Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T14:21:59.540Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized Two Temperatures Thermoelasticity of Micropolar Porous Circular Plate with Three Phase Lag Model

Published online by Cambridge University Press:  24 August 2017

R. Kumar ,
A. Miglani  and
R. Rani
R. Kumar*
Affiliation:
Department of MathematicsKurukhsetra UniversityKurukshetra, India
A. Miglani
Affiliation:
Department of MathematicsChoudhary Devilal UniversitySirsa, India
R. Rani
Affiliation:
Department of MathematicsChoudhary Devilal UniversitySirsa, India
*
*Corresponding author (rajneesh_kuk@rediffmail.com)
Get access

Abstract

The present study is to focus on the two dimensional problem of micropolar porous circular plate with three phase lag model within the context of two temperatures generalized thermoelasticity theory. The problem is solved by applying Laplace and Hankel transforms after using potential functions. The expressions of displacements, microrotation, volume fraction field, temperature distribution and stresses are obtained in the transformed domain. To show the utility of the approach, normal force and thermal source are taken. The numerical inversion techniques of transforms have been carried out in order to evaluate the resulting quantities in the physical domain. Finally, the resulting quantities are depicted graphically to show the effect of porosity, two temperatures and phase lags.

Keywords

Micropolar porousTwo temperature thermoelasticityThree phase lag modelLaplace and Hankel transforms
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 6 , December 2018 , pp. 779 - 789
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Nowacki, W., “Couple Stresses in the Theory of Thermoelasticity,” Proceeding of IUTAM Symposia, Vienna (1966).Google Scholar
2. Eringen, A. C., “Foundations of Micropolar Thermoelasticity,” Course and Lectures, 23, Springer-Verlag, Berlin (1970).Google Scholar
3. Tauchert, T. R., Claus, W. D. Jr. and Ariman, T., “The Linear Theory of Micropolar Thermoelasticity,” International Journal of Engingineering Science, 6, pp. 36–47 (1968).Google Scholar
4. Tauchert, T. R., “Thermal Stresses in Micropolar Elastic Solids,” Acta Mechanica, 11, pp. 155–169 (1971).Google Scholar
5. Nowacki, W. and Olszak, W., “Micropolar Thermoelasticity, in Micropolar Thermoelasticity,” Courses and Lectures, 151, Springer-Verlag, Vienna (1974).Google Scholar
6. Dost, S. and Tabarrok, B., “Generalized Micropolar Thermoelasticity,” International Journal of Engineering Science, 16, pp. 173–178 (1978).Google Scholar
7. Chandrasekharaiah, D. S., “Heat Flux Dependent Micropolar Thermoelasticity,” International Journal of Engineering Science, 24, pp. 1389–1395 (1986).Google Scholar
8. Dhaliwal, R. S. and Singh, A., “Micropolar Thermoelasticity”, Thermal Stresses II, Mechanical and Mathematical Methods, 2, North Holland, Amsterdam (1987).Google Scholar
9. Marin, M., “On Existence and Uniqueness in Thermoelasticity of Micropolar Bodies,” Comptes Rendus Del Academic Des Sciences Serie II Fascicule B-Mecanique Physique Astronomie, 321, pp. 475–480 (1995).Google Scholar
10. Marin, M. and Marinescu, C., “Thermoelasticity of Initially Stressed Bodies, Asymptotic Equipartition of Energies,” International Journal of Engineering Science, 36, pp. 73–86 (1998).Google Scholar
11. Iesan, D., “Shock Waves in Micropoar Elastic Materials with Voids,” Analele Stiintifice Ale Universitatu Alexandru Ioan Cuza, Din Iasi Sectiunea La Matematica, 31, pp. 177–186 (1985).Google Scholar
12. Scarpetta, E., “On the Fundamental Solutions in Micropolar Elasticity with Voids,” Acta Mechanica, 82, pp. 151–158 (1990).Google Scholar
13. Marin, M., “Some Basic Theorems in Elastostatics of Micropolar Materials with Voids,” Journal of Computational and Applied Mathematics, 70, pp. 115–126 (1996).Google Scholar
