Modelling Pennes’, bioheat transfer equation in thermoelasticity with one relaxation time

References

• Karvonen MJ. Applied physiology. Suom Laakaril. 1962;17:1865–1871.
   PubMedGoogle Scholar
• Pina HLG. Heat transfer applications. NATO ASI Ser Ser E Appl Sci. 1984: 8:111–125.
   Google Scholar
• Wissler EH. 50 years of JAP: Pennes’ 1948 paper revisited. J Appl Physiol. 1998;85:35–41. doi:10.1152/jappl.1998.85.1.35
   PubMed Web of Science ®Google Scholar
• Okajima J, Maruyama S, Takeda H, et al. Dimensionless solutions and general characteristics of bioheat transfer during thermal therapy. J Therm Biol. 2009;34:377–384. doi:10.1016/j.jtherbio.2009.08.001
   Web of Science ®Google Scholar
• Sarkar N. A novel Pennes’ bioheat transfer equation with memory-dependent derivative. Math Model Eng. 2016;2:151–157. doi:10.21595/mme.2016.18024
   Google Scholar
• Kumar R, Vashishth AK, Ghangas S. Fundamental solution and study of plane waves in bio-thermoelastic medium with DPL. J Solid Mech. 2020;12:278–296.
   Google Scholar
• Youssef HM, Alghamdi NA. Modeling of one-dimensional thermoelastic dual-phase-Lag skin tissue subjected to different types of thermal loading. Sci Rep [Internet]. 2020: 1–12. doi:10.1038/s41598-020-60342-6
   PubMed Web of Science ®Google Scholar
• Zhang Q, Sun Y, Yang J. Bio-heat response of skin tissue based on three-phase-lag model. Sci Rep [Internet]. 2020;10:1–14. doi:10.1038/s41598-020-73590-3
   PubMedGoogle Scholar
• Boley BA, Tolins IS. Transient coupled thermoelastic boundary value problems in the half-space. J Appl Mech Trans ASME. 1960;29:637–646. doi:10.1115/1.3640647
   Google Scholar
• Lord HW, Shulman Y. A generalized dynamical theory of thermoelasticity. J Mech Phys Solids. 1967;15:299–309. doi:10.1016/0022-5096(67)90024-5
   Web of Science ®Google Scholar
• Green AE, Lindsay KA. Thermoelasticity. J Elast. 1972;2:1–7. doi:10.1007/BF00045689
   Google Scholar
• Green AE, Laws N. On a global entropy production inequality. Q J Mech Appl Math. 1972;25:1–11. doi:10.1093/qjmam/25.1.1
   Web of Science ®Google Scholar
• Green AE, Naghdi PM. Thermoelasticity without energy dissipation. J Elast. 1993;31:189–208. doi:10.1007/BF00044969
   Web of Science ®Google Scholar
• Chandrasekharalah DS. Thermoelasticity with second sound: a rewiew. Appl Mech Rev. 1986;39:355–376. doi:10.1115/1.3143705
   Google Scholar
• Tzou DY. A unified field approach for heat conduction from macro- to micro-scales. J Heat Transfer. 1995;117:8–16. doi:10.1115/1.2822329
   Web of Science ®Google Scholar
• Mahdy AMS, Lotfy K, El-Bary A, et al. Effect of rotation and magnetic field on a numerical-refined heat conduction in a semiconductor medium during photo-excitation processes. Eur Phys J Plus [Internet]. 2021;136:553. doi:10.1140/epjp/s13360-021-01552-3
   Web of Science ®Google Scholar
• Ezzat MA, El-Bary AA, Morsey MM. Space approach to the hydro-magnetic flow of a dusty fluid through a porous medium. Comput Math with Appl [Internet]. 2010;59:2868–2879. doi:10.1016/j.camwa.2010.02.004
   Web of Science ®Google Scholar
• Ezzat MA, El-Bary AA. Effects of variable thermal conductivity on Stokes’ flow of a thermoelectric fluid with fractional order of heat transfer. Int J Therm Sci [Internet]. 2016;100:305–315. doi:10.1016/j.ijthermalsci.2015.10.008
   Web of Science ®Google Scholar
• Ezzat M, El-Bary AA, Ezzat S. Combined heat and mass transfer for unsteady MHD flow of perfect conducting micropolar fluid with thermal relaxation. Energy Convers Manag [Internet]. 2011;52:934–945. doi:10.1016/j.enconman.2010.08.021
   Web of Science ®Google Scholar
• Yasein M, Mabrouk N, Lotfy K, et al. The influence of variable thermal conductivity of semiconductor elastic medium during photothermal excitation subjected to thermal ramp type. Results Phys [Internet]. 2019;15:102766. doi:10.1016/j.rinp.2019.102766
   Web of Science ®Google Scholar
• Dhaliwal RS, Sherief HH. Generalized thermoelasticity for anisotropic media. Q Appl Math. 1980;38:1–8. doi:10.1090/qam/575828
   Web of Science ®Google Scholar
• Othman MIA, Ali MGS, Farouk RM. The effect of relaxation time on the heat transfer and temperature distribution in tissues. World J Mech. 2011;01:283–287. doi:10.4236/wjm.2011.16035
   Google Scholar
• Lotfy K, El-Bary A, Atef HM. The thermoelectric effect of a refined heat equation during the photothermal excitation due to two-temperature theory with laser pulses. J Appl Phys. 2020;128. doi:10.1063/5.0014907
   Web of Science ®Google Scholar
• El-Bary AA, Atef HM. Fundamental solution of generalized magneto-thermo-viscoelasticity with two relaxation times for a perfect conductor cylindrical region. Waves Random Complex Media [Internet]. 2021. doi:10.1080/17455030.2021.1898696
   Web of Science ®Google Scholar
• Mahdy AMS, Lotfy K, El-Bary A, et al. Influence of variable thermal conductivity on wave propagation for a ramp-type heating semiconductor magneto-rotator hydrostatic stresses medium during photo-excited microtemperature processes. Waves Random Complex Media [Internet]. 2021. doi:10.1080/17455030.2021.1886375
   Web of Science ®Google Scholar
• Othman MIA, Atef HM, El-Bary AA. A novel model of multi-temperatures theory in generalized thermo-viscoelasticity. Waves Random Complex Media [Internet]. 2021. doi:10.1080/17455030.2021.1962019
   Web of Science ®Google Scholar
• Ezzat MA. Fractional thermo-viscoelastic response of biological tissue with variable thermal material properties. J Therm Stress [Internet]. 2020;43:1120–1137. doi:10.1080/01495739.2020.1770643
   Web of Science ®Google Scholar