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Journal
2011 | 9 | 1 | 138-145
Article title

Acoustic heating produced in the thermoviscous flow of a Bingham plastic

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Content
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EN
Abstracts
EN
This study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic’s viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation governing acoustic heating, and to retain those belonging to the thermal mode. The nonlinear terms of the final equation are a result of interaction between sounds and the thermal mode. In the field of intense sound, the resulting nonlinear acoustic terms form a driving force for the heating. The final governing dynamic equation of the thermal mode is valid in a weakly nonlinear flow. It is instantaneous, and does not imply that sounds be periodic. The equations governing the dynamics of both sounds and the thermal mode depend on sign of the shear rate. An example of the propagation of a bipolar initially acoustic pulse and the evolution of the heating induced by it is illustrated and discussed.
Publisher

Journal
Year
Volume
9
Issue
1
Pages
138-145
Physical description
Dates
published
1 - 2 - 2011
online
24 - 9 - 2010
Contributors
  • Faculty of Applied Physics and Mathematics, Gdansk University of Technology, ul. Narutowicza 11/12, 80-233, Gdansk, Poland, anpe@mif.pg.gda.pl
References
  • [1] E.C. Bingham, U.S. Bureau of Standards Bulletin 13, 309 (1916)
  • [2] S. Benito et al., Eur. Phys. J. E 25, 225 (2008) http://dx.doi.org/10.1140/epje/i2007-10284-2[Crossref]
  • [3] E.D. Kravtsova, E.M. Gil’derbrandt, V.K. Frizorger, Russ. J. Non-Ferr. Met.+ 50, 114 (2009) (in Russian) http://dx.doi.org/10.3103/S1067821209020072[Crossref]
  • [4] O.V. Rudenko, S.I. Soluyan, Theoretical foundations of nonlinear acoustics (Plenum, New York, 1977)
  • [5] S. Makarov, M. Ochmann, Acustica 82, 579 (1996)
  • [6] C.L. Hartman et al., J. Acoust. Soc. Am. 91, 513 (1992) http://dx.doi.org/10.1121/1.402740[Crossref]
  • [7] O.V. Rudenko, Phys.-Usp.+ 50, 359 (2007) http://dx.doi.org/10.1070/PU2007v050n04ABEH006236[Crossref]
  • [8] A. Perelomova, Acta Acust. United Ac. 89, 754 (2003)
  • [9] A. Perelomova, Phys. Lett. A 357, 42 (2006) http://dx.doi.org/10.1016/j.physleta.2006.04.014[Crossref]
  • [10] A. Perelomova, Acta Acust. 94, 382 (2008) http://dx.doi.org/10.3813/AAA.918045[Crossref]
  • [11] B.-T. Chu, L.S.G. Kovasznay, J. Fluid. Mech. 3, 494 (1958) http://dx.doi.org/10.1017/S0022112058000148[Crossref]
  • [12] B. Riemann, The collected works of Bernard Riemann (Dover, New York, 1953)
  • [13] V. Gusev, J. Acoust. Soc. Am. 107, 3047 (2000) http://dx.doi.org/10.1121/1.429333[Crossref]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-010-0043-7
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