14. Marin, M., “Generalized Solutions in Elasticity of Micropolar Bodies with Voids,” Revista de la Academia Canaria de Ciencias, 8, pp. 101–106 (1996).Google Scholar
15. Kumar, R., Sharma, K. D. and Garg, S. K., “Deformation Due to Various Sources in Micropolar Elastic Solid with Voids under Inviscid Liquid Half Space,” Global Journal of Science Frontier Research, 12, pp. 1–11 (2012).Google Scholar
16. Sharma, K. and Kumar, P. “Propagation of Plane Waves and Fundamental Solution in Thermoviscoelastic Medium with Voids,” Journal of Thermal Stresses, 36, pp. 94–111 (2013).Google Scholar
17. Othman, M. I. A., Tantawi, R. S. and Abd-Elaziz, E. M., “Effect of Initial Stress on a Thermoelastic Medium with Voids and Microtemperatures,” Journal of Porous Media, 19, pp. 155–172 (2016).Google Scholar
18. Marin, M., “An Approach of a Heat Flux Dependent Theory for Micropolar Porous Media,” Meccanica, 51, pp. 1127–1133 (2016).Google Scholar
19. Kumar, R. and Abbas, I. A., “Interaction Due to Various Sources in Saturated Porous Media with Incompressible Fluid,” Journal of Central South University, 23, pp. 1232–1242 (2016).Google Scholar
20. Roychoudhuri, S. K., “On a Thermoelastic Three Phase Lag Model,” Journal of Thermal Stresses, 30, pp. 231–138 (2007).Google Scholar
21. Lord, H. W. and Shulman, Y., “A Generalized Dynamical Theory of Thermoelasticity,” Journal of Mechanics and Physics of Solids, 15, pp. 299–309 (1967).Google Scholar
22. Tzou, D. Y., “A Unified Approach for Heat Conduction from Macro-to-Micro-Scales,” Journal of Heat Transfer, 117, pp. 8–16 (1995).Google Scholar
23. Tzou, D. Y., “The Generalized Lagging Response in Small Scale and High Rate Heating,” International Journal of Heat Transfer, 38, pp. 3231–3240 (1995).Google Scholar
24. Quintanilla, R., “A Well Posed Problem for the Three Dual Phase Lag Heat Conduction,” Journal of Thermal Stresses, 32, pp. 1270–1278 (2009).Google Scholar
25. El-Karamany, A. S. and Ezzat, M. A., “On the Three Phase Lag Linear Micropolar Thermoelasticity Theory,” European Journal of Mechanics, 40, pp. 198–208 (2013).Google Scholar
26. Said, S. M. and Othman, M. I. A., “Influence of the Mechanical Force and the Magnetic Field on Fibre-Reinforced Medium for Three Phase Lag Model,” European Journal of Computational Mechanics, 24, pp. 210–231 (2015).Google Scholar
27. Abbas, I. A., “Generalized Thermoelastic Interaction in Functional Graded Material with Fractional Order Three Phase Lag Heat Transfer,” Journal of Central South University, 22, pp. 1606–1613 (2015).Google Scholar
28. Othman, M. I. A., Hasona, W. M. and Abd-Elaziz, E., “Effect of Rotation and Initial Stress on Generalized Micropolar Thermoelastic Medium with Three Phase Lag,” Journal of Computational and Theoretical Nanoscience, 12, pp. 2030–2040 (2015).Google Scholar
29. Kumar, R. and Gupta, V., “Plane Wave Propagation and Domain of Influence in Fractional Order Thermoelastic Materials with Three Phase Lag Heat Transfer,” Mechanics of Advanced Materials and Structures, 23, pp. 896–908 (2016).Google Scholar
30. Said, S. M., “Influence of Gravity on Generalized Magneto-Thermoelastic Medium for Three Phase Lag Model,” Journal of Computational and Applied Mathematics, 291, pp. 142–157 (2016).Google Scholar
31. Chen, P. J. and Gurtin, M. E., “On a Theory of Heat Conduction Involving Two Temperatures,” Journal of Applied Mathematics and Physics (ZAMP), 19, pp. 614–627 (1968).Google Scholar
32. Chen, P. J., Gurtin, M. E. and Williams, W. O., “A Note on Non-Simple Heat Conduction,” Journal of Applied Mathematics and Physics (ZAMP), 19, pp. 969–970 (1968).Google Scholar
33. Chen, P. J., Gurtin, M. E. and Williams, W. O., “On the Thermodynamics of Non-Simple Elastic Materials with Two Temperatures,” Journal of Applied Mathematics and Physics (ZAMP), 20, pp. 107–112 (1969).Google Scholar
34. Youssef, H. M., “Theory of Two Temperature Generalized Thermoelasticity,” IMA Journal of Applied Mathematics, 713, pp. 383–390 (2006).Google Scholar
