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Photothermal-induced interactions in a semiconductor solid with a cylindrical gap due to laser pulse duration using a fractional MGT heat conduction model

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Abstract

Optical and photo-thermal effects have emerged in many fields, including thermal characterization, spectroscopy, transportation, and non-destructive examinations. In this study, the Moore-Gibson-Thompson (MGT) thermoelastic model is used to explore the photo-thermal coupling of an isotropic, homogeneous, semiconducting and thermomagnetic solid. The heat conduction law is modified to include the time derivative of fractional order and theoretically formulate the system of governing equations. Using the extended Mittag–Leffler functions as nonsingular kernels, the Atangana and Baleanu derivatives considers the features of fractional derivatives. As measured by an external reference frame, it is taken into account that the medium rotates with a constant angular velocity about the axis of symmetry. The cavity boundaries undergo thermal shock and time-varying heat flux. It has been shown that the Laplace transform method is a powerful technique for solving such problems that link the plasma and heat transfer with phase delays. It is finally aimed to describe the numerical results for changes in carrier density as a function of time and radial distance, temperature increment, strain, thermal stresses, and displacement using a photo-induced carrier with different values of physical relaxation time and fractional operator.

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References

  1. von Allmen, M., Blatter, A.: Laser beam interactions with materials. Springer, Berlin (1995)

    Book  Google Scholar 

  2. Rekhi, S., Tempere, J., Silvera, I.F.: Temperature determination for nanosecond pulsed laser heating. Rev. Sci. Instrum. 74(8), 3820–3825 (2003)

    Article  Google Scholar 

  3. Anzellini, S., Boccato, S.: A practical review of the laser-heated diamond anvil cell for university laboratories and synchrotron applications. Crystals 10(6), 459 (2020)

    Article  Google Scholar 

  4. Niemeyer, M., Bessel, P., Rusch, P., Himstedt, R., Kranz, D., Borg, H., Bigall, N.C.: Dorfs, D Nanosecond pulsed laser-heated nanocrystals inside a metal-organic framework matrix. Chem. Nano. Mat. 8, e20220016 (2022)

    Google Scholar 

  5. Nettesheim, S., Zenobi, R.: Pulsed laser heating of surfaces: nanosecond timescale temperature measurement using black body radiation. Chem. Phys. Lett. 255(1–3), 39–44 (1996)

    Article  Google Scholar 

  6. Yan, J., Karpovych, V., Sulkes, M.: Pulsed laser surface heating: a tool for studying pyrolysis product chemistry in molecular beams. Chem. Phys. Lett. 762, 138122 (2021)

    Article  Google Scholar 

  7. Pasternak, S., Aquilanti, G., Pascarelli, S., Poloni, R., Canny, B., Coulet, M.-V., Zhang, L.: A diamond anvil cell with resistive heating for high pressure and high temperature x-ray diffraction and absorption studies. Rev. Sci. Instrum. 79(8), 085103 (2008)

    Article  Google Scholar 

  8. Yilbas, B.S., Al-Dweik, A.Y., Al-Aqeeli, N., Al-Qahtani, H.M.: Laser pulse heating of surfaces and thermal stress analysis. Springer International Publishing, Verlag (2014)

    Book  Google Scholar 

  9. Zhang, Z., Zhang, Q., Wang, Y., Xu, J.: Modeling of the temperature field in nanosecond pulsed laser ablation of single crystalline diamond. Diam. Relat. Mater. 116, 108402 (2021)

    Article  Google Scholar 

  10. Abouelregal, A.E., Sedighi, H.M., Shirazi, A.H.: The effect of excess carrier on a semiconducting semi-infinite medium subject to a normal force by means of Green and Naghdi approach. Silicon 14, 4955–4967 (2022)

    Article  Google Scholar 

  11. Gordon, J.P., Leite, R.C.C., Moore, R.S., Porto, S.P.S., Whinnery, J.R.: Long-transient effects in lasers with inserted liquid samples. J. Appl. Phys. 36(1), 3–8 (1965)

