Propagation of Waves at an Interface of Heat Conducting Elastic Solid and Micropolar Fluid Media

Subject Areas : Engineering

R Kumar ¹ , M Kaur ² , S.C Rajvanshi ³

1 - Department of Mathematics, Kurukshetra University
2 - Department of Applied Sciences, Guru Nanak Dev Engineering College, Ludhiana
3 - Department of Applied Sciences, Gurukul Vidyapeeth, Institute of Engineering and Technology

Received: 2012-06-05 Accepted : 2012-07-05 Published : 2012-06-30

Keywords: Reflection coefficient, Elastic solid, Micropolar fluid, Thermoelastic, Transmission coefficient, Angle of incidence,

Abstract :

The present investigation is concerned with the reflection and transmission coefficients of plane waves at the interface of generalized thermoelastic solid half space and heat conducting micropolar fluid half- space. The amplitude ratios of various reflected and transmitted waves with various angle of incidence have been computed numerically and depicted graphically. Micropolarity and thermal relaxation effects are shown on the amplitude ratios for specific model. Some special and particular cases are also deduced from the present investigation.

References:

[1] Eringen A.C., 1964, Simple microfluids, International Journal of Engineering Science 2: 205-217.

[2] Eringen A.C., 1966 a, Theory of microfluids, Journal of Applied Mathematics and Mechanics 16: 1-18.

[3] Ariman T., Sylvester N.D., Turk M.A., 1973, Microcontinuum fluid mechanics-a review, International Journal of Engineering Science 11: 905-930.

[4] Ariman T., Sylvester N.D., Turk M.A., 1974, Review article applications of microcontinuum fluid mechanics, International Journal of Engineering Science 12: 273-293.

[5] Riha P., 1975, On the theory of heat-conducting micropolar fluid with microtemperature, Acta Mechanica 23: 1-8.

[6] Eringen A.C., Kafadar C.B.,1976, Polar Field Theories, In Continuum Physics ,Edited by A.C. Eringen, Vol. IV. Academic Press, New York.

[7] Brulin O., 1982, Linear Micropolar Media, In Mechanics of Micropolar Media ,Edited by O. Brulin and R.K.T. HSIEH, World Scientific, Singapore.

[8] Gorla R.S.R.,1989, Combined forced and free convection in the boundary layer flow of a micropolar fluid on a continuous moving vertical cylinder, International Journal of Engineering Science 27: 77-86.

[9] Eringen A.C., 1990, Theory of Microstretch and Bubbly Liquid, International Journal of Engineering Science 28: 133-143.

[10] Aydemir N.U., Venart J.E.S., 1990, Flow of a thermomicropolar fluid with stretch, International Journal of Engineering Science 28: 1211-1222.

[11] Hsia S.Y., Cheng J.W., 2006, Longitudinal plane waves propagation in elastic micropolar porous media, Japanese Journal of Applied Physics 45: 1743-1748.

[12] Hsia S.Y., Chiu S.M., Su C.C., Chen T.H., 2007, Propagation of transverse waves in elastic micropolar porous semispaces, Japanese Journal of Applied Physics 46: 7399-7405.

[13] Biot M., 1956, Thermoelasticity and Irreversible Thermodynamics, Journal of Applied Physics 27: 240-253.

[14] Lord H., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.

[15] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.

[16] Dhaliwal R.S., Singh A., 1980, Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.

[17] Ignaczak J., Starzewski M.O., 2010, Thermoelasticity with Finite Wave Speeds, Oxford Science Publisher.

[18] Tomar S.K., Gogna M.L., 1992, Reflection and refraction of a longitudinal microrotational wave at an interface between two micropolar elastic solids in welded contact, International Journal of Engineering Science 30: 1637-1646.

[19] Tomar S.K., Gogna M.L., 1995 a, Reflection and refraction of a longitudinal displacement wave at an interface between two micropolar elastic solids in welded contact, Journal of the Acoustical Society of America 97: 827-830.

[20] Tomar S.K., Gogna M.L., 1995 b, Reflection and refraction of a coupled transverse and microrotational waves at an interface between two different micropolar elastic solids in welded contact, International Journal of Engineering Science 30: 485-496.

[21] Kumar R., Sharma N., Ram P., 2008 a, Reflection and transmission of micropolar elastic waves at an imperfect boundary, Multidiscipline Modelling in Materials and Structures (MMMS) 4: 15-36.

[22] Kumar R., Sharma N., Ram P., 2008 b, Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media, Theoretical and Applied Fracture Mechanics 49: 305-312.

[23] Singh D., Tomar S. K., 2008, Longitudinal waves at a micropolar fluid/solid interface, International Journal of Solids And Structures 45: 225-244.

[24] Ciarletta M., 2001, Spatial decay estimates for heat conducting micropolar fluids, International Journal of Engineering Science 39: 655-668.