DOI QR코드

DOI QR Code

Thermomechanical interactions in a transversely isotropic thermoelastic media with diffusion due to inclined load

  • Parveen Lata (Department of Mathematics, Punjabi University) ;
  • Heena (Department of Mathematics, Punjabi University)
  • 투고 : 2023.02.02
  • 심사 : 2024.04.11
  • 발행 : 2024.05.10

초록

This research deals with the study of two-dimensional deformation in transversely isotropic thermoelastic diffusion medium. This investigation integrates the effect of diffusion and thermal effects in transversely isotropic thermoelastic solids under inclined load. Inclined load is taken as linear combination of normal load and tangential load. Laplace and Fourier transformation techniques are employed to transform the physical domain and then transformed solutions are inverted with the aid of numerical inversion techniques. Concentrated and distributed load are considered to exemplify its utility. Graphical representation of variation in displacement, stresses, temperature and concentration distribution with distance is depicted by taking inclination at different angles. Some particular cases are studied.

키워드

참고문헌

  1. Abbas, I.A. (2014), "The effect of thermal source with mass diffusion in a transversely isotropic thermoelastic infinite medium", J. Measure. Eng., 2(4), 175-184. 
  2. Abbas, I.A. (2015), "Generalized thermoelastic interaction in functionally graded material with fractional order three -phase lag heat transfer", J. Central South Univ., 22, 1606-1613. https://doi.org/10.1007/s11771-015-2677-5 . 
  3. Abbas, I.A., Hobiny, A. and Marin, M. (2020), "Photo-thermal interactions in a semi-conductor materials with cylindrical cavities and variable thermal conductivity", J. Taibah Univ. Sci., 14(1), 1369-1376. https://doi.org/10.1080/16583655.2020.1824465. 
  4. Abbas, I.A., Marin, M., Abouelregal, E.I. and Kumar, R. (2015), "A green and naghdi model in a two-dimensional thermoelastic diffusion problem for a half space", J. Comput. Theor. Nanosci., 12(2), 280-286. https://doi.org/10.1166/jctn.2015.3729. 
  5. Alzahrani, F.S. and Abbas, I.A. (2019), "Analytical estimations of temperature in a living tissue generated by laser irradiation using experimental data", J. Therm. Biol., 85, 102421. https://doi.org/10.1016/j.jtherbio.2019.102421. 
  6. Alzahrani, F.S. and Abbas, I.A. (2022), "Eigenvalues approach on thermos-elastic diffusions problem for an infinite material containing spherical holes.", Wave. Random Complex Media, 1-13. https://doi.org/10.1080/17455030.2021.2024622. 
  7. Aouadi, M. (2006), "Generalized thermoelastic diffusion problem for an infinitely long solid cylinder", Int. J. Math. Math. Sci., 2006, Article ID 025976. https://doi.org/10.1155/IJMMS/2006/25976. 
  8. Biot, M.A. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27(3), 240-253. https://doi.org/10.1063/1.1722351. 
  9. Chawla, V. and Kamboj, D. (2020), "A general study of fundamental solutions in aniotropicthermoelastic media with mass diffusion and voids", Int. J. Appl. Mech. Eng., 25(4), 22-41. http://doi.org/10.2478/ijame-2020-0047. 
  10. Dhaliwal, R. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publicaion Co., New Delhi, India.
  11. El-Karamany, A.S. and Ezzat, M.A. (2014), "On the dual-phase-lag thermoelasticity theory", Meccanica, 49, 79-89. http://doi.org/10.1007/s11012-013-9774-z. 
  12. El-Karamany, A.S., Ezzat, M.A. and El-Bary, A.A. (2018), "Thermodiffusion with two time delays and kernel functions", Math. Mech. Solid., 23(2), 195-208. https://doi.org/10.1177/1081286516676870. 
  13. Ezzat, M.A. (1993), "Steady space approach to unsteady two-dimensional free convection flow through a porous medium", Can. J. Phys., 72(5-6), 311-317. https://doi.org/10.1139/p94-045. 
  14. Ezzat, M.A. and Fayik, M.A. (2011), "Fractional order theory of thermoelastic diffusion", J. Therm. Stress., 34(8), 851-872. https://doi.org/10.1080/01495739.2011.586274. 
