Journal of Applied and Computational Mechanics
Thermoelastic Modeling with Dual Porosity Interacting with an Inviscid Liquid
Document Type : Research Paper
Authors
1 Department of Mathematics, Indira Gandhi University, Meerpur, 123401, India
2 Department of Mathematics, HPU Regional Centre, Dharamshala, 176218, India
3 Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, 42210, Saudi Arabia
4 Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey
5 Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Abstract
This study introduces a two-dimensional thermoelastic model for a homogeneous isotropic half-space with double porosity underlying an inviscid liquid half-space featuring temperature variations. The model incorporates the three-phase lag (TPL) heat equation and reveals that in the solid half-space, four coupled longitudinal waves intertwine with one uncoupled transverse wave, while one mechanical wave ripples through the liquid half-space. The investigation highlights dispersion, attenuation, and other effects affected by the thermal properties and the presence of voids. Using plane wave solutions and boundary conditions at the interface, a concise expression for the frequency equation of the model has been derived. Furthermore, the magnitudes of the displacements in the solid half-space and liquid half-spaces, the temperature change, and the volume fractional fields at the interface have been precisely determined. In the graphical section, computer-simulated results of various wave profiles for magnesium crystal material have been generated for different heat conduction thermoelastic models. The study's implications span various fields, such as hydrology, engineering, ultrasonics, navigation, and electronics.
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Main Subjects
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[2] Green, A.E., Lindsay, K.A., Thermoelasticity, J. Elast., 1972, 2, 1–7.
[3] Green, A.E., Naghdi, P.M., Thermoelasticity without energy dissipation, J. Elast., 1993, 31, 189–208.
[4] Tzou, D.Y., A unified field approach for heat conduction from macro- to micro-scales, J. Heat Transfer, 1995, 117, 8–16.
[5] Choudhuri, S.R., On a thermoelastic three-phase-lag model, J. Therm. Stress., 2007, 30, 231–238.
[6] Nunziato, J.W., Cowin, S.C., A nonlinear theory of elastic materials with voids, Arch. Ration. Mech. Anal., 1979, 72, 175–201.
[7] Aifantis, E.C., Introducing a multi-porous medium, Dev. Mech., 1977, 8, 209–211.
[8] Iesan, D., A theory of thermoelastic materials with voids, Acta Mech., 1986, 60, 67–89.
[9] Svanadze, M., Fundamental solution in the theory of consolidation with double porosity, J. Mech. Behav. Mater., 2005, 16, 123–130.
[10] Sharma, J.N., Kumar, S., Sharma, Y.D., Propagation of rayleigh surface waves in microstretch thermoelastic continua under inviscid fluid loadings, J. Therm. Stress., 2008, 31, 18–39.
[11] Iesan, D., Quintanilla, R., On a theory of thermoelastic materials with a double porosity structure, J. Therm. Stress., 2014, 37, 1017–1036.
[12] Straughan, B., Stability and uniqueness in double porosity elasticity, Int. J. Eng. Sci., 2013, 65, 1–8.
[13] Kumar, M., Barak, M.S., Kumari, M., Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dualpermeability materials, Pet. Sci., 2019, 16, 298–317.
[14] Kumar, R., Vohra, R., Steady state response due to moving load in thermoelastic material with double porosity, Mater. Phys. Mech., 2020, 44, 172–185.
[15] Sharma, J.N., Pathania, V., Generalized thermoelastic lamb waves in a plate bordered with layers of inviscid liquid, J. Sound Vib., 2003, 268, 897–916.
[16] Singh, D., Kumar, D., Tomar, S.K., Plane harmonic waves in a thermoelastic solid with double porosity, Math. Mech. Solids, 2020, 25, 869–886.
[17] Chirita, S., Arusoaie, A., Thermoelastic waves in double porosity materials, Eur. J. Mech. - A/Solids, 2021, 86, 104177.
[18] Pathania, V., Dhiman, P., On lamb type waves in a porothermoelastic plate immersed in the inviscid fluid, Waves in Random and Complex Media, 2021, 2021, 1–27.
[19] Svanadze, M., Potential method in the coupled theory of elastic double-porosity materials, Acta Mech., 2021, 232, 2307–2329.
[20] Pathania, V., Joshi, P., Waves in thermoelastic solid half-space containing voids with liquid loadings, ZAMM - J. Appl. Math. Mech. / Zeitschrift für Angew. Math. und Mech., 2021, 101, 1–19.
[21] Barak, M.S., Kumar, R., Kumar, R., Gupta, V., Energy analysis at the boundary interface of elastic and piezothermoelastic half-spaces, Indian J. Phys, 2023, 2023.
[22] Barak, M.S., Kumar, R., Kumar, R., Gupta, V., The effect of memory and stiffness on energy ratios at the interface of distinct media, Multidiscip. Model. Mater. Struct., 2023, 19, 464–492.
[23] Gupta, V., Barak, M.S., Quasi-p wave through orthotropic piezo-thermoelastic materials subject to higher order fractional and memory-dependent derivatives, Mech. Adv. Mater. Struct., 2023, 0, 1–15.
[24] Gupta, V., Kumar, R., Kumar, R., Barak, M.S., Energy analysis at the interface of piezo/thermoelastic half spaces, Int. J. Numer. Methods Heat Fluid Flow, 2023, 33, 2250–2277.
[25] Biswas, S., Fundamental solution of steady oscillations for porous materials with dual-phase-lag model in micropolar thermoelasticity, Mech. Based Des. Struct. Mach., 2019, 47, 430–452.
[26] Hobiny, A., Abbas, I., Generalized thermoelastic interaction in a two-dimensional porous medium under dual phase lag model, Int. J. Numer. Methods Heat Fluid Flow, 2020, 30, 4865–4881.
[27] Quintanilla, R., Racke, R., A note on stability in three-phase-lag heat conduction, Int. J. Heat Mass Transf., 2008, 51, 24–29.
[28] Shaw, S., Mukhopadhyay, B., Analysis of rayleigh surface wave propagation in isotropic micropolar solid under three-phase-lag model of thermoelasticity, Eur. J. Comput. Mech., 2015, 24, 64–78.
[29] Kalkal, K.K., Kadian, A., Kumar, S., Three-phase-lag functionally graded thermoelastic model having double porosity and gravitational effect, J. Ocean Eng. Sci., 2021, 2021.
[30] Biswas, S., Three-dimensional vibration analysis of porous cylindrical panel with a three-phase-lag model, Waves in Random and Complex Media, 2021, 31, 1879–1904.
[31] Biot, M.A., Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 1956, 27, 240–253.
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