    Article  Google Scholar 

  12. Todorović, D.M., Nikolić, P.M., Bojičić, A.I.: Photoacoustic frequency transmission technique: electronic deformation mechanism in semiconductors. J. Appl. Phys. 85(11), 7716–7726 (1999)

    Article  Google Scholar 

  13. Song, Y., Todorovic, D.M., Cretin, B., Vairac, P.: Study on the generalized thermoelastic vibration of the optically excited semiconducting microcantilevers. Int. J. Solid Struct. 47, 1871–1875 (2010)

    Article  MATH  Google Scholar 

  14. Song, Y.Q., Bai, J.T., Ren, Z.Y.: Study on the reflection of photo-thermal waves in a semiconducting medium under generalized thermoelastic theory. Acta Mech. 2010(223), 1545–1557 (2012)

    Article  MATH  Google Scholar 

  15. Abouelregal, A.E., Moaaz, O., Khalil, K.M., Abouhawwash, M., Nasr, M.E.: Micropolar thermoelastic plane waves in microscopic materials caused by hall-current effects in a two-temperature heat conduction model with higher-order time derivatives. Arch. Appl. Mech. (2023). https://doi.org/10.1007/s00419-023-02362-y

    Article  Google Scholar 

  16. Todorović, D., Plasma, D.M.: Thermal, and elastic waves in semiconductors. Rev. Sci. Instrum. 74(1), 582–585 (2003)

    Article  Google Scholar 

  17. Diethelm, K., Garrappa, R., Giusti, A., Stynes, M.: Why fractional derivatives with nonsingular kernels should not be used. Fract. Calc. Appl. Anal. 23, 610–634 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  18. Caputo, A., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1, 73–85 (2015)

    Google Scholar 

  19. Atangana, A., Baleanu, D.: New fractional derivatives with nonlocal and nonsingular kernel: theory and application to heat transfer model. Therm. Sci. 20(2), 763–769 (2016)

    Article  Google Scholar 

  20. Atangana, A., Baleanu, D.: Caputo–Fabrizio derivative applied to groundwater flow within confined aquifer. J. Eng. Mech. 2016, D4016005 (2016)

    Google Scholar 

  21. Al-Refai, M.: On weighted Atangana–Baleanu fractional operators. Adv. Diff. Equ. 2020(1), 3 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hattaf, K.: A new generalized definition of fractional derivative with nonsingular kernel. Computation 8, 1–9 (2020)

    Article  Google Scholar 

  23. Morales-Delgado, V.F., Gómez-Aguilar, J.F., Saad, K.M., Khan, M.A., Agarwal, P.: Analytic solution for oxygen diffusion from capillary to tissues involving external force effects: a fractional calculus approach. Phys. A 523, 48–65 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  24. Saad, K.M., Baleanu, D., Atangana, A.: New fractional derivatives applied to the Korteweg–de Vries and Korteweg–de Vries–Burger’s equations. Comput. Appl. Math. 37(4), 5203–5216 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  25. Khan, M.A.: The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators. Adv. Mech. Eng. 11(7), 1–12 (2019)

    Article  Google Scholar 

  26. Nadeem, M., He, J.-H., He, C.-H., Sedighi, H.M., Shirazi, A.H.: A numerical solution of nonlinear fractional newell-whitehead-segel equation using natural transform. Twms J. Pure Appl. Math. 13(2), 168–182 (2022)

    Google Scholar 

  27. Baleanu, D., Fernandez, A.: On some new properties of fractional derivatives with Mittag-Leffler kernel. Commun. Nonlinear Sci. Numer. Simul. 59, 444–462 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  28. Mandelis, A.: Diffusion waves and their use. Phys. Today 53(8), 29–36 (2000)

