PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Global stability for double-diffusive convection in a couple-stress fluid saturating a porous medium

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that the global non-linear stability threshold for convection in a double-diffusive couple-stress fluid saturating a porous medium is exactly the same as the linear instability boundary. The optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It is also found that couple-stress fluid saturating a porous medium is thermally more stable than the ordinary viscous fluid, and the effects of couple-stress parameter (F) , solute gradient (S f) and Brinkman number (Da) on the onset of convection is also analyzed.
Wydawca
Rocznik
Strony
13--20
Opis fizyczny
Bibliogr. 42 poz., rys.
Twórcy
  • Department of Mathematics, Uttaranchal University, Dehradun, Uttarakhand 248007, India
autor
  • Department of Mathematics, National Institute of Technology, Hamirpur, Himachal Pradesh 177005, India
Bibliografia
  • [1] Joseph, D.D. (1976). Stability of Fluid Motions. Vols. I-II, Springer, Berlin.
  • [2] Orr, W. McF. (1907). Stability or instability of the steady motions of a perfect liquid. Proceedings of the Royal Irish Academy, A 37, 9.
  • [3] Serrin, J. (1959). On the stability of viscous fluid motions. Archive for Rational Mechanics and Analysis, 3, 1.
  • [4] Joseph, D.D. (1965). On the stability of the Boussinesq equations. Archive for Rational Mechanics and Analysis, 20, 59.
  • [5] Joseph, D.D. (1966). Nonlinear stability of the Boussinesq equations by the method of energy. Archive for Rational Mechanics and Analysis, 22, 163.
  • [6] Galdi, G.P., Padula, M. (1990). A new approach to energy theory in the stability of fluid motion. Archive for Rational Mechanics and Analysis, 110, 187.
  • [7] Straughan, B., Explosive Instabilities in Mechanics, Springer, Berlin, 1998.
  • [8] Straughan, B. (2004). The Energy Method, Stability, and Nonlinear Convection. Springer-Verlag, New York.
  • [9] Straughan, B. (2005). A sharp nonlinear stability threshold in rotating porous convection. Proceedings of the Royal Society of London Series A, 457, 87.
  • [10] Kaloni, P.N., Qiao, Z. (1997). Non-linear stability of convection in a porous medium with inclined temperature gradient. International Journal of Heat and Mass Transfer, 40, 1611.
  • [11] Kaloni, P.N., Qiao, Z. (1997). Nonlinear convection with inclined temperature gradient and horizontal mass flow. International Journal of Engineering Science, 35, 299.
  • [12] Kaloni, P.N., Qiao Z. (2001). Non-linear convection in a porous medium with inclined temperature gradient and variable gravity effects. International Journal of Heat and Mass Transfer, 44, 1585.
  • [13] Guo, J., Kaloni, P.N. (1995). Nonlinear stability problem of a rotating doubly diffusive porous layer. Journal of Mathematical Analysis and Applications, 190, 373.
  • [14] Guo, J., Qin, Y., Kaloni, P.N. (1994). Non-linear stability problem of a rotating doubly diffusive fluid layer. International Journal of Engineering Science, 32, 1207.
  • [15] Payne, L.E., Straughan, B. (2000). Unconditional nonlinear stability in temperature – dependent viscosity flow in a porous medium. Studies in Applied Mathematics, 105, 59.
  • [16] Stokes, V.K. (1966). Couple stresses in fluids. The Physics of Fluids, 9, 1709.
  • [17] Ramanaiah, G., Sarkar, P. (1979). Slider bearings lubricated by fluids with couple stress. Wear, 52, 27.
  • [18] Sharma R. C., Thakur K. D. (2000). On couple-stress fluid heated from below in porous medium in hydromagnetics. Czechoslovak Journal of Physics, 50, 753.
  • [19] Sharma R. C., Sunil, Pal M. (2000). On couple-stress fluid heated from below in porous medium in presence of rotation. Applied Mechanical Engineering, 5(4), 883.
  • [20] Sunil, Mahajan A. (2008a). A nonlinear stability analysis for magnetized ferrofluid heated from below. Proceedings of the Royal Society A, 464, 83.
