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Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

Published online by Cambridge University Press:  03 June 2015

Rajneesh Kumar  and
Tarun Kansal
Rajneesh Kumar*
Affiliation:
Department of Mathematics, Kurukshetra University, Kurukshetra-136 119, India
Tarun Kansal*
Affiliation:
Department of Mathematics, Kurukshetra University, Kurukshetra-136 119, India
*
Corresponding author. Email: rajneeshkuk@rediffmail.com
Email: tarun1_kansal@yahoo.co.in
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Abstract

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller’s method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.

Keywords

35Q8037D3574F0576N1780A17Viscous compressible fluidisotropicthermoelastic diffusionphase velocityattenuation coefficient
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 2 , April 2011 , pp. 219 - 238
Copyright
Copyright © Global-Science Press 2011

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References

[1] Aouadi, M., Variable electrical and thermal conductivity in the theory of generalized thermodiffusion, ZAMP., 57(2) (2006), pp. 350–366.Google Scholar
[2] Aouadi, M., A generalized thermoelastic diffusion problem for an infinitely long solid cylinder, Int. J. Math. Sci., (2006), pp. 1–15.Google Scholar
[3] Aouadi, M., A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion, Int. J. Solids. Struct., 44 (2007), pp. 5711–5722.Google Scholar
[4] Aouadi, M., Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion, J. Therm. Stresses., 30 (2007), pp. 665–678.Google Scholar
[5] Aouadi, M., Generalized theory of thermoelastic diffusion for anisotropic media, J. Therm. Stresses., 31 (2008), pp. 270–285.Google Scholar
[6] Ashour, A. S., Wave motion in a fluid-filled fracture, Int. J. Engg. Sci., 38 (2000), pp. 505–515.Google Scholar
[7] Chanderashekhariah, D. S., Thermoelasticity with second: a review, Appl. Mech. Rev., 39 (1986), pp. 355–376.Google Scholar
[8] Dhaliwal, R. S., and Sherief, H., Generalized thermoelasticity for anisotropic media, Quart. Appl. Math., 33 (1980), pp. 1–8.Google Scholar
[9] Gawinecki, J. A., and Szymaniec, A., Global solution of the Cauchy problem in nonlinear thermoelastic diffusion in solid body, Proc. Appl. Math. Mech., 1 (2002), pp. 446–447.Google Scholar
[10] Gawinecki, J. A., Kacprzyk, P., and Bar-yoseph, P., Initial boundary value problem for some coupled nonlinear parabolic system of partial differential equations appearing in thermoe-lastic diffusion in solid body, Anal. Appl., 19 (2000), pp. 121–130.Google Scholar
[11] Green, A. E., and Lindsay, K. A., Thermoelasticity, J. Elasticity., 2 (1972), pp. 1–7.Google Scholar
[12] Hasheminejad, S. M., and Safari, N., Dynamic viscoelastic effects on sound wave diffraction by spherical and cylindrical shells submerged in and filled with viscous compressible fluids, Shock. Vib., 10 (2003), pp. 339–363.Google Scholar
[13] Hasheminejad, S. M., and Safari, N., Acoustic scattering from viscoelastically coated spheres and cylinders in viscous fluids, J. Sound. Vib., 280 (2005), pp. 101–125.Google Scholar
[14] Hetnarski, R. B., and Ignaczak, J., Generalized thermoelasticity, J. Thermal. Stress., 22 (1999), pp. 451–476.Google Scholar
[15] Kumar, R., and Kansal, T., Propagation of lamb waves in transversely isotropic thermoelastic diffusive plate, Int. Solids. Struct., 45 (2008), pp. 5890–5913.Google Scholar
[16] Lord, H. W., and Shulman, Y., A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids., 15 (1967), pp. 299–309.Google Scholar
[17] Nayfeh, A. H., and Nagy, P. B., Excess attenuation of leaky lamb waves due to viscous fluid loading, J. Acoustic. Soc. America., 101(5) (1997), pp. 2649–2658.Google Scholar
[18] Nowacki, W., Dynamical problems of thermodiffusion in solids-I, Bulletin of Polish Academy of Sciences Series, Science and Technology., 22 (1974), pp. 55–64.Google Scholar
[19] Nowacki, W., Dynamical problems of thermodiffusion in solids-II, Bulletin of Polish Academy of Sciences Series, Science and Technology., 22 (1974), pp. 129–135.Google Scholar
[20] Nowacki, W., Dynamical problems of thermodiffusion in solids-III, Bulletin of Polish Academy of Sciences Series, Science and Technology., 22 (1974), pp. 275–276.Google Scholar
[21] Nowacki, W., Dynamical problems of thermodiffusion in solids, Eng. Fract. Mech., 8 (1976), pp. 261–266.Google Scholar
[22] Sherief, H. H., Hamza, F., and Saleh, H., The theory of generalized thermoelastic diffusion, Int. J. Eng. Sci., 42 (2004), pp. 591–608.Google Scholar
[23] Sherief, H. H., and Saleh, H., A half space problem in the theory of generalized thermoelastic diffusion, Int. J. Solids. Struct., 42 (2005), pp. 4484–4493.Google Scholar
[24] Singh, B., Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion, J. Earth. System. Sci., 114(2) (2005), pp. 159–168.Google Scholar
[25] Singh, B., Reflection of SV waves from free surface of an elastic solid in generalized thermodiffusion, J. Sound. Vib., 291(3-5) (2006), pp. 764–778.Google Scholar
[26] Sorokin, S. V., and Terentiev, A. V., Flow-induced vibrations of an elastic cylindrical shell conveying of a compressible fluid, J. Sound. Vib., 296 (2006), pp. 777–796.Google Scholar
[27] Sorokin, S. V., Analysis of time harmonic wave propagation in an elastic layer under heavy fluid loading, J. Sound. Vib., 305 (2007), pp. 689–702.Google Scholar
[28] Sorokin, S. V., and Chubinskij, A. V., On the role of fluid viscosity in wave propagation in elastic plates under heavy fluid loading, J. Sound. Vib., 311 (2008), pp. 1020–1038.Google Scholar