Representations of Solutions in Generalized Theory of Micropolar Thermoelastic Diffusion with Triple Porosity
Markanda National College
Department of Mathematics
Shahabad Markanda, 136135, India
E-mail: tarun1_kansal@yahoo.co.in
Received:
Received: 10 June 2025; accepted: 17 November 2025
DOI: 10.12921/cmst.2025.0000011
Abstract:
The goal of this paper is to define the basic governing equations for a medium with anisotropic micropolar thermoelastic properties, including mass diffusion and triple porosity. Additionally, this paper also aims to develop the fundamental solutions for the system of equations under different conditions, such as steady, pseudo-, quasi-static oscillations, and equilibrium.
Key words:
pores, steady oscillations, thermoelastic diffusion, triple porosity
References:
[1] A. C. Eringen, Foundations of micropolar thermoelasticity, vol. International Center for Mechanical Science, Courses and Lectures, no. 23. Berlin: Springer, 1970.
[2] A. C. Eringen, Microcontinuum field theory I: Foundations and solids. Verlag, Berlin: Springer, 1999.
[3] W. Nowacki, “Couple stresses in the theory of thermoelasticity I.,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 14, pp. 129–138, 1966.
[4] W. Nowacki, “Couple stresses in the theory of thermoelasticity II.,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 14, pp. 263–272, 1966.
[5] W. Nowacki, “Couple stresses in the theory of thermoelasticity III.,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 14, pp. 801–809, 1966.
[6] E. Boschi and D. Iesan, “A generalized theory of linear micropolar thermoelasticity.,” Meccanica, vol. 8, pp. 154–157, 1973.
[7] W. Nowacki, “Dynamical problems of thermodiffusion in solids-I,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 22, pp. 55–64, 1974.
[8] W. Nowacki, “Dynamical problems of thermodiffusion in solids-II,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 22, pp. 205–211, 1974.
[9] W. Nowacki, “Dynamical problems of thermodiffusion in solids-III,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 22, pp. 257–266, 1974.
[10] W. Nowacki, “Dynamical problems of thermodiffusion in solids,” Engineering Fracture Mechanics, vol. 8, pp. 261–266, 1976.
[11] H. H. Sherief, F. A. Hamza, and H. A. Saleh, “The theory of generalized thermoelastic diffusion,” International Journal of Engineering Science, vol. 42, pp. 591–608, 2004.
[12] M. Aouadi, “Generalized theory of thermoelastic diffusion for anisotropic media,” Journal of Thermal Stresses, vol. 31, pp. 270–285, 2008.
[13] T. Kansal and R. Kumar, “Variational principle, uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion material,” Qscience connect, vol. 2013, pp. 1–18, 2013.
[14] M. Aouadi, “Theory of generalized micropolar thermoelastic diffusion under Lord-Shulman model,” Journal of Thermal Stresses, vol. 32, pp. 923–942, 2009.
[15] M. Svanadze, “Fundamental solutions in the theory of elasticity for triple porosity materials.,” Meccanica, vol. 51, pp. 1825–1837, 2016.
[16] B. Straughan, “Uniqueness and stability in triple porosity thermoelasticity,” Rendiconti Lincei-Matematica E Applicazioni, vol. 28, pp. 191–208, 2017.
[17] T. Kansal, “Fundamental solutions in generalized theory of thermoelastic diffusion with triple porosity,” Engineering Transactions, vol. 71, pp. 473–505, 2023.
[18] M. Svanadze, “External boundary value problems in the quasi static theory of elasticity for triple porosity materials,” PAMM, vol. 16, pp. 495–496, 2016.
[19] M. Svanadze, “Boundary value problems in the theory of thermoelasticity for triple porosity materials,” Mechanics of Solids, Structures and Fluids; NDE, Diagnosis and Prognosis, vol. 9, pp. 1–10, 2016.
[20] M. Svanadze, “External boundary value problems in the quasi static theory of triple porosity thermoelasticity,” PAMM, vol. 17, pp. 471–472, 2017.
[21] M. Svanadze, “Potential method in the theory of elasticity for triple porosity materials,” Journal of Elasticity, vol. 130, pp. 1–24, 2018.
[22] M. Svanadze, “Potential method in the linear theory of triple porosity thermoelasticity,” Journal of Mathematical Analysis and Applications, vol. 461, pp. 1585–1605, 2018.
[23] M. Svanadze, “On the linear equilibrium theory of elasticity for materials with triple voids,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 71, pp. 329–348, 2018.
[24] B. Straughan, “Mathematical aspects of multi-porosity continua,” Advances in Mechanics and Mathematics, vol. 38, pp. 1–208, 2017.
[25] M. Svanadze, “Fundamental solutions in the linear theory of thermoelasticity for solids with triple porosity,” Mathematics and Mechanics of Solids, vol. 24, pp. 919–938, 2019.