35. Marin, M., “A Domain of Influence Theorem for Microstretch Elastic Materials,” Nonlinear Analysis: Real World Applications, 11, pp. 3446–3452 (2010).Google Scholar
36. Ezzat, M. A. and El-Karamany, A. S., “Two Temperature Theory in Generalized Magneto Thermoelasticity with Two Relaxation Times,” Meccanica, 46, pp. 785–794 (2011).Google Scholar
37. Banik, S. and Kanoria, M., “Effects of Three Phase Lag on Two Temperature Generalized Thermoelasticity for Infinite Medium with Spherical Cavity,” Applied Mathematics and Mechanics, 33, pp. 483–498 (2012).Google Scholar
38. Sharma, K., “Reflection at Free Surface in Micropolar Thermoelastic Solid with Two Temperatures,” International Journal of Applied Mechanics and Engineering, 18, pp. 217–234 (2013).Google Scholar
39. Kumar, R. and Abbas, I. A., “Deformation Due to Thermal Source in Micropolar Thermoelastic Media with Thermal and Conductive Temperatures,” Journal of Computational and Theoretical Nanoscience, 10, pp. 2241–2247 (2013).Google Scholar
40. Shaw, S. and Mukhopadhyay, B., “Moving Heat Source Response in Micropolar Half-Space with Two-Temperature Theory,” Continuum Mechanics and Thermodynamics, 25, pp. 523–535 (2013).Google Scholar
41. Youssef, H. M., “State-Space Approach to Two-Temperature Generalized Thermoelasticity without Energy Dissipation of Medium Subjected to Moving Heat Source,” Applied Mathematics and Mechanics -English Edition, 34, pp. 63–74 (2013).Google Scholar
42. Kumar, R., Kaur, M. and Rajvanshi, S. C., “Wave Propagation in Micropolar Thermoelastic Layer with Two Temperatures,” Journal of Vibration and Control, 20, pp. 458–469 (2014).Google Scholar
43. Abbas, I. A., Marin, M. and Kumar, R., “Analytical Numerical Solution of Thermoelastic Interactions in a Semi Infinite Medium with One Relaxation Time,” Journal of Computational and Theoretical Nanoscience, 12, pp. 1–5 (2015).Google Scholar
44. Deswal, S. and Kalkal, K. K., “Three Dimensional Half Space Problem within the Framework of Two Temperatures Thermo-Viscoelasticity with Three Phase Lag Effects,” Applied Mathematical Modeling, 39, pp. 7003–7112 (2015).Google Scholar
45. Ezzat, M. A. and El-Bary, A. A., “Memory Dependent Derivatives Theory of Thermo-Viscoelasticity Involving Two Temperatures,” Journal of Mechanical Science and Technology, 29, pp. 4273–4279 (2015).Google Scholar
46. Abbas, I. A., Marin, M., Abouelmagad, E. I. and Kumar, R., “A Green Naghdi Model in a Two Dimensional Thermoelastic Diffusion Problem for a Half Space,” Journal of Computational and Theoretical Nanoscience, 12, pp. 1–7 (2015).Google Scholar
47. Kumar, R., Sharma, N. and Lata, P. “Effects of Hall Current and Two Temperatures in Transversely Isotropic Magneto Thermoelastic with and without Energy Dissipation due to Ramp Type Heating,” Mechanics of Advanced Materials and Structures, http://dx.doi.org./10.1080/15376494.2016.119 (In Press).Google Scholar
48. Kumar, R., Kaur, M. and Rajvanshi, S. C., “Response of Two Temperatures on Wave Propagation in Micropolar Thermoelastic Materials with One Relaxation Time Bordered with Layers or Half Spaces of Inviscid Liquid,” Journal of Solid Mechanics, 8, pp. 495–510 (2016).Google Scholar
49. Kumar, R. and Partap, G., “Porosity Effect on Circular Crested Waves in Micropolar Thermoelastic Homogeneous Isotropic Plate,” International Journal of Applied Mathematics and Mechanics, 4, pp. 1–18 (2008).Google Scholar
50. Ezzat, M. A. and Awad, E. S., “Constitutive Relations, Uniqueness of Solution and Thermal Shock Application in the Linear Theory of Micropolar Generalized Thermoelasticity Involving Two Temperatures,” Journal of Thermal Stresses, 33, pp. 226–250 (2010).Google Scholar
51. Eringen, A. C., “Plane Waves in Non Local Micropolar Elasticity,” International Journal of Engineering Science, 22, pp. 1113–1121 (1984).Google Scholar
52. Dhaliwal, R. S. and Singh, A., Dynamical Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi (1980).Google Scholar