    Article  Google Scholar 

  29. Kaur, I., Singh, K.: Thermoelastic dam** in a thin circular transversely isotropic Kirchhoff-Love plate due to GN theory of type III. Arch. Appl. Mech. 91, 2143–2157 (2021)

    Article  Google Scholar 

  30. Biot, M.A.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27, 240–253 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  31. Lord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15(5), 299–309 (1967)

    Article  MATH  Google Scholar 

  32. Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2(1), 1–7 (1972)

    Article  MATH  Google Scholar 

  33. Green, A.E., Naghdi, P.M.: A re-examination of the basic postulates of thermomechanics. Proc. R. Soc. Math. Phys. Eng. Sci. 432, 171–194 (1991)

    MathSciNet  MATH  Google Scholar 

  34. Green, A.E., Naghdi, P.M.: On undamped heat waves in an elastic solid. J. Therm. Stress. 15(2), 253–264 (1992)

    Article  MathSciNet  Google Scholar 

  35. Green, A.E., Naghdi, P.M.: Thermoelasticity without energy dissipation. J. Elast. 31(3), 189–208 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  36. Akgöz, B., Civalek, Ö.: Buckling analysis of functionally graded tapered microbeams via rayleigh-ritz method. Mathematics 10, 4429 (2022)

    Article  Google Scholar 

  37. Abouelregal, A.E., Ersoy, H., Civalek, Ö.: Solution of Moore–Gibson–Thompson equation of an unbounded medium with a cylindrical hole. Mathematics 9(13), 1536 (2021)

    Article  Google Scholar 

  38. Youssef, H.M., Al-Lehaibi, E.A.N.: 2-D mathematical model of hyperbolic two-temperature generalized thermoelastic solid cylinder under mechanical damage effect. Arch. Appl. Mech. 92, 945–960 (2022)

    Article  Google Scholar 

  39. Dastjerdi, S., Akgöz, B., Civalek, Ö.: On the effect of viscoelasticity on behavior of gyroscopes. Int. J. Eng. Sci. 149, 103236 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  40. Abbas, I.A., Alzahrani, F.S.: A Green–Naghdi model in a 2D problem of a mode I crack in an isotropic thermoelastic plate. Phys. Mesomech. 21(2), 99–103 (2018)

    Article  Google Scholar 

  41. Lasiecka, I., Wang, X.: Moore–Gibson–Thompson equation with memory, part II: general decay of energy. J. Diff. Eqns. 259, 7610–7635 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  42. Quintanilla, R.: Moore-Gibson-Thompson thermoelasticity. Math. Mech. Solids 24, 4020–4031 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  43. Quintanilla, R.: Moore-Gibson-Thompson thermoelasticity with two temperatures. Appl. Eng. Sci. 1, 100006 (2020)

    Google Scholar 

  44. Abouelregal, A.E., Ahmed, I.-E., Nasr, M.E., Khalil, K.M., Zakria, A., Mohammed, F.A.: Thermoelastic processes by a continuous heat source line in an infinite solid via Moore–Gibson–Thompson thermoelasticity. Materials 13(19), 4463 (2020)

    Article  Google Scholar 

  45. Abouelregal, A.E., Ahmad, H., Nofal, T.A., Abu-Zinadah, H.: Moore–Gibson–Thompson thermoelasticity model with temperature-dependent properties for thermo-viscoelastic orthotropic solid cylinder of infinite length under a temperature pulse. Phys. Scr. 96(10), 105201 (2021)

    Article  Google Scholar 

  46. Aboueregal, A.E., Sedighi, H.M.: The effect of variable properties and rotation in a visco-thermoelastic orthotropic annular cylinder under the Moore–Gibson–Thompson heat conduction model. Proc. Instit. Mech. Eng. Part L J. Mater. Des. Appl. 235(5), 1004–1020 (2021)

    Google Scholar 

  47. Aboueregal, A.E., Sedighi, H.M., Shirazi, A.H., Malikan, M., Eremeyev, V.A.: Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on nonlocal Moore–Gibson–Thompson approach. Continuum Mech. Thermodyn. 34, 1067–1085 (2022)