  • [21] Sunil, Mahajan A. (2008b). A nonlinear stability analysis for rotating magnetized ferrofluid heated from below. Applied Mathematics and Computation, 204, 299
  • [22] Sunil, Mahajan A. (2008c). A nonlinear stability analysis of a double-diffusive magnetized ferrofluid. Zeitschrift für Naturforschung, 63a, 797.
  • [23] Sunil, Mahajan A. (2008d). A nonlinear stability analysis in a double-diffusive magnetized ferrofluid layer saturating a porous medium. Journal of Geophysics and Engineering, 5(3), 311.
  • [24] Sunil, Choudhary S., Bharti P. (2013). Global stability for thermal convection in a couple-stress fluid with temperature and pressure dependent viscosity. Studia Geotechnica et Mechanica, 35(3), 85.
  • [25] Sunil, Choudhary S., Bharti P. (2012). Global stability for thermal convection in a couple-stress fluid saturating a porous medium with temperature and pressure dependent-dependent viscosity. International Journal of Applied Mechanics and Engineering, 17(2), 583.
  • [26] Hsu C. H., Lin J. R., Chiang H.L. (2003). Combined effects of couple stresses and surface roughness on the lubrication of short journal bearings. Industrial Lubrication and Tribology, 55, 233.
  • [27] Lahmar, M. (2005). Elastohydrodynamic analysis of double-layered journal bearings lubricated with couple-stress fluids. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 219, 145.
  • [28] Nield, D.A., Bejan A. (2006). Convection in Porous Media, Springer, New York.
  • [29] Veronis, G. (1968). Effect of a stabilizing gradient of solute on thermal convection. Journal of Fluid Mechanics, 34, 315.
  • [30] Banies, P.G., Gill A. E. (1969). On thermohaline convection with linear gradients. Journal of Fluid Mechanics, 37, 289.
  • [31] Joseph, D.D. (1970). Global stability of the conduction-diffusion solution. Archive for Rational Mechanics and Analysis, 36, 285.
  • [32] Griffiths, R.W. (1981). Layered double-diffusive convection in porous media. Journal of Fluid Mechanics, 102, 221.
  • [33] Sunil, Sharma, D., Sharma, R.C. (2004). Effect of rotation on ferromagnetic fluid heated and soluted from below saturating a porous medium. Journal of Geophysics and Engineering, 1, 116.
  • [34] Sunil, Sharma, A., Sharma, R.C. (2006). Effect of dust particles on ferrofluid heated and soluted from below. International Journal of Thermal Sciences, 45, 347.
  • [35] Sunil, Sharma, A., Bharti, P.K., Shandil, R.G. (2007). Linear stability of double-diffusive convection in a micropolar ferromagnetic fluid saturating a porous medium. International Journal of Mechanical Sciences, 49, 1047.
  • [36] Sunil, Sharma, P., Mahajan, A. (2009). A nonlinear stability analysis of a rotating double-diffusive magnetized ferrofluid saturating a porous medium. Heat Transfer Research, 40, 351.
  • [37] Sunil, Sharma, P., Mahajan, A. (2010). Onset of Darcy– Brinkman double-diffusive convection in a magnetized ferrofluid layer using a thermal non-equilibrium model: a nonlinear stability analysis. Journal of Geophysics and Engineering, 7, 417.
  • [38] Mahajan, A., Nandal, R. (2017). On the stability of penetrative convection in a couple-stress fluid. International Journal of Applied and Computational Mathematics, 3(4), 3745-3758.
  • [39] Nandal, R., Mahajan, A. (2018). Penetrative convection in couple-stress fluid via internal heat source/sink with the boundary effects. Journal of Non-Newtonian Fluid Mechanics, 260, 133-141.
  • [40] Qin, Y., Kaloni, P.N. (1995). Nonlinear stability problem of a rotating porous layer. Quarterly of Applied Mathematics, 53, 129.
  • [41] Finlayson, B.A. (1970). Convective instability of ferromagnetic fluids. Journal of Fluid Mechanics, 40, 753.
  • [42] Chandrasekhar, S. (1981). Hydrodynamic and Hydromagnetic Stability, Dover, New York.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ade219e6-2aa6-4126-a20d-06c91f883335
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.