Rajneesh Kumar, Mandeep Kaur, S. C. Rajvanshi. Wave Propagation at an Interface of Heat Conducting Micropolar Solid and Fluid Media[J]. Applied Mathematics and Mechanics, 2011, 32(7): 826-847. doi: 10.3879/j.issn.1000-0887.2011.07.007
Citation: Rajneesh Kumar, Mandeep Kaur, S. C. Rajvanshi. Wave Propagation at an Interface of Heat Conducting Micropolar Solid and Fluid Media[J]. Applied Mathematics and Mechanics, 2011, 32(7): 826-847. doi: 10.3879/j.issn.1000-0887.2011.07.007

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

doi: 10.3879/j.issn.1000-0887.2011.07.007
  • Received Date: 2010-11-16
  • Rev Recd Date: 2011-05-09
  • Publish Date: 2011-07-15
  • Wave propagation at an in terface of micropolar generalized thermoelastic solid half space and heat conducting micropolar fluid half space was investigated. Reflection and tran smission phenomenon of plane waves mipinging obliquely at aplane in terface between amicropolar generalized therm oelastic solid half space and heat conducting micropolar fluid half space were investigated. The incident wave was assumed to be striking at the plane interface after propagating through the micropolar generalized thermoelastic solid. Amplitude ratios of the various reflected and transmitted waves were obtained in closed form and it was found that these were functions of angle of incidence, frequency and were affected by the elastic properties of the media. Micropolarity and thermal relaxation effects are shown on these amplitude ratios fo raspecific model. Results of some earlier workers have also been deduced from the present investigation.
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  • [1]
    Eringen A C. Simple microfluids[J]. International Journal of Engineering Science, 1964, 2(2): 205-217. doi: 10.1016/0020-7225(64)90005-9
    [2]
    Eringen A C. Theory of microfluids[J]. Journal of Applied Mathematics and Mechanics, 1966, 16(1): 1-18.
    [3]
    Ariman T, Sylvester N D, Turk M A. Microcontinuum fluid mechanics―a review[J]. International Journal of Engineering Science, 1973, 11(8): 905-930. doi: 10.1016/0020-7225(73)90038-4
    [4]
    Ariman T, Turk M A, Sylvester N D. Applications of microcontinuum fluid mechanics[J]. International Journal of Engineering Science, 1974, 12(4): 273-293. doi: 10.1016/0020-7225(74)90059-7
    [5]
    Riha P. On the theory of heat-conducting micropolar fluid with microtemperature[J]. Acta Mechanic, 1975, 23(1/2): 1-8. doi: 10.1007/BF01177664
    [6]
    Eringen A C, Kafadar C B. Polar field theories[C]Eringen A C. Continuum Physics. Vol 4. New York:Academic Press, 1976.
    [7]
    Brulin O. Linear micropolar media[C]Brulin O, Hsieh R K T. Mechanics of Micropolar Media. Singapore:World Scientific, 1982.
    [8]
    Aggarwal R S, Dhanapal C. Flow and heat transfer in a micropolar fluid past a flate plate with suction and heat sources[J]. International Journal of Engineering Science, 1988, 26(12): 1257-1266. doi: 10.1016/0020-7225(88)90045-6
    [9]
    Payne L E,Straughan B. Critical Rayleigh numbers for oscillatory and non linear convection in an isotropic thermomicropolar fluid[J]. International Journal of Engineering Science, 1989, 27(7): 827-836. doi: 10.1016/0020-7225(89)90048-7
    [10]
    Gorla R S R. Combined forced and free convection in the boundary layer flow of a micropolar fluid on a continuous moving vertical cylinder[J]. International Journal of Engineering Science, 1989, 27(1): 77-86. doi: 10.1016/0020-7225(89)90169-9
    [11]
    Eringen A C. Theory of micro-stretch and bubbly liquids[J]. International Journal of Engineering Science, 1990, 28(2): 133-143. doi: 10.1016/0020-7225(90)90063-O
    [12]
    Aydemir N U, Venart J E S. Flow of a thermomicropolar fluid with stretch[J]. International Journal of Engineering Science, 1990, 28 (12): 1211-1222. doi: 10.1016/0020-7225(90)90069-U
    [13]
    Yerofeyev V I, Soldatov I N. A shear surface wave at the interface of an elastic body and a micropolar liquid[J]. Journal of Applied Mathematics and Mechanics, 1999, 63(2): 277-281. doi: 10.1016/S0021-8928(99)00036-2
    [14]
    Yeremeyev V A, Zubov L M. The theory of elastic and viscoelastic micropolar liquids[J]. Journal of Applied Mathematics and Mechanics, 1999, 63(5): 755-767. doi: 10.1016/S0021-8928(99)00096-9
    [15]
    Hsia S Y, Cheng J W. Longitudinal plane waves propagation in elastic micropolar porous media[J]. Japanese Journal of Applied Physics, 2006, 45: 1743-1748. doi: 10.1143/JJAP.45.1743
    [16]
    Hsia S Y, Chiu S M, Su C C, Chen T H. Propagation of transverse waves in elastic micropolar porous semispaces[J]. Japanese Journal of Applied Physics, 2007, 46: 7399-7405. doi: 10.1143/JJAP.46.7399
    [17]
    Eringen A C. Linear theory of micropolar elasticity[J]. Journal of Applied Mathematics and Mechanics, 1966, 15: 909-923.
