Advances in materials Research

  • 제11권2호
  • /
  • Pages.111-120
  • /
  • 2022
  • /
  • 2234-0912(pISSN)
  • /
  • 2234-179X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Nonlocal heat conduction approach in biological tissue generated by laser irradiation

  • Abbas, Ibrahim A. (Department of Mathematics, Faculty of Science, Sohag University) ;
  • Abdalla, Aboelnour (Department of Mathematics, Faculty of Science, Sohag University) ;
  • Sapoor, Hussien (Department of Mathematics, Faculty of Science, Sohag University)
  • 투고 : 2021.07.23
  • 심사 : 2021.12.05
  • 발행 : 2022.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

A novel nonlocal model with one thermal relaxation time is presented to investigates the thermal damages and the temperature in biological tissues generated by laser irradiations. To obtain these models, we used the theory of the non-local continuum proposed by Eringen. The thermal damages to the tissues are assessed completely by the denatured protein ranges using the formulations of Arrhenius. Numerical results for temperature and the thermal damage are graphically presented. The effects nonlocal parameters and the relaxation time on the distributions of physical fields for biological tissues are shown graphically and discussed.

키워드

과제정보

This work was funded by the Academy of Scientific Research and Technology, Egypt, under Science UP grant No. (6513). The authors, therefore, acknowledge with thanks the Academy of Scientific Research and Technology for financial support.