    Article  MathSciNet  Google Scholar 

  48. Abouelregal, A.E., Ahmad, H.: A modified thermoelastic fractional heat conduction model with a single-lag and two different fractional-orders. J. Appl. Comput. Mech. 7(3), 1676–1686 (2021). https://doi.org/10.22055/jacm.2020.33790.2287

    Article  Google Scholar 

  49. Atta, D.: Thermal diffusion responses in an infinite medium with a spherical cavity using the Atangana–Baleanu fractional operator. J. Appl. Comput. Mech. 8(4), 1358–1369 (2022). https://doi.org/10.22055/jacm.2022.40318.3556

    Article  MathSciNet  Google Scholar 

  50. Abouelregal, A.E., Sedighi, H.M., Sofiyev, A.H.: Modeling photoexcited carrier interactions in a solid sphere of a semiconductor material based on the photothermal Moore–Gibson–Thompson model. Appl. Phys. A 127(11), 1–4 (2021)

    Article  Google Scholar 

  51. Abouelregal, A.E., Sedighi, H.M.: A new insight into the interaction of thermoelasticity with mass diffusion for a half-space in the context of Moore–Gibson–Thompson thermodiffusion theory. Appl. Phys. A 127(8), 1–4 (2021)

    Article  Google Scholar 

  52. Sladek, J., Sladek, V., Repka, M.: The heat conduction in nanosized structures. Phys. Mesomech. 24(5), 611–617 (2021)

    Article  Google Scholar 

  53. Al-Basyouni, K.S., Dakhel, B., Ghandourah, E., Algarni, A.: An analytical solution for the problem of stresses in magneto-piezoelectric thermoelastic material under the influence of rotation. Phys. Mesomech. 23(4), 362–368 (2020)

    Article  Google Scholar 

  54. Yavari, A., Abolbashari, M.H.: Generalized thermoelastic waves propagation in non-uniform rational B-spline rods under quadratic thermal shock loading using isogeometric approach. Iran. J. Sci. Technol. Trans. Mech. Eng. 46, 43–59 (2022). https://doi.org/10.1007/s40997-020-00391-4

    Article  Google Scholar 

  55. Abouelregal, A.E., Atta, D., Sedighi, H.M.: Vibrational behavior of thermoelastic rotating nanobeams with variable thermal properties based on memory-dependent derivative of heat conduction model. Arch. Appl. Mech.1–24 (2022).

  56. Vasilev, A.N., Sandomirskii, V.B.: Photoacoustic effects in finite semiconductors. Sov. Phys. Semicond. 18, 1095 (1984)

    Google Scholar 

  57. Cattaneo, C.: A form of heat-conduction equations which eliminates the paradox of instantaneous propagation. Compt. Rend 247, 431–433 (1958)

    MATH  Google Scholar 

  58. Vernotte, P.: Les paradoxes de la theorie continue de l’equation de lachaleur. Compt. Rend 246, 3154–3155 (1958)

    MATH  Google Scholar 

  59. Vernotte, P.: Some possible complications in the phenomena of thermal conduction. Compt. Rend 252, 2190–2191 (1961)

    Google Scholar 

  60. Caputo, M., Mauro, F.: A new definition of fractional derivative without singular kernel. Prog Fract Differ Appl 1, 1–13 (2015)

    Google Scholar 

  61. Caputo, M., Fabrizio, M.: On the notion of fractional derivative and applications to the hysteresis phenomena. Meccanica 52, 3043–3052 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  62. Nadeem, M., He, J.H., He, C.H., Sedighi, H.M., Shirazi, A.: A numerical solution of nonlinear fractional newell-whitehead-segel equation using natural transform. Twms J. Pure Appl. Math. 13(2), 168–82 (2022)

