Document Type : Research Paper

**Authors**

^{1}
Department of Mathematics, Kurukshetra University Kurukshetra-136119, Haryana ,India

^{2}
Indira Gandhi National College, Ladwa(Dhanora), Haryana ,India

**Abstract**

The present investigation deals with the reflection and transmission phenomenon due to incident plane longitudinal wave at a plane interface between inviscid fluid half-space and a thermoelastic diffusion solid half-space with dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models. The theory of thermoelasticity with dual-phase-lag heat transfer developed by Roychoudhary [10] has been employed to develop the equation for thermoelastic diffusion with dual-phase-lag heat transfer and dual-phase-lag diffusion model. Amplitude ratios and energy ratios of various reflected and transmitted waves are obtained. It is found that these are the functions of angle of incidence, frequency of incident wave and are influenced by thermoelastic diffusion properties of media. The nature of dependence of amplitude ratios and energy ratios with the angle of incidence have been computed numerically for a particular model. The variations of energy ratios with angle of incidence are also shown graphically. The conservation of energy at the interface is verified. Some special cases are also deduced from the present investigation.

**Keywords**

[2] Hetnarski R.B., Ignaczak J., 1999, Generalized thermoelasticity, Journal of Thermal Stresses 22: 451- 476.

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

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

[5] Hetnarski R.B., Ignaczak J., 1996, Solution-like waves in a low temperature non-linear thermoelastic solid , International Journal of Engineering Science 34: 1767-1787.

[6] Green A.E., Nagdhi P.M., 1992, Thermoelasticity without energy dissipation, Journal of Elasticity 31: 189-208.

[7] Green A.E., Nagdhi P.M., 1991, A re-examination of the basic posulates of thermomechanics, Proceedings of the Royal Society of London 432: 171-194.

[8] Tzou D.Y., 1995, A unified field approach for heat conduction from macro to micro Scales, The ASME Journal of Heat Transfer 117: 8-16.

[9] Chandrasekharaiah D.S., 1998, Hyperbolic thermoelasticity: a review of recent literature, Applied Mechanics Reviews 51: 705-729.

[10] Roychoudhary S.K., 2007, On a thermoelastic three-phase-lag model, Journal of Thermal Stresses 30: 231-238.

[11] Sinha S.B., Elsibai K.A., 1997, Reflection and refraction of thermoelastic waves at an interface of two semi-infinite media with two relaxation times, Journal of Thermal Stresses 20: 129-145.

[12] Kumar R., Sharma J.N., 2005, Reflection of plane waves from the boundaries of a micropolar thermoelastic half space without energy dissipation, International Journal of Applied Mechanics and Engineering 10: 631-645.

[13] Kumar R., Sarthi P., 2006, Reflection and refraction of thermoelastic plane waves at an interface of two thermoelastic media without energy dissipation, Archives of Mechanics 58: 155-185.

[14] Kumar R., Singh M., 2007, Propagation of plane waves in thermoelastic cubic material with two relaxation times, Applied Mathematics and Mechanics 28(5): 627-641.

[15] Kumar R., Kansal T., 2011, Reflection of plane waves at the free surface of a transversely isotropic thermoelastic diffusive solid half-space, International Journal of Applied Mathematics and Mechanics 7(14): 57-78.

[16] Kumar R., Kansal T., 2012, Reflecction and refraction of plane waves at the interface of an elastic solid half-space and a thermoelastic diffusive solid half-space, Archives of Mechanics 64(3): 293-317.

[17] Podstrigach Ya. S., 1961, Differential equations of the problem of thermodiffusion in a solid deformable isotropic body, Dop. Akad. Nauk. Ukr. RSR 2: 169-172.

[18] Podstrigach Ya. S., Pavlina V. S., 1965, The differential equations of thermodynamic processes in an n-component solid solution, Fiziko Khimicheskaya Mekhanika Materialov 1(4): 383-389.

[19] Podstrigach Ya. S., 1964, The diffusion theory of strain of an isotropic solid medium ,Vopr. Mekh. Real. Tver. Tela 2 : 71-99.

[20] Podstrigach Ya. S., 1965, The diffusion theory of inelasticity of metals, Zh. Prikl. Mekh. Tekh. Fiz 2 : 67-72.

[21] Podstrigach Ya. S., Pavlina V. S., 1974, Diffusion processes in a viscoelastic deformable body, Prikl. Mekh 10(5): 47-53.

[22] Podstrigach Ya. S., Pavlina V. S., 1977, Diffusion processes in a viscoelastic deformable layer, Fiziko Khimicheskaya Mekhanika Materialov 13(1): 76-81.

[23] Podstrigach Ya. S., Shvets R. N., Pavlina V. S., 1971, The quasistatic thermodiffusion problem for deformable solid bodies, Prikl. Mekh 7(12): 11-16.

[24] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-I, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 55-64.

[25] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-II, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 129-135.

[26] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-III, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 275-276.

[27] Nowacki W., 1976, Dynamical problems of diffusion in solids, Engineering Fracture Mechanics 8: 261-266.

[28] Dudziak W., Kowalski S.J., 1989, Theory of thermodiffusion for solids, International Journal of Heat and Mass transfer 32: 2005-2013.

[29] Olesiak Z.S., Pyryev Y.A., 1995, A coupled quasi-stationary problem of thermodiffusion for an elastic cylinder, International Journal of Engineering Science 33: 773-780.

[30] Gawinecki J.A., Szymaniec A., 2002, Global solution of the cauchy problem in nonlinear thermoelastic diffusion in solid body, Proceedings in Applied Mathematics and Mechanics 1: 446- 447.

[31] Wu J., Zhu Z., 1992, The propagaton of Lamb waves in a plate bordered with layers of a liquid, The Journal of the Acoustical Society of America 91: 861-867.

[32] Sharma J.N., Kumar S., Sharma Y.D., 2008, Propagation of rayleigh waves in microstretch thermoelastic continua under inviscid fluid loadings, Journal of Thermal Stresses 31: 18-39.

[33] Kumar R., Pratap G., 2009, Wave propagation in microstretch thermoelaastic plate bordered with layers of inviscid liquid, Multidiscipline Modeling in Materials and Structures 5: 171-184.

[34] Sharma M.D., 2004, 3-D wave propagation in a general anisotropic poroelastic medium: reflection and refraction at an interface with fluid, Geophysical Journal International 157: 947-958.

[35] Sherief H.H., Hamza F.A. Saleh H.A.,2004, The theory of generalized thermoelastic diffusion, The International Journal of Engineering Science 42: 591-608.

[36] Achenbach J.D.,1973, Wave Propagation in Elastic Solids, North –Holland, Amstendam.

[37] Borcherdt R.D., 1982, Reflection-refraction of general P and type-I S waves in elastic and anelastic solids, Geophysical Journal of Royal Astronomical Society 70: 621-638.

[38] Sherief H.H., Saleh H.A., 2005, A half space problem in the theory of thermoelastic diffusion, International Journal of Solid and Structures 42: 4484- 4493.

Summer 2015

Pages 312-326