    [18]
    Biot M. Thermoelasticity and irreversible thermodynamics[J]. Journal of Applied Physics, 1956, 27(3): 240-253. doi: 10.1063/1.1722351
    [19]
    Lord H, Shulman Y. A generalized dynamical theory of thermoelasticity[J]. Journal of the Mechanics and Physics of Solids, 1967, 15(5): 299-309. doi: 10.1016/0022-5096(67)90024-5
    [20]
    Muller I M. The coldness, a universal function in thermoelastic bodies[J]. Archive for Rational Mechanics and Analysis, 1971, 41(5): 319-332.
    [21]
    Green A E, Laws N. On the entropy production inequality[J]. Archive for Rational Mechanics and Analysis, 1972, 45(1): 47-53.
    [22]
    Green A E, Lindsay K A. Thermoelasticity[J]. Journal of Elasticity, 1972, 2(1): 1-7. doi: 10.1007/BF00045689
    [23]
    Suhubi E S. Thermoelastic solids[C] Eringen A C. Continuum Physics. 2. Part 2, Chapter 2. New York: Academic Press, 1975.
    [24]
    Tomar S K, Gogna M L. Reflection and refraction of a longitudinal microrotational wave at an interface between two micropolar elastic solids in welded contact[J]. Journal of Applied Mathematics and Mechanics, 1992, 30(11): 1637-1646.
    [25]
    Tomar S K, Gogna M L. Reflection and refraction of a longitudinal displacement wave at an interface between two micropolar elastic solids in welded contact[J]. Journal of the Acoustical Society of America, 1995, 97: 827-830.
    [26]
    Tomar S K, Gogna M L. Reflection and refraction of a coupled transverse and micro-rotational waves at an interface between two different micropolar elastic media in welded contact[J]. International Journal of Engineering Science,1995, 33(4): 485-496. doi: 10.1016/0020-7225(94)00077-8
    [27]
    Kumar R, Sharma N, Ram P. Reflection and transmission of micropolar elastic waves at an imperfect boundary[J]. Multidiscipline Modelling in Materials and Structures, 2008, 4(1): 15-36. doi: 10.1163/157361108783470388
    [28]
    Kumar R, Sharma N, Ram P. Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media[J]. Theoretical and Applied Fracture Mechanics, 2008, 49(3): 305-312. doi: 10.1016/j.tafmec.2008.02.007
    [29]
    Singh D, Tomar S K. Longitudinal waves at a micropolar fluid/solid interface[J]. Journal of Applied Mathematics and Mechanics, 2008, 45(1): 225-244.
    [30]
    Ciarletta M. Spatial decay estimates for heat conducting micropolar fluids[J]. Journal of Applied Mathematics and Mechanics, 2001, 39(6): 655-668.
    [31]
    Parfit V R, Eringen A C. Reflection of plane waves from the flat boundary of a micropolar elastic half space[J]. Journal of the Acoustical Society of America, 1969, 45(5): 1258-1272. doi: 10.1121/1.1911598
    [32]
    Dhaliwal R S, Singh A. Dynamic Coupled Thermoelasticity[M]. New Delhi, India: Hindustan Publication Corporation, 1980.
    [33]
    Singh B, Kumar R. Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half-space[J]. Journal of Applied Mathematics and Mechanics, 1998, 36 (7/8): 865-890.
    [34]
    Schoenberg M. Transmission and reflection of plane waves at an elastic-viscoelastic interface[J]. Geophysics Journal of Royal Astronomical Society, 1971, 25 (1/3): 35-47. doi: 10.1111/j.1365-246X.1971.tb02329.x
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