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A Study of Photo-Thermoelastic Wave in Semiconductor Materials with Spherical Holes Using Analytical-Numerical Methods

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Abstract

Analytical and numerical solutions are two basic tools in the study of photothermal interaction problems in semiconductor medium. In this paper, we compare the analytical solutions with the numerical solutions for thermal interaction in semiconductor mediums containing spherical cavities. The governing equations are given in the domain of Laplace transforms and the eigenvalues approaches are used to obtained the analytical solution. The numerical solutions are obtained by applying the implicit finite difference method (IFDM). A comparison between the numerical solutions and analytical solution are presented. It is found that the implicit finite difference method (IFDM) is applicable, simple and efficient for such problems.

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References

  1. Todorović D (2003) Photothermal and electronic elastic effects in microelectromechanical structures. Rev Sci Instrum 74(1):578–581

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Song Y, Cretin B, Todorovic DM, Vairac P (2008) Study of photothermal vibrations of semiconductor cantilevers near the resonant frequency. J Phys D Appl Phys 41(15):155106

    Article  Google Scholar 

  4. Abbas I, Hobiny A, Marin M (2020) Photo-thermal interactions in a semi-conductor material with cylindrical cavities and variable thermal conductivity. Journal of Taibah University for Science 14(1):1369–1376

    Article  Google Scholar 

  5. Hobiny A, Abbas I (2019) A GN model on photothermal interactions in a two-dimensions semiconductor half space. Results in Physics 15:102588

    Article  Google Scholar 

  6. Lotfy K, El-Bary A, Hassan W, Alharbi A, Almatrafi M (2020) Electromagnetic and Thomson effects during photothermal transport process of a rotator semiconductor medium under hydrostatic initial stress. Results in Physics 16:102983

    Article  Google Scholar 

  7. Lotfy K, Hassan W, El-Bary A, Kadry MA (2020) Response of electromagnetic and Thomson effect of semiconductor medium due to laser pulses and thermal memories during photothermal excitation. Results in Physics 16:102877

    Article  Google Scholar 

  8. Abbas IA, Aly K, Dahshan A (2018) Analytical solutions of plasma and Thermoelastic waves Photogenerated by a focused laser beam in a semiconductor material. Silicon 10(6):2609–2616

    Article  CAS  Google Scholar 

  9. Lotfy K, El-Bary A, Tantawi R (2019) Effects of variable thermal conductivity of a small semiconductor cavity through the fractional order heat-magneto-photothermal theory. The European Physical Journal Plus 134(6):280

    Article  Google Scholar 

  10. Alzahrani F (2020) The effects of variable thermal conductivity in semiconductor materials Photogenerated by a focused thermal shock. Mathematics 8(8):1230

    Article  Google Scholar 

  11. Alzahrani FS, Abbas IA (2019) Photo-thermo-elastic interactions without energy dissipation in a semiconductor half-space. Results in Physics 15:102805

    Article  Google Scholar 

  12. Hobiny AD, Abbas IA (2017) A study on photothermal waves in an unbounded semiconductor medium with cylindrical cavity. Mechanics of Time-Dependent Materials 21(1):61–72

    Article  CAS  Google Scholar 

  13. Das B, Ghosh D, Lahiri A (2021) Electromagnetothermoelastic analysis for a thin circular semiconducting medium. J Therm Stresses:1–14

  14. Mondal S, Sur A, Kanoria M (2019) Photo-thermo-elastic wave propagation under the influence of magnetic field in presence of memory responses. Mechanics Based Design of Structures and Machines:1–22

  15. Mondal S, Sur A (2020) Photo-thermo-elastic wave propagation in an orthotropic semiconductor with a spherical cavity and memory responses. Waves Random Complex Media:1–24

  16. Sarkar N, Mondal S, Othman MI (2020) L–S theory for the propagation of the photo-thermal waves in a semiconducting nonlocal elastic medium. Waves Random Complex Media:1–14

  17. Mukhopadhyay S, Kumar R (2009) Solution of a problem of generalized thermoelasticity of an annular cylinder with variable material properties by finite difference method. Computational Methods in Science and Technology 15(2):169–176

    Article  Google Scholar 

  18. Abd-Alla AM, Abo-Dahab SM, Kilany AA Finite difference technique to solve a problem of generalized thermoelasticity on an annular cylinder under the effect of rotation. Numerical Methods for Partial Differential Equations

  19. Patra S, Shit G, Das B (2020) Computational model on magnetothermoelastic analysis of a rotating cylinder using finite difference method. Waves Random Complex Media:1–18

  20. Abd-Alla A, El-Naggar A, Fahmy M (2003) Magneto-thermoelastic problem in non-homogeneous isotropic cylinder. Heat Mass Transf 39(7):625–629

    Article  Google Scholar 

  21. Abd-Alla A, Salama A, Abd-Ei-Salam M, Hosham H (2007) An implicit finite-difference method for solving the transient coupled thermoelasticity of an annular fin. Appl Math Inf Sci 1(1):79–93

    Google Scholar 

  22. Abbas IA (2014) The effects of relaxation times and a moving heat source on a two-temperature generalized thermoelastic thin slim strip. Can J Phys 93(5):585–590

    Article  Google Scholar 

  23. Zenkour AM, Abbas IA (2014) A generalized thermoelasticity problem of an annular cylinder with temperature-dependent density and material properties. Int J Mech Sci 84:54–60

    Article  Google Scholar 

  24. Abbas IA (2014) Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties. Meccanica 49(7):1697–1708

    Article  Google Scholar 

  25. Lotfy K (2019) Effect of variable thermal conductivity during the photothermal diffusion process of semiconductor medium. Silicon 11(4):1863–1873

