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Combined effect of temperature and gravity modulations on the onset of convection in an anisotropic porous medium

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Języki publikacji
PL
Abstrakty
EN
The combined effect of time-periodic boundary temperature (TBT, also called temperature modulation) and time-periodic body force (TBF, also called gravity modulation) of small amplitude on convection in an anisotropic porous medium is investigated by making a linear stability analysis. A regular perturbation method is used to arrive at an expression for the correction Rayleigh number that throws light on the possibility of sub-critical motions. With respect to synchronous TBT and TBF for moderate frequency values, the role of the Prandtl number, horizontal porous parameter, mechanical and thermal anisotropy parameters and the Brinkman number in inducing sub-critical instability is delineated. An asymptotic analysis is also presented for small and large frequencies. A comparison is made between the effects of temperature, gravity and combined (temperature + gravity) modulations on convection. The problem illustrates a method of regulating convection.
Rocznik
Strony
267--291
Opis fizyczny
Bibliogr. 25 poz., tab., wykr.
Twórcy
Bibliografia
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  • Caltagirone J.P. (1976): Stabilite d'une couche poreuse horizontale soumise a des conditions aux limite periodiques. - Int. J. Heat Mass Transfer, vol.19, pp.815-820.
  • Caltagirone J.P. (1980): Stability of a saturated porous layer subject to a sudden rise in surface temeprature : Comparison between the linear and energy method. - Quar. J. Mech. Appl. Math., vol.33, pp.47-58.
  • Castinel G. and Combarnous M. (1974): Critere d'apparition de la convection naturelle dans une couche poreuse anisotrope horizontal. - C.R. Acad. Sci., B 278, pp.701-704.
  • Chandrasekhar S. (1961): Hydrodynamic and Hydromagnetic Stability. - London: Oxford University Press.
  • Epherre J.F. (1975): Critere d'apparition de la convection naturelle dans une couche poreuse anisotrope. - Rev. Gen Thermique, vol.168, pp.949-950.
  • Govender S. (2004a). Stability of convection in a gravity modulated porous layer heated from below. - Transport in Porous Media, vol.57, pp.113-124.
  • Govender S. (2005). Linear stability and convection in a gravity modulated porous layer heated from below: Transition from synchronous to subharmonic solutions. - Transport in Porous Media, vol.59, pp.227-238.
  • Kvernvold O. and Tyvand P.A. (1979): Nonlinear thermal convection in anisotropic porous media. - J. Fluid Mech., vol.90, pp.609-624.
  • Mahabaleswar U.S. (2007): Combined effect of temperature and gravity modulations on the onset of magneto-convection in weak electrically conducting micropolar liquids. - Int. J. Engg Sci., vol.45, pp.525-540.
  • Malashetty M.S. and Basavaraja D. (2002): Rayleigh-Bénard convection subject to time dependent wall temperature/gravity in a fluid-saturated anisotropic porous medium. - Heat and Mass Transfer (Springer-Verlag), vol.38, pp.551-563.
  • Malashetty M.S. and Padmavathi V. (1997a): Effect of Gravity modulation on the onset of convection in a porous layer. - J. Porous Media, vol.1, pp.219-230.
  • Malashetty M.S. and Padmavathi V. (1997b): Effect of Gravity modulation on the onset of convection in a fluid and porous layer. - Int. J. Engg. Sci., vol.35, pp.829-840.
  • Malashetty M.S., Siddheshwar P.G. and Mahantesh Swamy (2006): Effect of thermal modulation on the onset of convection in a viscoelastic fluid saturated porous layer. - Transport in Porous Media, vol.62, pp.55-79.
  • Malashetty M.S. and Veeranna S. Wadi (1999): Rayleigh-Benard convection subjected to time dependent wall temperature in a fluid saturated porous layer. - Fluid Dynamics Research, vol.24, pp.293-308.
  • Malkus W.V.R. and Veronis G. (1958): Finite amplitude cellular convection. - J. Fluid Mech., vol.4, pp.225-260.
  • Nilsen J. and Storesletten L. (1990): An analytical study on natural convection in isotropic and anisotropic porous channels. - Trans. ASME J. Heat Transfer, vol.112, pp.396-401.
  • Qin Y. and Kaloni P.N. (1994): Convective instabilities in anisotropic porous media. - Studies in Appl. Math., vol.91, pp.189-204.
  • Rosenberg N.D., Spera F.J. and Haymon R.M. (1993): The relationship between flow and permeability field in seafloor hydrothermal systems. - Earth and Planetary Science Letters, vol.116, pp.135-153.
  • Rudraiah N. and Malashetty M.S. (1989): Effect of modulation on the onset of convection in a porous medium. - Vignana Bharathi a Bangalore University Journal, vol.10, pp.19-44.
  • Rudraiah N. and Malashetty M.S. (1990): Effect of modulation on the onset of convection in a sparsely packed porous layer. - ASME J. Heat Transfer, vol.122, pp.685-689.
  • Storesletten L. (1998): Effects of anisotropy on convective flow through porous media. Transport Phenomena in Porous Media, Derek B. Ingham and I. Pop (Ed.). - Oxford: Pergamon Press, vol.261-283.
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  • Yoo J.S. and Schultz W.W. (2003): Thermal convection in a horizontal porous layer with spatially periodic boundary temperatures: Small Ra flow. - Int. J. Heat Mass Transfer, vol.46, pp.4747-4750.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0003-0034
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