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

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

Dr. Soumen Shaw

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Basudeb Mukhopadhyay

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α Indian Institute of Engineering Science and Technology, Shibpur

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

Reference Format

H Lord,Y Shulman (1967). A generalized dynamical theory of thermoelasticity.
A Green,K Lindsay (1972). Thermoelasticity.
R Dhaliwal,H Sherief (1980). Generalized thermoelasticity for anisotropic media.
A Green,P Naghdi (1991). A re-examination of the basic postulates of thermomechanics.
A Green,P Naghdi (1992). ON UNDAMPED HEAT WAVES IN AN ELASTIC SOLID.
A Green,P Naghdi (1993). Thermoelasticity without energy dissipation.
D Chandrasekharaiah (1998). Hyperbolic thermoelasticity: a review of recent literature.
W Nowacki (1974). Dynamical problems of thermodiffusion in solids I.
W Nowacki (1974). Dynamical problems of thermodiffusion in solids II.
W Nowacki (1974). Dynamic problems of diffusion in solids.
J Nowacki,P Glockner (1974). Some dynamical problems of thermoelastic dielectrics.
H Sherief,F Hamza,H Saleh (2004). The theory of generalized thermoelastic diffusion.
Hany Sherief,Heba Saleh (2005). A half-space problem in the theory of generalized thermoelastic diffusion.
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.
B Singh (2005). Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion.
B Singh (2006). Reflection of SV waves from free surface of an elastic solid in generalized thermodiffusion.
Rajneesh Kumar,Tarun Kansal (2008). Propagation of Rayleigh waves on free surface of transversely isotropic generalized thermoelastic diffusion.
R Kumar,T Kansal (2008). Propagation of Lamb waves in transversely isotropic thermoelastic diffusion plate.
J Sharma (2007). Generalized thermoelastic diffusive waves in heat conducting materials.
J Sharma,Y Sharma,P Sharma (2008). On the propagation of elasto-thermodiffusive surface waves in heat-conducting materials.
N Sharma,R Kumar (2008). Paras Ram, Plane strain deformation in generalized thermoelastic diffusion.
A Eringen (1966). LINEAR THEORY OF MICROPOLAR ELASTICITY.
A Eringen (1999). Microcontinuum field theories, I. Foundations and solids.
W Nowacki (1970). Theory of micropolar elasticity.
W Nowacki (1977). Theory of disclinations elastic cosserat media.
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.
R Kumar,L Rani (2003). Elastodynamics of time harmonic sources in a thermally conducting cubic crystal.
R Kumar,P Ailawalia (2007). Mechanical/ Thermal sources in a micropolar thermoelastic medium possessing cubic symmetry without energy dissipation.
R Kumar,P Ailawalia (2006). Deformation due to time harmonic sources in micropolar thermoelastic medium possessing cubic symmetry with two relaxation times.
M Caputo (1967). Linear Models of Dissipation whose Q is almost Frequency Independent--II.
M Caputo,F Mainardi (1971). A new dissipation model based on memory mechanism.
H Sherief,A Ei-Sayed,A Ei-Latief (2010). Fractional order theory of thermoelasticity.
K Miller,B Ross (1993). An introduction to the fractional calculus and fractional differential equations.
I Podlubny (1999). Fractional differential equations.
Y Povstenko (2009). Thermoelasticity that uses fractional heat conduction equation.
Y Povstenko (2005). FRACTIONAL HEAT CONDUCTION EQUATION AND ASSOCIATED THERMAL STRESS.
Yuriy Povstenko (2005). Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation.
M Biot (1959). New thermomechanical reciprocity relations with application to thermal stresses.
Hamdy Youssef,Eman Al-Lehaibi (1010). Variational principle of fractional order generalized thermoelasticity.
M Biot (1956). Thermoelasticity and irreversible thermo-dynamics.

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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. \u201cA Unified Field Approach On Fractional-Ordered Micropolar Thermoelasticity with Diffusion\u201d. Global Journal of Research in Engineering - I: Numerical Methods GJRE-I Volume 11 (GJRE Volume 11 Issue I7): .

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GJRE Volume 11 Issue I7
Pg. 39- 50

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Journal Specifications

Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

Keywords

fractional calculus Micropolar elasticity Thermodiffusion Uniqueness theorem Variational principle

Submission ReceivedNovember 2, 2011
Peer Review Double Blind
Handling Editor
Accepted December 2, 2011
Published December 16, 2011

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v1.2

Issue date

December 28, 2011

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Article Matrices

Total Score: 107

Country: India

Subject: Global Journal of Research in Engineering - I: Numerical Methods

Authors: Dr. Soumen Shaw , Basudeb Mukhopadhyay (PhD/Dr. count: 1)

View Count (all-time): 207

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Publish Date: 2011 12, Wed

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Total Views: 5334

Total Downloads: 2855

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