Effect of a moving thermal load in a modified couple stress medium with double porosity and hyperbolic two-temperature theory

Pragati; Rajneesh Kumar; Sachin Kaushal

doi:10.46481/jnsps.2026.2959

Authors

Pragati
Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University-144411 Phagwara, India
Rajneesh Kumar
Department of Mathematics, Kurukshetra University, Kurukshetra-136119 Haryana, India
Sachin Kaushal
[email protected]

Department of Mathematics, School of Chemical Engineering and Physical Science Lovely Professional University Phagwara-Punjab.

Keywords:

Modified couple stress, Double porosity, Hyperbolic two temperature, Normal mode analysis

Abstract

In this study, a two-dimensional thermoelastic problem is investigated within the framework of Modified Couple Stress Theory (MCST) incorporating double porosity and governed by the Hyperbolic Two-Temperature (HTT) model under the influence of a moving thermal source. The governing equations are reformulated in non-dimensional form and potential function techniques are employed to simplify the analysis. By applying normal mode analysis, closed-form analytical expressions are derived for key physical fields including displacement components, stress distributions, equilibrated stress tensors and temperature profiles. Numerical computations are carried out using MATLAB and the effects of the HTT model and the moving thermal load on the thermoelastic response are illustrated through graphical representations. Several particular cases of interest are examined to validate and interpret the model’s behaviour under different physical conditions. The problem finds practical significance in areas such as microelectronics, civil engineering and biomedical devicedesign particularly in areas involving thermal shock.

Dimensions

REFERENCES

[1] R. K. Wilson & E. C. Aifantis, “On the theory of consolidation with double porosity”, International Journal of Engineering Science 20 (1982) 1009. https://doi.org/10.1016/0020-7225(82)90036-2.

[2] D. E. Beskos & E. C. Aifantis, “On the theory of consolidation with double porosity II”, International Journal of Engineering Science 24 (1986) 1697. https://doi.org/10.1016/0020-7225(86)90076-5.

[3] M. Svanadze, “Fundamental solution in the theory of consolidation with double porosity”, Journal of Mechanical Behavior of Materials 16 (2005) 123. http://dx.doi.org/10.1515/JMBM.2005.16.1-2.123.

[4] M. Svanadze, “Dynamical problems on the theory of elasticity for solids with double porosity”, Proceedings in Applied Mathematics and Mechanics 10 (2010) 209. http://dx.doi.org/10.1002/pamm.201010147.

[5] M. Svanadze, “Plane waves and boundary value problems in the theory of elasticity for solids with double porosity”, Acta Applicandae Mathematicae 122 (2012) 461. https://doi.org/10.1007/s10440-012-9756-5.

[6] M. Svanadze, “On the theory of viscoelasticity for materials with double porosity”, Discrete and Continuous Dynamical Systems-B 19 (2014) 2335. https://doi.org/10.3934/dcdsb.2014.19.2335.

[7] M. Svanadze, “Uniqueness theorems in the theory of thermoelasticity for solids with double porosity”, Meccanica 49 (2014) 2099. https://doi.org/10.1007/s11012-014-9876-2.

[8] E. Scarpetta, M. Svanadze & V. Zampoli, “Fundamental solutions in the theory of thermoelasticity for solids with double porosity”, Journal of Thermal Stresses 37 (2014) 727. https://doi.org/10.1080/01495739.2014.885337.

[9] R. D. Mindlin & H. F. Tiersten, “Effects of couple-stresses in linear elasticity”, Archive for Rational Mechanics and Analysis 11 (1962) 415. https://doi.org/10.1007/BF00253946.

[10] F. Yang, A. C. M. Chong, D. C. C. Lam & P. Tong, “Couple stress based strain gradient theory for elasticity”, International Journal of Solids and Structures 39 (2002) 2731. https://doi.org/10.1016/S0020-7683(02)00152-X.

[11] M. E. Gurtin & W. O. Williams, “On the Clausius-Duhem inequality”, Journal of Applied Mathematics and Physics (ZAMP) 17 (1966) 626. https://doi.org/10.1007/BF01597243.

[12] M. E. Gurtin & W. O. Williams, “An axiomatic foundation for continuum thermodynamics”, Archive for Rational Mechanics and Analysis 26 (1967) 83. http://dx.doi.org/10.1007/BF00285676.

[13] H. M. Youssef & A. A. El-Bary, “Theory of hyperbolic two temperature generalized thermoelasticity”, Material Physics and Mechanics 40 (2018) 158. https://doi.org/10.18720/MPM.4022018_4.

[14] D. Y. Tzou, “A unified field approach for heat conduction from macro-to micro-scales”, Journal of Heat Transfer 117 (1995) 8. https://doi.org/10.1115/1.2822329.

[15] S. Sharma & S. Khator, “Power generation planning with reserve dispatch and weather uncertainties including penetration of renewable sources”, International Journal of Smart Grid and Clean Energy 1 (2021) 292. https://doi.org/10.12720/sgce.10.4.292-303.

[16] S. Sharma & S. Khator, “Micro-grid planning with aggregator’s role in the renewable inclusive prosumer market”, Journal of Power and Energy Engineering 10 (2022) 47. https://doi.org/10.4236/jpee.2022.104004.

[17] K. Gajroiya & J. S. Sikka, “Reflection and transmission of plane waves from the interface of a porothermoelastic solid and a double porosity solid”, European Physical Journal Plus 139 (2024) 468. https://doi.org/10.1140/epjp/s13360-024-05215-x.

[18] 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 32 (2024) 1. https://doi.org/10.1080/15376494.2024.2370523.

[19] C. S. Mahato & S. Biswas, “Thermomechanical interactions in nonlocal thermoelastic medium with double porosity structure”, Mechanics of Time-Dependent Materials 28 (2024) 1073. https://doi.org/10.1007/s11043-024-09669-5.

[20] A. Miglani, R. Kumar, A. Kaur & M. Karla, “Axisymmetric deformation of a circular plate of double-porous fractional order thermoelastic medium with dual-phase-lag”, Acta Mechanica 235 (2024) 7263. https://doi.org/10.1007/s00707-024-04092-w.

[21] M. Khatri, S. Deswal & K. K. Kalkal, “Fiber-reinforced material in a double porous transversely isotropic medium with rotation and variable thermal conductivity”, Acta Mechanica 236 (2025) 1819. https://doi.org/10.1007/s00707-025-04238-4.

[22] D. Iesan & R. Quintanilla, “On a theory of thermoelastic materials with a double porosity structure”, Journal of Thermal Stresses 37 (2014) 1017. http://dx.doi.org/10.1080/01495739.2014.914776.

[23] R. Kumar, S. Devi & V. Sharma, “Axisymmetric problem of thick circular plate with heat source in modified couple stress theory”, Journal of Solid Mechanics 9 (2017) 157. https://oiccpress.com/jsm/article/view/12587.

[24] H. H. Sherief & H. Saleh, “A half-space problem in the theory of generalized thermoelastic diffusion”, International Journal of Solids and Structures 42 (2005) 4484. https://doi.org/10.1016/j.ijsolstr.2005.01.001.