참고문헌

  1. Ahmadikia, H., Fazlali, R. and Moradi, A. (2012), "Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue", Int. Commun. Heat Mass Transf., 39(1), 121-130. https://doi.org/10.1016/j.icheatmasstransfer.2011.09.016
  2. Alzahrani, F.S. and Abbas, I.A. (2020), "Fractional order gl model on thermoelastic interaction in porous media due to pulse heat flux", Geomech. Eng., Int. J., 23(3), 217-225. https://doi.org/10.12989/gae.2020.23.3.217
  3. Andreozzi, A., Brunese, L., Iasiello, M., Tucci, C. and Vanoli, G.P. (2019), "Modeling Heat Transfer in Tumors: A Review of Thermal Therapies", Annals Biomed. Eng., 47(3), 676-693. https://doi.org/10.1007/s10439-018-02177-x
  4. Anya, A.I. and Khan, A. (2019), "Reflection and propagation of plane waves at free surfaces of a rotating micropolar fibre-reinforced medium with voids", Geomech. Eng., Int. J., 18(6), 605-614. https://doi.org/10.12989/gae.2019.18.6.605
  5. Charny, C.K. (1992), Mathematical Models of Bioheat Transfer,
  6. Debnath, L. and Bhatta, D. (2014), Integral Transforms and their Applications, Chapman and Hall/CRC.
  7. Dhaliwal, J. (1993), "Uniqueness in generalized nonlocal thermoelasticity", J. Thermal Stress., 16(1), 71-77. https://doi.org/10.1080/01495739308946217
  8. Eringen, A.C. (1974), "Theory of nonlocal thermoelasticity", Int. J. Eng. Sci., 12(12), 1063-1077. https://doi.org/10.1016/0020-7225(74)90033-0
  9. Eringen, A.C. (1984a), "Electrodynamics of memory-dependent nonlocal elastic continua", J. Math. Phys., 25(11), 3235-3249. https://doi.org/10.1063/1.526070
  10. Eringen, A.C. (1984b), "Plane waves in nonlocal micropolar elasticity", Int. J. Eng. Sci., 22(8-10), 1113-1121. https://doi.org/10.1016/0020-7225(84)90112-5
  11. Eringen, A.C. (1991), "Memory-dependent nonlocal electromagnetic elastic solids and superconductivity", J. Math. Phys., 32(3), 787-796. https://doi.org/https://doi.org/10.1063/1.529372
  12. Eringen, A.C. (2012), Microcontinuum field theories: I. Foundations and solids, Springer Science & Business Media.
  13. Ezzat, M.A. (2020), "Modeling of gn type III with MDD for a thermoelectric solid subjected to a moving heat source", Geomech. Eng., Int. J., 23(4), 393-403. https://doi.org/10.12989/gae.2020.23.4.393
  14. Ezzat, M.A. and El-Bary, A.A. (2017), "Fractional magneto-Thermoelastic materials with phase-lag GreenNaghdi theories", Steel Compos. Struct., Int. J., 24(3), 297-307. https://doi.org/10.12989/scs.2017.24.3.297
  15. Gardner, C.M., Jacques, S.L. and Welch, A.J. (1996), "Light transport in tissue: Accurate expressions for one-dimensional fluence rate and escape function based upon Monte Carlo simulation", Lasers Surgery Med.: Official J. Am. Soc. Laser Med. Surgery, 18(2), 129-138. https://doi.org/10.1002/(SICI)1096-9101(1996)18:2
  16. Hassan, M., Marin, M., Ellahi, R. and Alamri, S.Z. (2018), "Exploration of convecti ve heat transfer and flow characteristics synthesis by Cu-Ag/Water hybrid-nanofluids", Heat Transfer Res., 49(18), 1837-1848. https://doi.org/10.1615/HeatTransRes.2018025569
  17. Henriques Jr, F. and Moritz, A. (1947), "Studies of thermal injury: I. The conduction of heat to and through skin and the temperatures attained therein. A theoretical and an experimental investigation", Am. J. Pathol., 23(4), 530.
  18. Hobiny, A.D. and Abbas, I.A. (2020), "Fractional order thermoelastic wave assessment in a two-dimension medium with voids", Geomech. Eng., Int. J., 21(1), 85-93. https://doi.org/10.12989/gae.2020.21.1.085
  19. Hobiny, A. and Abbas, I. (2021a), "Analytical solutions of fractional bioheat model in a spherical tissue", Mech. Based Des. Struct. Mach., 49(3), 430-439. https://doi.org/10.1080/15397734.2019.1702055
  20. Hobiny, A.D. and Abbas, I.A. (2021b), "Generalized thermo-elastic interaction in a fiber-reinforced material with spherical holes", Struct. Eng. Mech., Int. J., 78(3), 297-303. https://doi.org/10.12989/sem.2021.78.3.297
  21. Hosseini, S.M. (2020), "A GN-based modified model for size-dependent coupled thermoelasticity analysis in nano scale, considering nonlocality in heat conduction and elasticity: An analytical solution for a nano beam with energy dissipation", Struct. Eng. Mech., Int. J., 73(3), 287-302. https://doi.org/10.12989/sem.2020.73.3.287
  22. Khan, A.A., Bukhari, S.R., Marin, M. and 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 Res., 50(11), 1061-1080. https://doi.org/10.1615/HeatTransRes.2018028397
  23. Kumar, R. and Gupta, R.R. (2008), "Response of temperature dependence of an elastic modulus in microstretch generalized thermoelasticity", Struct. Eng. Mech., Int. J., 30(5), 577-592. https://doi.org/10.12989/sem.2008.30.5.577
  24. Kumar, D. and Rai, K.N. (2020), "Three-phase-lag bioheat transfer model and its validation with experimental data", Mech. Based Des. Struct. Mach. https://doi.org/10.1080/15397734.2020.1779741
