Effects of modified Ohm's and Fourier's laws on generalized magneto-viscoelastic thermoelasticity with relaxation volume properties

International Journal of Engineering Science

Volumn 48, Issue 4, 2010, Pages 460-472

  Ezzat, Magdy A ^a   Zakaria, M ^a   El Karamany, Ahmed S ^b  

^a Alexandria University   (Egypt)

^b Nizwa University   (Oman)

Author keywords

Elasticity; Fourier's law; Heat transfer; Magneto thermo viscoelasticity; Ohm's law

Indexed keywords

CURRENT DENSITY EFFECTS; EXACT FORMULAS; FOURIER'S LAW; ISOTROPIC MEDIA; LINEAR THEORY; NORMAL MODE ANALYSIS; OHM'S LAW; RHEOLOGICAL PROPERTY; TEMPERATURE GRADIENT; THERMOVISCOELASTICITY; VOLUME PROPERTIES;

ELECTRIC FIELDS; ELECTRIC PROPERTIES; FOURIER TRANSFORMS; HEAT EXCHANGERS; HEAT TRANSFER; MAGNETIC FIELDS; MAGNETOS; RHEOLOGY; VISCOELASTICITY; VISCOSITY;

ELASTICITY;

EID: 76749120939     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2009.11.006     Document Type: Article

References (44)

1. Rajagopal K.R., and Růžička M. Mathematical modeling of electrorheological materials. Continuum Mech. Thermodyn. 13 (2001) 59-78
2. Brigadnov I.A., and Dorfmann A. Mathematical modeling of magnetorheological fluids. Continuum Mech. Thermodyn. 17 (2005) 29-42
3. Dorfmann A., and Ogden R.W. Magnetoelastic modelling of elastomers. Euro. J. Mech. A/Solids 22 (2000) 497-507
4. Carlson J.D., and Jolly M.R. MR fluid, foam and elastomer devices. Mechatronics 10 (2000) 555-569
5. Wineman A.S., and Rajagopal K.R. On constitutive equations for electrorheological materials. Continuum Mech. Thermdynam. 7 (1995) 1-22
6. Rigbi Z., and Jilkén L. The response of an elastomer filled with soft ferrite to mechanical and magnetic in puences. J. Magn. Magn. Mater. 37 (1983) 67-276
7. Ginder J.M. Rheology controlled by magnetic fields. Encyl. Appl. Phys. 16 (1996) 487-503
8. Kankanala S.V., and Triantafyllidis N.J. On finitely strained magnetorheological elastomers. Mech. Phys. Solids 52 (2004) 2869-2908
9. Duhamel J.H. Second memoir, sur les phenomenes thermomechanique. J. de L' Ecole Polytechnique 15 (1837)
10. Biot M. Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27 (1956) 40-253
11. Cattaneo C. Sullacondizione del calore. Atti. Sem. Mat. Fis Univ. Modena 3 (1948)
12. Truesdell A., and Muncaster R.G. Fundamental of Maxwell's Kinetic Theory of a Simple Monatomic Gas (1980), Academic Press, New York
13. Glass D.E., and Vick B. Hyperbolic heat conduction with surface radiation. Int. J. Heat Mass Transfer 28 (1985) 1823-1830
14. Joseph D., and Preziosi L. Heat waves. Rev. Modern Phys. 61 (1989) 41-73
15. Chandrasekharaiah D.S. Hyperbolic thermoelasticity. A review of recent literature. Appl. Mech. Rev. 51 (1998) 705-729
16. Lord H.W., and Shulman Y. A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15 (1967) 299-309
17. Müller I. The coldness, a universal function in thermo-elastic solids. Arch. Rat. Mech. Anal. 41 (1971) 319-332
18. Green A., and Laws A. On the entropy production inequality. Arch. Rat. Anal. 54 (1972) 7-23
19. Green A., and Lindsay K. Thermoelasticity. J. Elast. 2 (1972) 1-7
20. oŞuhubi E. Thermoelastic Solids. In: Eringen A.C. (Ed). Cont. Phys. vol. II (1975), Academic Press, New York (Chapter 2)
21. Ezzat M.A. Fundamental solution in thermoelasticity with two relaxation times for cylindrical regions. Int. J. Eng. Sci. 33 (1995) 2011-2020
22. Tzou D.Y. A unified approach for heat conduction from macro to micro-scales. J. Heat Transfer 117 (1995) 8-16
23. Gross B. Mathematical Structure of the Theories of Viscoelasticity (1955), Hemann, Paris
24. Staverman A.J., and Schwarzl F. In: Stuart H.A. (Ed). Die Physik der Hochpolymeren vol. 4 (1956), Springer Verlag (Chapter 1)
25. Alfrey T., and Gurnee E. In: Erich F.R. (Ed). Rheology: theory and applications vol. 1 (1956), Academic Press, New York
26. Ferry J.D. Viscoelastic Properties of Polymers (1970), John Wiley and Sons, New York
27. Wineman A.S., and Rajagopal K.R. Mechanical Response of Polymers (2000), Cambridge University Press
28. Biot M. Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena. J. Appl. Phys. 25 (1954) 385-1391
29. Morland L.W., and Lee E.H. Stress analysis for linear viscoelastic materials with temperature variation. Trans. Soc. Rheol. 4 (1960) 233-263
30. Tanner R.I. Engineering Rheology (1988), Oxford University Press, Oxford
31. Bland D.R. The Theory of Linear Viscoelasticity (1969), Pergamon Press, Oxford
32. Gurtin M.E., and Sternberg E. On the linear theory of viscoelasticity. Arch. Rat. Mech. Anal. 11 (1962) 291-356
33. Ilioushin A.A., and Pobedria B.E. Fundamentals of the Mathematical Theory of Thermal Viscoelasticity (1970), Nauka, Moscow, Russian
34. Pobedria B.E. Coupled problems in continuum mechanics. J. Durability Plasticity 2 (1984) 224-253
35. M.A. Koltunov, Creeping and relaxation, Izd.Vishaya, Shkola, Moscow, 1976.
36. Ezzat M.A., and El-Karamany A.S. The uniqueness and reciprocity theorems for generalized thermo-viscoelasticity with two relaxation times. Int. J. Eng. Sci. 40 (2002) 1275-1284
37. Ezzat M.A., and El-Karamany A.S. On uniqueness and reciprocity theorems for generalized thermo-viscoelasticity with thermal relaxation. Canad. J. Phys. 81 (2003) 823-833
38. Ezzat M.A., and El-Karamany A.S. The uniqueness and reciprocity theorems for generalized thermo-viscoelasticity for anisotropic media. J. Thermal Stresses 25 (2002) 507-522
39. Ezzat M., El-Karamany A., and Samaan A. State space formulation to generalized thermo-viscoelasticity with thermal relaxation. J. Thermal Stresses 24 (2001) 823-846
40. Ezzat M., Othman M., and El-Karamany A. State space approach to two-dimensional generalized thermo-viscoelasticity with two relaxation times. Int. J. Eng. Sci. 40 (2002) 1251-1274
41. Ezzat M.A. The relaxation effects of the volume properties of electrically conducting viscoelastic material. Mater. Sci. Eng. 130 (2006) 11-23
42. Ezzat M.A., and Awad E.S. Micropolar generalized magneto-thermoelasticity with modified Ohm's and Fourier's laws. J. Math. Anal. Appl. 353 (2009) 99-113
43. Rabotnov Yu.N. Elements of Hereditary Solid Mechanics (1980), Mir, Moscow
44. Christensen R.M. Theory of Viscoelasticity. An Introduction (1971), Academic Press, New York