[26] W. Nowacki, The theory of asymmetric elasticity, vol. 1-383. Warszawa: Polish Scientific Publishers, 1986.
The goal of this paper is to define the basic governing equations for a medium with anisotropic micropolar thermoelastic properties, including mass diffusion and triple porosity. Additionally, this paper also aims to develop the fundamental solutions for the system of equations under different conditions, such as steady, pseudo-, quasi-static oscillations, and equilibrium.
Key words:
pores, steady oscillations, thermoelastic diffusion, triple porosity
References:
[1] A. C. Eringen, Foundations of micropolar thermoelasticity, vol. International Center for Mechanical Science, Courses and Lectures, no. 23. Berlin: Springer, 1970.
[2] A. C. Eringen, Microcontinuum field theory I: Foundations and solids. Verlag, Berlin: Springer, 1999.
[3] W. Nowacki, “Couple stresses in the theory of thermoelasticity I.,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 14, pp. 129–138, 1966.
[4] W. Nowacki, “Couple stresses in the theory of thermoelasticity II.,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 14, pp. 263–272, 1966.
[5] W. Nowacki, “Couple stresses in the theory of thermoelasticity III.,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 14, pp. 801–809, 1966.
[6] E. Boschi and D. Iesan, “A generalized theory of linear micropolar thermoelasticity.,” Meccanica, vol. 8, pp. 154–157, 1973.
[7] W. Nowacki, “Dynamical problems of thermodiffusion in solids-I,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 22, pp. 55–64, 1974.
[8] W. Nowacki, “Dynamical problems of thermodiffusion in solids-II,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 22, pp. 205–211, 1974.
[9] W. Nowacki, “Dynamical problems of thermodiffusion in solids-III,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 22, pp. 257–266, 1974.
[10] W. Nowacki, “Dynamical problems of thermodiffusion in solids,” Engineering Fracture Mechanics, vol. 8, pp. 261–266, 1976.
[11] H. H. Sherief, F. A. Hamza, and H. A. Saleh, “The theory of generalized thermoelastic diffusion,” International Journal of Engineering Science, vol. 42, pp. 591–608, 2004.
[12] M. Aouadi, “Generalized theory of thermoelastic diffusion for anisotropic media,” Journal of Thermal Stresses, vol. 31, pp. 270–285, 2008.
[13] T. Kansal and R. Kumar, “Variational principle, uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion material,” Qscience connect, vol. 2013, pp. 1–18, 2013.
[14] M. Aouadi, “Theory of generalized micropolar thermoelastic diffusion under Lord-Shulman model,” Journal of Thermal Stresses, vol. 32, pp. 923–942, 2009.
[15] M. Svanadze, “Fundamental solutions in the theory of elasticity for triple porosity materials.,” Meccanica, vol. 51, pp. 1825–1837, 2016.
[16] B. Straughan, “Uniqueness and stability in triple porosity thermoelasticity,” Rendiconti Lincei-Matematica E Applicazioni, vol. 28, pp. 191–208, 2017.
[17] T. Kansal, “Fundamental solutions in generalized theory of thermoelastic diffusion with triple porosity,” Engineering Transactions, vol. 71, pp. 473–505, 2023.
[18] M. Svanadze, “External boundary value problems in the quasi static theory of elasticity for triple porosity materials,” PAMM, vol. 16, pp. 495–496, 2016.
[19] M. Svanadze, “Boundary value problems in the theory of thermoelasticity for triple porosity materials,” Mechanics of Solids, Structures and Fluids; NDE, Diagnosis and Prognosis, vol. 9, pp. 1–10, 2016.
[20] M. Svanadze, “External boundary value problems in the quasi static theory of triple porosity thermoelasticity,” PAMM, vol. 17, pp. 471–472, 2017.
[21] M. Svanadze, “Potential method in the theory of elasticity for triple porosity materials,” Journal of Elasticity, vol. 130, pp. 1–24, 2018.
[22] M. Svanadze, “Potential method in the linear theory of triple porosity thermoelasticity,” Journal of Mathematical Analysis and Applications, vol. 461, pp. 1585–1605, 2018.
[23] M. Svanadze, “On the linear equilibrium theory of elasticity for materials with triple voids,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 71, pp. 329–348, 2018.
[24] B. Straughan, “Mathematical aspects of multi-porosity continua,” Advances in Mechanics and Mathematics, vol. 38, pp. 1–208, 2017.
[25] M. Svanadze, “Fundamental solutions in the linear theory of thermoelasticity for solids with triple porosity,” Mathematics and Mechanics of Solids, vol. 24, pp. 919–938, 2019.
[26] W. Nowacki, The theory of asymmetric elasticity, vol. 1-383. Warszawa: Polish Scientific Publishers, 1986.