  25. Lata, P. and Kaur, H. (2019), "Deformation in transversely isotropic thermoelastic medium using new modified couple stress theory in frequency domain", Geomech. Eng., Int. J., 19(5), 369-381. https://doi.org/10.12989/gae.2019.19.5.369
  26. Lata, P. and Kaur, H. (2021), "Interactions in a homogeneous isotropic modified couple stress thermoelastic solid with multi-dual-phase-lag heat transfer and two temperature", Steel Compos. Struct., Int. J., 38(2), 213-221. https://doi.org/10.12989/scs.2021.38.2.213
  27. Lata, P. and Singh, S. (2020), "Deformation in a nonlocal magneto-thermoelastic solid with hall current due to normal force", Geomech. Eng., Int. J., 22(2), 109-117. https://doi.org/10.12989/gae.2020.22.2.109
  28. Lata, P. and Singh, S. (2021), "Stoneley wave propagation in nonlocal isotropic magneto-thermoelastic solid with multi-dual-phase lag heat transfer", Steel Compos. Struct., Int. J., 38(2), 141-150. https://doi.org/10.12989/scs.2021.38.2.141
  29. Lata, P., Kumar, R. and Sharma, N. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., Int. J., 22(3), 567-587. https://doi.org/10.12989/scs.2016.22.3.567
  30. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solids, 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  31. Marin, M. (1996), "Generalized solutions in elasticity of micropolar bodies with voids", Revista de la Academia Canaria de Ciencias:= Folia Canariensis Academiae Scientiarum, 8(1), 101-106.
  32. Marin, M. (2010), "Some estimates on vibrations in thermoelasticity of dipolar bodies", JVC/J Vib Control, 16(1), 33-47. https://doi.org/10.1177/1077546309103419
  33. Marin, M., Vlase, S. and Paun, M. (2015), "Considerations on double porosity structure for micropolar bodies", AIP Adv., 5(3). https://doi.org/10.1063/1.4914912
  34. Moritz, A.R. and Henriques, F.C. (1947), "Studies of Thermal Injury: II. The Relative Importance of Time and Surface Temperature in the Causation of Cutaneous Burns", Am. J. Pathol., 23(5), 695-720.
  35. Noroozi, M.J. and Goodarzi, M. (2017), "Nonlinear analysis of a non-Fourier heat conduction problem in a living tissue heated by laser source", Int. J. Biomathe., 10(8). https://doi.org/10.1142/S1793524517501078
  36. Pennes, H.H. (1948), "Analysis of tissue and arterial blood temperatures in the resting human forearm", J. Appl. Physiol., 1(2), 93-122. https://doi.org/10.1152/jappl.1948.1.2.93
  37. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bouiadjra, R.B., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., Int. J., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065
  38. Saeed, T. and Abbas, I. (2020), "Finite element analyses of nonlinear DPL bioheat model in spherical tissues using experimental data", Mech. Based Des. Struct. Mach. https://doi.org/10.1080/15397734.2020.1749068
  39. Saeed, T., Abbas, I. and Marin, M. (2020), "A GL model on thermo-elastic interaction in a poroelastic material using finite element method", Symmetry, 12(3). https://doi.org/10.3390/SYM12030488
  40. Sarkar, N. (2020), "Thermoelastic responses of a finite rod due to nonlocal heat conduction", Acta Mech., 231(3), 947-955. https://doi.org/10.1007/s00707-019-02583-9
  41. Sarkar, N., De, S. and Sarkar, N. (2019), "Waves in nonlocal thermoelastic solids of type II", J. Thermal Stress., 42(9), 1153-1170. https://doi.org/10.1080/01495739.2019.1618760
  42. Sarkar, N., Bachher, M., Das, N., De, S. and Sarkar, N. (2020a), "Waves in nonlocal thermoelastic solids of type III", ZAMM Z. Angew. Math. Mech., 100(4). https://doi.org/10.1002/zamm.201900074
  43. Sarkar, N., Mondal, S. and Othman, M.I.A. (2020b), "Effect of the laser pulse on transient waves in a nonlocal thermoelastic medium under Green-Naghdi theory", Struct. Eng. Mech., Int. J., 74(4), 471-479. https://doi.org/10.12989/sem.2020.74.4.471
  44. Sharma, D.K., Bachher, M., Manna, S. and Sarkar, N. (2020), "Vibration analysis of functionally graded thermoelastic nonlocal sphere with dual-phase-lag effect", Acta Mech., 231(5), 1765-1781. https://doi.org/10.1007/s00707-020-02612-y
  45. Stehfest, H. (1970), "Algorithm 368: Numerical inversion of Laplace transforms [D5]", Commun. ACM, 13(1), 47-49. https://doi.org/10.1145/361953.361969
  46. Wang, J. and Dhaliwal, R.S. (1993), "On some theorems in the nonlocal theory of micropolar elasticity", Int. J. Solids Struct., 30(10), 1331-1338. https://doi.org/10.1016/0020-7683(93)90215-S
  47. Xu, F., Seffen, K.A. and Lu, T.J. (2008), "Non-Fourier analysis of skin biothermomechanics", Int. J. Heat Mass Transf., 51(9-10), 2237-2259. https://doi.org/10.1016/j.ijheatmasstransfer.2007.10.024
  48. Zhang, L., Bhatti, M.M., Marin, M. and Mekheimer, K.S. (2020), "Entropy analysis on the blood flow through anisotropically tapered arteries filled with magnetic zinc-oxide (ZnO) nanoparticles", Entropy, 22(10), 1070. https://doi.org/10.3390/E22101070