  15. Ezzat, M.A., El-Bary, A.A. and Fayik, M.A. (2013), "Fractional fourier law with three-phase lag of thermoelasticity", Mech. Adv. Mater. Struct., 20, 593-602. https://doi.org/10.1080/15376494.2011.643280. 
  16. Ezzat, M.A., Othman, M.I. and Helmy, K.A. (2000), "A problem of a micropolar magnetohydrodynamic boundary-layer flow", Can. J. Phys., 77(10), 813-827. https://doi.org/10.1139/p99-061. 
  17. Green, A.E. and Lindsay, K. (1972), "Thermoelasticity", J. Elast., 2(1), 1-7. https://doi.org/10.1007/BF00045689. 
  18. Hobiny, A. and Abbas, I.A. (2019), "Analytical solutions of fractional bioheat model in a spherical tissue", Mech. Bas. Des. Struct. Mach., 49(3), 430-439. https://doi.org/10.1080/15397734.2019.1702055. 
  19. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of laplace transforms", J. Comput. Appl. Math., 10(1), 113-132. https://doi.org/10.1016/0377-0427(84)90075-X. 
  20. Kaur, I. and Lata, P. (2020), "Axisymmetric deformation in transversely isotropic magneto-thermoelastic solid with Green-Naghdi III due to inclined load", Int. J. Mech. Mater. Eng., 15(1), 1-9. http://doi.org/10.1186/s40712-019-0111-8. 
  21. Kumar, R. and Rani, L. (2005), "Response of thermoelastic half-space with voids due to inclined load", Int. J. Appl. Mech. Eng., 10(2), 281-294. 
  22. Kumar, R., Kaushal, S. and Marin, M. (2018), "Propagation of waves in micropolar thermodiffusion elastic half-space", Afrika Matematika, 29, 451-462. http://doi.org/10.1007/s133700180553-9. 
  23. Kuo, J.T. (1969), "Static response of a multilayered medium under inclined surface loads", J. Geophys. Res., 74(12), 3195-3207. https://doi.org/10.1029/JB074i012p03195. 
  24. Lata, P. and Kaur, I. (2019), "Effect of inclined load on transversely isotropic magneto thermoelastic rotating solid with time harmonic source", Adv. Mater. Res., 8(2), 83-102. http://doi.org/10.12989/amr.2019.8.2.083. 
  25. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5. 
  26. Marin, M., Abbas, I. and Kumar, R. (2014), "Relaxed saint-venant principle for thermoelastic micropolar diffusion", Struct. Eng. Mech., 51(4), 651-662. https://doi.org/10.12989/sem.2014.51.4.651. 
  27. Marin, M., Hobiny, A. and Abbas, I. A. (2021), "The effects of fractional time derivatives in porothermoelastic materials using finite element method", Math., 9(14), 1606. https://doi.org/10.3390/math9141606. 
  28. Nowacki, W. (1974), "Dynamic problems of thermos diffusion in elastic solids", Proc. Vib. Prob., 15, 105-128. 
  29. Nowacki, W. (1975), "Thermodiffusion in solids", J. Theor. Appl. Mech., 13(2), 143-158. 
  30. Nowacki, W. (1976), "Dynamic problems of diffusion in solids", Eng. Fract. Mech., 8(1), 261-266. https://doi.org/10.1016/0013-7944(76)90091-6. 
  31. Press, W.H., Teukolsky, S.A., Vellerling, W.T. and Flannery, B.P. (1986), Numerical Recipes in Fortran, Cambridge University Press, Cambridge. 
  32. Sharma, N., Kumar, R. and Lata, P. (2015), "Disturbance due to inclined load in transversely isotropic thermoelastic medium with two temperatures and without energy dissipation", Mater. Phys. Mech., 22(2), 107-117. 
  33. Sherief, H.H. and Saleh, H.A. (2005), "A half-space problem in the theory of generalized thermoelastic diffusion", Int. J. Solid. Struct., 42(15), 4484-4493. https://doi.org/10.1016/j.ijsolstr.2005.01.001. 
  34. Sherief, H.H., Hamza, F.A. and Saleh, H.A. (2004), "The theory of generalized thermoelastic diffusion", Int. J. Eng. Sci., 42(5-6), 591-608. https://doi.org/10.1016/j.ijengsci.2003.05.001. 
  35. Wu, J.J. (2007), "Vibration analyses of an inclined flat plate subjected to moving loads", J. Sound Vib., 299(1-2), 373-387. https://doi.org/10.1016/j.jsv.2006.07.002. 
  36. Zenkour, A. (2022), "Thermal diffusion of an unbounded solid with a spherical cavity via refined three-phase-lag green-naghdi models", Ind. J. Phys., 96(4), 1087-1104. http://doi.org/10.1007/s12648-021-02042-z.