  49. M Schoenberg and D Censor, Q. J. Appl. Math. 31(1), 115 (1973)

    Article  Google Scholar 

  50. S S Sheoran, S Kundu and P Kundu, Int. J. Adv. Appl. Math. Mech. 3, 91 (2016)

    MathSciNet  Google Scholar 

  51. A M Zenkour and A E Abouelregal, J. Therm. Sci. Technol. 10, JTST0019 (2015), https://doi.org/10.1299/jtst.2015jtst0019

    Article  Google Scholar 

  52. G Honig and U Hirdes, J. Comput. Appl. Math. 10, 113 (1984), https://doi.org/10.1016/0377-0427(84)90075-X

    Article  MathSciNet  Google Scholar 

  53. D Y Tzou, Macro-to-microscale heat transfer: The lagging behavior (John Wiley & Sons, 2014)

  54. S Xia, J Cai, X Zhang, J Li, G Jin and X Chang, Pramana – J. Phys. 95, 171 (2021), https://doi.org/10.1007/s12043-021-02203-z

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The corresponding author, Ali F Rashid, wishes to thank Prof. Ahmed E Abouelregal for kindly providing precious notes and recommendations on this paper. Furthermore, special thanks are due to Prof. Kadry Zakaria and Prof. Magdy A Sirwah for their revision and valuable notes.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Tanta University, Tanta, 31511, Egypt

    Kadry Zakaria, Magdy A Sirwah & Ali F Rashid

  2. Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayat, Saudi Arabia

    Ahmed E Abouelregal

  3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Ahmed E Abouelregal

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  1. Kadry Zakaria
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  2. Magdy A Sirwah
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  3. Ahmed E Abouelregal
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Correspondence to Ahmed E Abouelregal.

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Zakaria, K., Sirwah, M.A., Abouelregal, A.E. et al. Photothermoelastic survey with memory-dependent response for a rotating solid cylinder under varying heat flux via dual phase lag model. Pramana - J Phys 96, 219 (2022). https://doi.org/10.1007/s12043-022-02452-6

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