    Article  CAS  Google Scholar 

  26. Lotfy K, Abo-Dahab S, Tantawy R, Anwar N (2019) Thermomechanical response model on a reflection photothermal diffusion waves (RPTD) for semiconductor medium. Silicon:1–11

  27. Hobiny A, Abbas I (2019) Fractional order GN model on photo-thermal interaction in a semiconductor plane. Silicon:1–8

  28. Itu C, Öchsner A, Vlase S, Marin MI (2019) Improved rigidity of composite circular plates through radial ribs. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 233(8):1585–1593

    Article  Google Scholar 

  29. Saeed T, Abbas I, Marin M (2020) A gl model on thermo-elastic interaction in a poroelastic material using finite element method. Symmetry 12(3):488

    Article  Google Scholar 

  30. Bhatti MM, Marin M, Zeeshan A, Ellahi R, Abdelsalam S (2020) Swimming of motile gyrotactic microorganisms and nanoparticles in blood flow through anisotropically tapered arteries. Front Phys 8:95

    Article  Google Scholar 

  31. Khan AA, Bukhari SR, Marin M, Ellahi R (2019) Effects of chemical reaction on third-grade MHD fluid flow under the influence of heat and mass transfer with variable reactive index. Heat Transfer Research 50(11)

  32. Marin M, Vlase S, Paun M (2015) Considerations on double porosity structure for micropolar bodies. AIP Adv 5(3):037113

    Article  Google Scholar 

  33. Marin M (1999) An evolutionary equation in thermoelasticity of dipolar bodies. J Math Phys 40(3):1391–1399

    Article  Google Scholar 

  34. El-Naggar A, Kishka Z, Abd-Alla A, Abbas I, Abo-Dahab S, Elsagheer M (2013) On the initial stress, magnetic field, voids and rotation effects on plane waves in generalized thermoelasticity. J Comput Theor Nanosci 10(6):1408–1417

    Article  CAS  Google Scholar 

  35. Abbas IA, Marin M (2017) Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating. Physica E: Low-dimensional Systems and Nanostructures 87:254–260

    Article  CAS  Google Scholar 

  36. Palani G, Abbas I (2009) Free convection MHD flow with thermal radiation from an impulsively-started vertical plate. Nonlinear Analysis: Modelling and Control 14(1):73–84

    Article  Google Scholar 

  37. Sarkar N, Mondal S (2019) Transient responses in a two-temperature thermoelastic infinite medium having cylindrical cavity due to moving heat source with memory-dependent derivative. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 99(6):e201800343

    Article  Google Scholar 

  38. Song Y, Bai J, Ren Z (2012) Study on the reflection of photothermal waves in a semiconducting medium under generalized thermoelastic theory. Acta Mech 223(7):1545–1557

    Article  Google Scholar 

  39. Mandelis A, Nestoros M, Christofides C (1997) Thermoelectronic-wave coupling in laser photothermal theory of semiconductors at elevated temperatures. Opt Eng 36(2):459–468

    Article  CAS  Google Scholar 

  40. Youssef HM, El-Bary AA (2018) Theory of hyperbolic two-temperature generalized thermoelasticity. Mater Phys Mech 40:158–171

    Google Scholar 

  41. Zenkour AM, Abbas IA (2014) Nonlinear transient thermal stress analysis of temperature-dependent hollow cylinders using a finite element model. Int J Struct Stab Dyn 14(07):1450025

    Article  Google Scholar 

  42. Debnath L, Bhatta D (2014) Integral transforms and their applications. Chapman and Hall/CRC

  43. Das NC, Lahiri A, Giri RR (1997) Eigenvalue approach to generalized thermoelasticity. Indian Journal of Pure and Applied Mathematics 28(12):1573–1594

    Google Scholar 

  44. Abbas IA (2014) Eigenvalue approach in a three-dimensional generalized thermoelastic interactions with temperature-dependent material properties. Comput Math Appl 68(12):2036–2056

    Article  Google Scholar 

  45. Abbas IA (2014) Eigenvalue approach for an unbounded medium with a spherical cavity based upon two-temperature generalized thermoelastic theory. J Mech Sci Technol 28(10):4193–4198

    Article  Google Scholar 

  46. Abbas IA (2015) A dual phase lag model on thermoelastic interaction in an infinite fiber-reinforced anisotropic medium with a circular hole. Mechanics Based Design of Structures and Machines 43(4):501–513

    Article  Google Scholar 

  47. Stehfest H (1970) Algorithm 368: numerical inversion of Laplace transforms [D5]. Commun ACM 13(1):47–49

    Article  Google Scholar 

  48. Song Y, Todorovic DM, Cretin B, Vairac P, Xu J, Bai J (2014) Bending of semiconducting cantilevers under Photothermal excitation. Int J Thermophys 35(2):305–319

    Article  CAS  Google Scholar 

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Acknowledgments

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. (G:104-130-1441). The authors, therefore, acknowledge with thanks DSR for technical and financial support.

Funding

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. (G:104–130-1441).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Faris S. Alzahrani & Ibrahim A. Abbas

  2. Department of mathematics, Faculty of Science, Sohag University, Sohag, Egypt

    Ibrahim A. Abbas

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  1. Faris S. Alzahrani
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  2. Ibrahim A. Abbas
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Correspondence to Ibrahim A. Abbas.

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Alzahrani, F.S., Abbas, I.A. A Study of Photo-Thermoelastic Wave in Semiconductor Materials with Spherical Holes Using Analytical-Numerical Methods. Silicon 14, 4027–4033 (2022). https://doi.org/10.1007/s12633-021-01178-1

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  • DOI: https://doi.org/10.1007/s12633-021-01178-1

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