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Global stability for thermal convection in a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that the global nonlinear stability threshold for convection in a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that the linearized instability theory has captured completely the physics of the onset of convection. Then the effect of couple stress parameter, variable dependent viscosity and Darcy-Brinkman number on the onset of convection are also analyzed.
Rocznik
Strony
583--602
Opis fizyczny
Bibliogr. 45 poz., wykr.
Twórcy
autor
autor
autor
  • Department of Mathematics, National Institute of Technology Hamirpur, (H.P.) - 177 005, INDIA, sunilnitham@gmail.com
Bibliografia
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  • Guo J., Qin Y. and Kaloni P.N. (1994): Nonlinear stability problem of a rotating doubly diffusive fluid layer.Int. J. Engg. Sci., vol.32, pp.1207-1219.
  • Guo J. and Kaloni P.N. (1995): Nonlinear stability problem of a rotating doubly diffusive porous layer.J. Math. Analysis, Appl., vol.190, pp.373-390.
  • Gupta R.S. and Sharma L.G. (1988): Analysis of couple-stress lubricant in hydrostatic thrust bearings.WEAR, vol.125, pp.257-269.
  • Hsu C.H., Lin J.R. and Chiang H.L. (2003): Combined effects of couple-stresses and surface roughness on the lubrication of short journal bearings.Indus. Lub. Tribol., vol.55, pp.233-243.
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  • Kaloni P.N. and Qiao Z. (1997): Non-linear stability of convection in a porous medium with inclined temperature gradient.Int. J. Heat Mass Transfer, vol.40, pp.1611-1615.
  • Kaloni P.N. and Qiao Z. (1997): Non-linear convection with inclined temperature gradient and horizontal mass flow.Int. J. Engg. Sci., vol.35, pp.299-309.
  • Kaloni P.N. and Qiao Z. (2001): Non-linear convection in a porous medium with inclined temperature gradient and variable gravity effects.Int. J. Heat Mass Transfer, vol.44, pp.1585-1591.
  • Lahmar M. (2005): Elastohydrodynamic analysis of double-layered journal bearings lubricated with couple-stress fluids.Proc. Instn. Mech. Engrs., Part J.J. Eng. Tribol., vol.219, pp.145-171.
  • Laun H.M. (2003): Pressure dependent viscosity and dissipative heating in capillary rheometry of polymer melts.Rheol. Acta, vol.42, pp.295-308.
  • Martin-Alfonso M.J., Martinez-Boza F.J., Partal P. and Gallegos C. (2006): Influence of pressure and temperature on the flow behavior of heavy fluid oils.Rheol. Acta, vol.45, pp.357-365.
  • Martin-Alfonso M.J., Martinez-Boza F.J., Navarro F.J., Fernandez M. and Gallegos C. (2007): Pressure-temperature-viscosity relationship for heavy petroleum fractions. Fuel, vol.86, pp.227- 233.
  • Nield D.A. and Bejan A. (2006): Convection in porous media. New York: Springer.
  • Orr W. McF. (1907): Stability or instability of the steady motions of a perfect liquid.Proc. Roy. Irish. Acad. Sect., A 27, pp.69-138.
  • Payne L.E. and Straughan B. (2000): Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium.Stud. Appl. Math., vol.105, pp.59-81.
  • Qin Y. and Kaloni P.N. (1995): Nonlinear stability problem of a rotating porous layer.Q. Appl. Math., vol.53, pp.129-142.
  • Rajagopal K.R., Saccomandi G. and Vergori L. (2009a): On the Oberbeck-Boussinesq approximation in fluids with pressure-dependent viscosities.Nonlinear Anal. Real Word Appl., vol.10, pp.1139-1150.
  • Rajagopal K.R., Saccomandi G. and Vergori L. (2009b): Stability analysis of the Rayleigh- Bènard convection for a fluid with temperature and pressure dependent viscosity.Z. Angew. Math. Phys., vol.60, pp.739-755.
  • Rajagopal K.R., Saccomandi G. and Vergori L. (2009c): A systematic approximation for the equation governing convection-diffusion in a porous medium.Nonlinear Anal. Real Word Appl., (accepted).
  • Rajagopal K.R., Saccomandi G. and Vergori L. (2011): Stability analysis of the Rayleigh- Bènard convection in a porous medium. ZAMP, vol.60, pp.149-160.
  • Ramanaiah G. (1979): Slider bearings lubricated by fluids with couple-stress.WEAR, vol.52, pp.27-36.
  • Rionero S. (1968): Metodi variazionali per la stabilita asintotica in media in magnetodroi-dinamica.Ann. Mate. Pura Appl., vol.78, pp.339-364.
  • Serrin J. (1959): On the stability of viscous fluid motions.Arch. Ration. Mech. Analysis, vol.3, pp.1-13.
  • Shehawey E.F.El. and Mekheimer K.S. (1994): Couple-stresses in peristaltic transport of fluids. J. Phys. D. Appl. Phys., vol.27, pp.1163-1170.
  • Straughan B. (1998): Explosive Instabilities in Mechanics. Berlin, Germany: Springer.
  • Straughan B. (2004): The Energy Method, Stability, and Nonlinear Convection.NewYork: SpringerVerlag.
  • Straughan B. (2001): A sharp nonlinear stability threshold in rotating porous convection.Proc. Roy. Soc. Lond., A vol.457, pp.87-93.
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  • Sunil and Mahajan A. (2008a): A nonlinear stability analysis for magnetized ferrofluid heated from below.Proc. Roy. Soc. Lond., A vol.464, pp.83-98.
  • Sunil and Mahajan A. (2008b): A nonlinear stability analysis for rotating magnetized ferrofluid heated from below.Appl. Math. Comp., vol.204, pp.299-310.
  • Sunil and Mahajan A. (2008c): A nonlinear stability analysis of a double-diffusive magnetized ferrofluid.Z. Naturforsch., A vol.63a, pp.797-807.
  • Sunil and Mahajan A. (2008d): A nonlinear stability analysis in a double-diffusive magnetized ferrofluid layer saturating a porous medium.J. Geophys. Eng., vol.5, pp.311-322.
  • Sunil and Mahajan A. (2009a): A nonlinear stability analysis for thermoconvective magnetized ferrofluid saturating a porous medium.Trans. Porous Media, vol.76, pp.327-343.
  • Sunil and Mahajan A. (2009b): A nonlinear stability analysis for rotating magnetized ferrofluidheated from below saturating a porous medium.ZAMP, vol.60, pp.344-362.
  • Sunil Devi R. and Mahajan A. (2011): Global stability for thermal convection in a couple-stress fluid.Int. Commun. Heat Mass Trans., (USA) (Accepted for publication).
  • Temam R. (1997): Infinite-dimensional dynamical system in mechanics and physics.Applied Mathematical Sciences, vol.68, Springer-Verlag, New York Berlin Heidelberg.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0027-0015
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