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A Unified Field Approach On Fractional-Ordered Micropolar Thermoelasticity with Diffusion

§ Bengal Engineering and Science university, Shibpur.

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A Unified Field Approach On Fractional-Ordered Micropolar  Thermoelasticity with Diffusion

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Abstract

The present paper is completely devoted on derivation of some basic fundamental relations in generalized thermodiffusive micropolar elasticity with fractional-ordered derivatives. The generalized heat conduction and mass diffusion equations have been modified by using fractional calculus. A variational principle is obtained and hence the uniqueness theorem for those equations has been proved.

References

40 Cites in Article
  1. 1. H Lord,Y Shulman (1967). A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15(5), 299-309.
  2. 2. A Green,K Lindsay (1972). Thermoelasticity. Journal of Elasticity, 2(1), 1-7.
  3. 3. R Dhaliwal,H Sherief (1980). Generalized thermoelasticity for anisotropic media. Quarterly Appl. Math, 33, 1-8.
  4. 4. A Green,P Naghdi (1991). A re-examination of the basic postulates of thermomechanics. Proc. Roy. Soc, 432, 171-194.
  5. 5. A Green,P Naghdi (1992). ON UNDAMPED HEAT WAVES IN AN ELASTIC SOLID. Journal of Thermal Stresses, 15(2), 253-264.
  6. 6. A Green,P Naghdi (1993). Thermoelasticity without energy dissipation. J. Elast, 31, 189-209.
  7. 7. D Chandrasekharaiah (1998). Hyperbolic thermoelasticity: a review of recent literature. J. Appl. Mech. Rev, 51, 705-729.
  8. 8. W Nowacki (1974). Dynamical problems of thermodiffusion in solids I. Bull. Acad. Pol. Sci. Ser. Tech, 22, 55-64.
  9. 9. W Nowacki (1974). Dynamical problems of thermodiffusion in solids II. Bull. Acad. Pol. Sci. Ser. Tech, 22, 129-135.
  10. 10. W Nowacki (1974). Dynamic problems of diffusion in solids. Engineering Fracture Mechanics, 8(1), 261-266.
  11. 11. J Nowacki,P Glockner (1974). Some dynamical problems of thermoelastic dielectrics. International Journal of Solids and Structures, 15(3), 183-191.
  12. 12. H Sherief,F Hamza,H Saleh (2004). The theory of generalized thermoelastic diffusion. Int. J. Eng. Sci, 42, 591-608.
  13. 13. Hany Sherief,Heba Saleh (2005). A half-space problem in the theory of generalized thermoelastic diffusion. International Journal of Solids and Structures, 42(15), 4484-4493.
  14. 14. Xia Rong-Hou,Tian Xiao-Geng,Shen Ya-Peng (2009). The influence of diffusion on generalized thermoelastic problems of infinite body with a cylindrical cavity. Int. J. Eng. Sci, 47, 669-679.
  15. 15. B Singh (2005). Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion. J. Earth Syst. Sci, 114(2), 159-168.
  16. 16. B Singh (2006). Reflection of SV waves from free surface of an elastic solid in generalized thermodiffusion. J. Sound Vib, 291, 764-778.
  17. 17. Rajneesh Kumar,Tarun Kansal (2008). Propagation of Rayleigh waves on free surface of transversely isotropic generalized thermoelastic diffusion. Applied Mathematics and Mechanics, 29(11), 1451-1462.
  18. 18. R Kumar,T Kansal (2008). Propagation of Lamb waves in transversely isotropic thermoelastic diffusion plate. Int. J. solids structures, 45, 5890-5913.
  19. 19. J Sharma (2007). Generalized thermoelastic diffusive waves in heat conducting materials. J. Sound Vib, 301, 979-993.
  20. 20. J Sharma,Y Sharma,P Sharma (2008). On the propagation of elasto-thermodiffusive surface waves in heat-conducting materials. Journal of Sound and Vibration, 315(4-5), 927-938.
