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Double diffusive convection in a high porosity anisotropic porous medium with externally regulated darcy and brinkman frictions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A linear stability analysis is performed on the double diffusive porous system using the Rayleigh-Ritz technique. The condition for direct and Hopf bifurcations is obtained as a function of the parameters of the problem. A unique feature in this problem is that Darcy and Brinkman friction are temperature-dependent and hence are amenable to regulation. The study reveals that this external regulation of convection results in a preference for stationary convection over oscillatory mode. A low-porosity medium results for "finger" and "diffusive" instabilities are also discussed in the case of constant viscosity liquids.
Rocznik
Strony
1147--1168
Opis fizyczny
Bibliogr. 43 poz., tab., wykr.
Twórcy
  • Department of Mathematics, Central College Campus Bangalore University Bangalore-560 001, INDIA, pgsmath@gmail.com
Bibliografia
  • Bejan A. and Lage J.L. (1991): Heat transfer from a surface covered with hair. - Convective Heat and Mass Transfer in Porous Media, Kluwer Academic, Dordrecht, pp.909-918.
  • Bera P. and Khalili A. (2002): Double diffusive natural convection in an (anisotropic porous cavity with opposing buoyancy forces: multiple (solutions and oscillations. - Int. J. Heat Mass Transfer, vol.45, pp.3205-3222.
  • Bhadauria B.S. (2007): Double diffusive convection in a rotating porous (layer with temperature modulation on the boundaries. - J. Porous Media, (vol.10, pp.569-584.
  • Boutana N., Bahloul A., Vasseur P. and Joly F. (2004): Soret and double (diffusive convection in a porous cavity. - J. Porous Media, vol.7, pp.41-57.
  • Chakraborty S. and Dutta P. (2003): Three dimensional double-diffusive convection and macro-segregation during non-equilibrium solidification of binary mixtures. - Int. J. Heat Mass Transfer, vol.46, pp.2115-2134.
  • Chandrasekhar S. (1961): Hydrodynamic and Hydromagnetic Stability. - London: Oxford (University Press.
  • Chen F. and Chen C.F. (1988): Onset of finger convection in a horizontal (porous layer underlying a fluid layer. - J. Heat Transfer, vol.110, pp.403-409.
  • Fu C., Zhang Z. and Tan W. (2007): Numerical simulation of thermal convection of a viscoelastic fluid in a porous square box heated from below. - Phy. of Fluids, vol.19, No.10, pp.104-107.
  • Givler R.C. and Altobelli S.A. (1994): Determination of the effective viscosity for the Brinkman-Forchheimer flow. - J. Fluid Mech., vol.258, pp.355-370.
  • Griffiths R.W. (1981): Layered double-diffusive convection in porous media. - J. Fluid Mech., vol.102, pp.221-248.
  • Guo J. and Kaloni P.N. (1995a): Double-diffusive convection in a porous (medium, non-linear stability and the Brinkman effect. - Stud. Appl. Math., vol.94, pp.341-358.
  • Guo J. and Kaloni P.N. (1995b): Non-linear stability problem of a rotating (double-diffusive porous layer. - J. Math. Anal. Appl., vol.2, pp.373-390.
  • Hyun J.M. and Lee J.W. (2003): Double-diffusive convection in a rectangle (with cooperating horizontal gradients of temperature and concentration. - Int. (J. Heat Mass Transfer, vol.33, pp.1605-1713.
  • Ingham D.B. and Pop I. (2002): Transport Phenomena in Porous Media. - Elsevier.
  • Kaloni P.N. and Guo J. (1996): Study of non-linear double-diffusive convection (in a porous medium based upon the Brinkman-Forchheimer model. - J. (Math., Anal. Appl., vol.204, pp.138-155.
  • Kamakura K. and Ozoe H. (1995): Effect of the temperature dependence of (fluid properties on the migration of an interface in double-diffusive natural (convection. - Int. J. Heat Mass Transfer, vol.38, pp.3413-3421.
  • Lin C. and Payne L.E. (2006): Structural stability for the Brinkman equations (of flow in double diffusive convection. - J. Math. Anal. and Applns., vol.325, pp.1479-1490.
  • Lin C. and Payne L.E. (2008): Continuous dependence on the Soret coefficient for double diffusive convectionin Darcy-flow. - J. Math. Anal. and Applns., vol.342, pp.311-322.
  • Malashetty M.S. (1993): Anisotropic thermo-convective effects on the onset of (double diffusive convection in a porous medium. - Int. J. Heat Mass (Transfer, vol.36, pp.2397-2401.