    Google Scholar 

  63. Bavi, R., Hajnayeb, A., Sedighi, H.M., Shishesaz, M.: Simultaneous resonance and stability analysis of unbalanced asymmetric thin-walled composite shafts. Int. J. Mech. Sci. 217, 107047 (2022)

    Article  Google Scholar 

  64. Bagheri, R.: Analytical solution of cracked functionally graded magneto-electro-elastic half-plane under impact loading. Iran. J. Sci. Technol. Trans. Mech. Eng. 45(4), 911–925 (2021)

    Article  Google Scholar 

  65. Sae-Long, W., Limkatanyu, S., Sukontasukkul, P., Damrongwiriyanupap, N., Rungamornrat, J., Prachasaree, W.: Fourth-order strain gradient bar-substrate model with nonlocal and surface effects for the analysis of nanowires embedded in substrate media. Facta Univ. Ser. Mech. Eng. 19(4), 657–680 (2021)

    Google Scholar 

  66. Nasrollah Barati, A.H., Etemadi Haghighi, A.A., Haghighi, S., Maghsoudpour, A.: Free and forced vibration analysis of shape memory alloy annular circular plate in contact with bounded fluid. Iran. J. Sci. Technol. Trans. Mech. Eng. 46(4), 1015–1030 (2022)

    Article  Google Scholar 

  67. Honig, G., Hirdes, U.: A method for the numerical inversion of laplace transform. J. Comp. Appl. Math. 10, 113–132 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  68. Tzou, D.Y.: Macro-to micro-scale heat transfer: the lagging behavior. Taylor & Francis, Abingdon, UK (1997)

    Google Scholar 

  69. Sumelka, W., Blaszczyk, T.: Fractional continua for linear elasticity. Arch. Mech. 66(3), 147–172 (2014)

    MathSciNet  MATH  Google Scholar 

  70. Meng, R., Yin, D., Zhou, C., Wu, H.: Fractional description of time-dependent mechanical property evolution in materials with strain softening behavior. Appl. Math. Model. 40(1), 398–406 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  71. Abouelregal, A.E.: Modified fractional photo-thermoelastic model for a rotating semiconductor half-space subjected to a magnetic field. Silicon 12, 2837–2850 (2020)

    Article  Google Scholar 

  72. Aboueregal, A.E., Sedighi, H.M.: The effect of variable properties and rotation in a visco-thermoelastic orthotropic annular cylinder under the Moore Gibson Thompson heat conduction model. Proc. Instit. Mech. Eng. Part L. J. Mater. Des. Appl. 235(5), 1004–1020 (2021)

    Google Scholar 

  73. Babič, M., Marinkovic, D., Bonfanti, M., Calì, M.: Complexity modeling of steel-laser-hardened surface microstructures. Appl. Sci. 12, 2458 (2022)

    Article  Google Scholar 

  74. Madić, M., Gostimirović, M., Rodić, D., Radovanović, M., Coteaţă, M.: Mathematical modelling of the CO2 laser cutting process using genetic programming. Facta Univ. Ser Mech Eng 20(3), 665–676 (2022)

    Google Scholar 

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Funding

Ahmed E. Abouelregal would like to thank the Deanship of Scientific Research at Jouf University for funding this work through research grant No. (DSR2022-RG-0137). He would also like to extend our sincere thanks to the College of Science and Arts in Al-Qurayyat for its technical support.

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Authors and Affiliations

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

    Ahmed E. Abouelregal

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

    Ahmed E. Abouelregal & Sami F. Megahid

  3. Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, 61357-43337, Iran

    Hamid M. Sedighi

  4. Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Hamid M. Sedighi

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  1. Ahmed E. Abouelregal
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Correspondence to Hamid M. Sedighi.

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Abouelregal, A.E., Sedighi, H.M. & Megahid, S.F. Photothermal-induced interactions in a semiconductor solid with a cylindrical gap due to laser pulse duration using a fractional MGT heat conduction model. Arch Appl Mech 93, 2287–2305 (2023). https://doi.org/10.1007/s00419-023-02383-7

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