  21. 21. N Sharma,R Kumar (2008). Paras Ram, Plane strain deformation in generalized thermoelastic diffusion. Int. J. Thermophys, 29, 1503-1522.
  22. 22. A Eringen (1966). LINEAR THEORY OF MICROPOLAR ELASTICITY. J. Math. Mech, 15, 909-923.
  23. 23. A Eringen (1999). Microcontinuum field theories, I. Foundations and solids. Microcontinuum field theories, I. Foundations and solids
  24. 24. W Nowacki (1970). Theory of micropolar elasticity.
  25. 25. W Nowacki (1977). Theory of disclinations elastic cosserat media. Arch. Mech, 29, 531-547.
  26. 26. S Minagawa,K Arakawa,M Yamada (1981). Dispersion curves for waves in a cubic micropolar medium with reference to estimations of the material constants for diamond. Bull. JSME, 24, 22-28.
  27. 27. R Kumar,L Rani (2003). Elastodynamics of time harmonic sources in a thermally conducting cubic crystal. Int. J. Appl. Mech. Engg, 8, 637-650.
  28. 28. R Kumar,P Ailawalia (2007). Mechanical/ Thermal sources in a micropolar thermoelastic medium possessing cubic symmetry without energy dissipation. Int. J. Thermophys, 28, 342-367.
  29. 29. R Kumar,P Ailawalia (2006). Deformation due to time harmonic sources in micropolar thermoelastic medium possessing cubic symmetry with two relaxation times. Appl. Math. Mech. (English Edition), 27, 781-792.
  30. 30. M Caputo (1967). Linear Models of Dissipation whose Q is almost Frequency Independent--II. Geophysical Journal International, 13(5), 529-539.
  31. 31. M Caputo,F Mainardi (1971). A new dissipation model based on memory mechanism. Pure Appl. Geophysics, 91(1)
  32. 32. H Sherief,A Ei-Sayed,A Ei-Latief (2010). Fractional order theory of thermoelasticity. Int. J. Solids Struc, 47, 269-275.
  33. 33. K Miller,B Ross (1993). An introduction to the fractional calculus and fractional differential equations. An introduction to the fractional calculus and fractional differential equations
  34. 34. I Podlubny (1999). Fractional differential equations. Fractional differential equations
  35. 35. Y Povstenko (2009). Thermoelasticity that uses fractional heat conduction equation. J. Appl. Math. Sci, 162(2), 296-305.
  36. 36. Y Povstenko (2005). FRACTIONAL HEAT CONDUCTION EQUATION AND ASSOCIATED THERMAL STRESS. Journal of Thermal Stresses, 28(1), 83-102.
  37. 37. Yuriy Povstenko (2005). Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation. Solid Mechanics and Its Applications, 257-285.
  38. 38. M Biot (1959). New thermomechanical reciprocity relations with application to thermal stresses. J. Aero-Space science, 26(7), 401-408.
  39. 39. Hamdy Youssef,Eman Al-Lehaibi (1010). Variational principle of fractional order generalized thermoelasticity. Applied Mathematics Letters, 23(10), 1183-1187.
  40. 40. M Biot (1956). Thermoelasticity and irreversible thermo-dynamics. J. Appl. Phys, 27, 240-253.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Dr. Soumen Shaw. 2011. "A Unified Field Approach On Fractional-Ordered Micropolar Thermoelasticity with Diffusion". Global Journal of Research in Engineering - I: Numerical Methods GJRE-I Volume 11 (GJRE Volume 11 Issue I7).

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Journal Specifications

Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

Keywords
Classification
GJRE-I Classification FOR Code: 020304
Version of record
v1.2

Issue date
December 28, 2011

Language
English
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A Unified Field Approach On Fractional-Ordered Micropolar Thermoelasticity with Diffusion

Dr. Shaw
Dr. Shaw Bengal Engineering and Science university, Shibpur.