  • Malashetty M.S. and Heera R. (2008): The effect of rotation on the onset of double diffusive convection in a horizontal anisotropic porous layer. - Transport in Porous Media, vol.74, pp.105-127.
  • Mojtabi A. and Charrier-Mojtabi M. (2000): Double diffusive convection in (porous media. - Handbook of Porous Media (Ed. Vafai, K.), Marcel Dekker (Inc., New York, pp.559-603.
  • Murray B.T. and Chen C.F. (1989): Double-diffusive convection in porous (medium. - J. Fluid Mech., vol.201, pp.147-166.
  • Nield D.A. (1968): Onset of thermo-haline convection in a porous medium. - Water Resources Res., vol.4, pp.553-560.
  • Nield D.A. (1996): The effect of temperature-dependent viscosity on the onset of convection in a saturated porous medium. - ASME J. Heat Transfer, vol.118 , pp.803-805.
  • Nield D.A. and Bejan A. (2006): Convection in Porous Media. - 3rd edition, Springer, Berlin.
  • Pillatsis G., Taslim M.E. and Narusawa V. (1987): Thermal instability of a (fluid saturated porous medium bounded by thin fluid layers. - J. Heat (Transfer, vol.109, pp.677-682.
  • Poulikakos D. (1986): Double-diffusive convection in a horizontal sparsely packed porous layer. - Int. Comm. Heat Mass Transfer, vol.13, pp.587-598.
  • Poulikakos D. and Kazmierczak (1989): Transient double-diffusive convection (experiments in a horizontal fluid layer extending over a bed of spheres. - Phy. of Fluids, A 1, pp.480-489.
  • Rubin H. (1973): Effect of solute dispersion on thermal convection in a porous (layer. - Water Resources Res., vol.9, pp.968-974.
  • Rudraiah N. and Malashetty M.S. (1986): The influence of coupled molecular (diffusion on double-diffusive convection in a porous medium. - J. Heat (Transfer (ASME), vol.108, pp.872-876.
  • Rudraiah N., Friedrich R. and Srimani P.K. (1982): Finite amplitude (convection in a two-component fluid-saturated layer. - Int. J. Heat Mass (Transfer, vol.25, pp.715-722.
  • Rudraiah N. and Siddheshwar P.G. (1998): A weak non linear stability (analysis of double diffusive convection with cross-diffusion in a fluid-(saturated porous medium. - Heat Mass Transfer, vol.33, pp.287-293.
  • Scheidegger A.E. (1974): The Physics of Flow through Porous Media. - Toronto: University of Toronto Press.
  • Sheela R. (1990): Stability of flow through and past porous media. - Ph.D. Thesis, Bangalore University.
  • Shivakumara I.S. and Sumithra R. (1999): Non-Darcian effects of double-diffusive convection in a porous medium. - Acta Mech., vol.132, pp.113-127.
  • Singh A.K., Leonardi E. and Thorpe G.R. (1993): Three-dimensional (natural convection in a confined fluid overlying a porous layer. - J. Heat (Transfer, vol.115, pp.631-638.
  • Sovran O., Charrier-Mojtabi M. and Mojtabi A. (2001). Onset of Soret-(driven convection in an infinite porous layer. - C.R. Acad. Sci. Paris, vol.329, (Series IIb, pp.287-293.
  • Taslim M.E. and Narusawa U. (1989): Binary fluid convection and double-(diffusive convection in a porous medium. - J. Heat Transfer, (ASME), vol.108, pp.221-224.
  • Vafai K. and Hamid A. (2000): Hand Book of Porous Media. - New York: Marcel Decker.
  • Wang S. and Masuoka T. (2007): Stability analysis of a Maxwell fluid in a porous medium heated from below. - Physics Letters A, vol.360, No.3, pp.454-460.
  • Wang S. and Tan W. (2008): Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below. - Physics Letters A, vol.372, No.17, pp.3046-3050.
  • Zhang Z., Fu C., Tan W. and Wang C.Y. (2007): Onset of oscillatory convection in a porous cylinder saturated with a viscoelastic fluid. - Phy. of Fluids, vol.19, No.9, pp.98-104.
  • Zhao P. and Chen C.F. (2001): Stability analysis of double diffusive (convection in suspended fluid and porous layers using one equation (model. - Int. J. Heat Mass Transfer, vol.44, pp.4625-4633.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0018-0015
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