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Wave Propagation in Biological Tissue with Hyperbolic Two-Temperature and Temperature Dependent Effects under MGT Model | ||
| Journal of Computational Applied Mechanics | ||
| دوره 57، شماره 1، فروردین 2026، صفحه 84-106 اصل مقاله (1.24 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jcamech.2025.404097.1646 | ||
| نویسندگان | ||
| Kunal Sharma1؛ Marin Marin* 2، 3؛ Rajneesh Kumar4 | ||
| 1Cheminde Chandieu 25,1006 Lausanne, Switzerland | ||
| 2Department of Mathematics and Computer Science, Transilyania University of Brasov, 500036 Brasov, Romania | ||
| 3Academy of Romanian Scientists, Ilfov Street, 3, 050045 Bucharest, Romania | ||
| 4Department of Mathematics, Kurukshetra University, Kurukshetra 136119, Haryana, India | ||
| چکیده | ||
| This paper presents a theoretical study on the reflection of plane waves in a homogeneous, isotropic bio-thermoelastic diffusion half-space incorporating hyperbolic two-temperature (HTT) effects within the framework of Moore-Gibson-Thompson (MGT) heat conduction. The analysis is performed in two dimensions using dimensionless variables and potential function techniques to simplify the governing equations. Employing normal mode analysis, the study identifies the existence of four distinct longitudinal wave types and a single shear vertical (SV) wave, each propagating with different phase velocities. Analytical expressions for the amplitude ratios corresponding to longitudinal (P), thermal (T), chemical potential (Po), and shear vertical (SV) waves are derived and explored as functions of the incident angle, wave frequency, and relevant material parameters. The effects of the HTT parameter, blood perfusion rate, and various thermoelastic theories on the reflection coefficients are investigated through graphical illustrations. Several special cases are also discussed. The findings are relevant to applications in geomechanics, ocean engineering, and biomedical diagnostics, offering valuable insights into wave behavior in bio-thermoelastic diffusion media under the influence of HTT and MGT models. This work contributes a multiscale framework for studying wave propagation in such complex environments. | ||
| کلیدواژهها | ||
| Bio-thermoelastcity؛ Diffusion؛ HTT, MGT heat equation, Impedance boundaries, Amplitude ratios | ||
| مراجع | ||
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[1] H. W. Lord, Y. Shulman, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids, Vol. 15, No. 5, pp. 299-309, 1967.
[2] A. E. Green, K. Lindsay, Thermoelasticity, Journal of elasticity, Vol. 2, No. 1, pp. 1-7, 1972.
[3] A. E. Abouelregal, S. S. Askar, M. Marin, B. Mohamed, The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod, Scientific Reports, Vol. 13, No. 1, pp. 9052, 2023/06/03, 2023.
[4] S. Sharma, S. Devi, R. Kumar, M. Marin, Examining basic theorems and plane waves in the context of thermoelastic diffusion using a multi-phase-lag model with temperature dependence, Mechanics of Advanced Materials and Structures, Vol. 32, pp. 1-18, 07/15, 2024.
[5] K. Sharma, M. Marin, Effect Of Distinct Conductive And Thermodynamic Temperatures On The Reflection Of Plane Waves In Micropolar Elastic Half-Space, Scientific Bulletin. Series A: Applied Mathematics and Physics. Politehnica University of Bucharest, Vol. 75, 01/01, 2013.
[6] A. Zeeshan, M. I. Khan, R. Ellahi, M. Marin, Computational Intelligence Approach for Optimising MHD Casson Ternary Hybrid Nanofluid over the Shrinking Sheet with the Effects of Radiation, Applied Sciences, Vol. 13, No. 17, pp. 9510, 2023.
[7] S. Sharma, M. Marin, H. Altenbach, Elastodynamic interactions in thermoelastic diffusion including non-local and phase lags, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 105, No. 1, pp. e202401059, 2025.
[8] M. Marin, S. Sharma, R. Kumar, S. Vlase, Fundamental solution and Green's function in orthotropic photothermoelastic media with temperature-dependent properties under the Moore–Gibson–Thompson model, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 105, No. 6, pp. e70124, 2025.
[9] A. Hobiny, I. Abbas, M. Marin, The Influences of the Hyperbolic Two-Temperatures Theory on Waves Propagation in a Semiconductor Material Containing Spherical Cavity, Mathematics, Vol. 10, No. 1, pp. 121, 2022.
[10] R. Kumar, S. Ghangas, A. Vashishth, Wave behavior at the interface of inviscid fluid and NL bio-thermoelastic diffusive media, Vol. 6, pp. 11-27, 12/16, 2022.
[11] R. Kumar, S. Ghangas, A. Vashishth, Waves at the imperfect boundary of elastic and bio-thermoelastic diffusive media, Indian Journal of Physics, Vol. 96, pp. 1-14, 04/01, 2021.
[12] A. K. Yadav, Effect of impedance on the reflection of plane waves in a rotating magneto-thermoelastic solid half-space with diffusion, AIP Advances, Vol. 10, No. 7, 2020.
[13] M. Marin, O. Florea, On Temporal Behaviour of Solutions in Thermoelasticity of Porous Micropolar Bodies, Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, Vol. 22, 01/10, 2014.
[14] K. Sachin, K. Rajneesh, B. Indu, S. Gulshan, Wave propagation at free surface in thermoelastic medium under modified Green-Lindsay model with non-local and two temperature, Structural engineering and mechanics : An international journal, Vol. 90, No. 2, pp. 209-218, 2024. English
[15] R. Kumar, S. Kaushal, A. Kochar, Analysis of Wave Motion in Micropolar Thermoelastic Medium Based on Moore–Gibson–Thompson Heat Equation Under Non-local and Hyperbolic Two-Temperature, International Journal of Applied and Computational Mathematics, Vol. 10, 03/01, 2024.
[16] R. Kumar, D. Batra, S. Sharma, Thermoelastic medium with swelling porous structure and impedance boundary under dual-phase lag, Engineering Solid Mechanics, Vol. 13, pp. 81-92, 01/01, 2025.
[17] X. Li, C. Li, Z. Xue, X. Tian, Analytical study of transient thermo-mechanical responses of dual-layer skin tissue with variable thermal material properties, International Journal of Thermal Sciences, Vol. 124, pp. 459-466, 2018/02/01/, 2018. | ||
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