Выходит 12 номеров в год
ISSN Печать: 1091-028X
ISSN Онлайн: 1934-0508
Indexed in
MARGINAL STABILITY ANALYSIS FOR A CONVECTIVE FLOW IN A POROUS MEDIUM WITH VERTICALLY VARYING RESISTIVITY
Краткое описание
We consider a convective flow in a horizontal porous medium to investigate the marginal stability due to linear variation in resistivity in the vertical direction. The flow in the porous medium can be described by a system of partial differential equations consisting of the continuity equation for conservation of mass, the heat equation for conservation of energy, and the momentum-Darcy equation for conservation of momentum. The resistivity of the medium is defined as the ratio of dynamic viscosity to permeability. Assuming a vertically varying basic state, we apply a linear stability approach to compute the critical Rayleigh and wave numbers from the linear system. Marginal stability curves and linear solutions are obtained numerically using fourth-order Runge-Kutta and shooting methods for different values of the resistivity parameter. This work is important for applications as in the case of a porous layer of underground water whose permeability varies vertically.
-
Abdullah, A.A. and Lindsay, K.A., Convection in a Porous Medium Confined between Vertical Boundaries and Saturated by Nanofluid, J. Porous Media, vol. 21, no. 3, pp. 257-277, 2018.
-
Aldoss, T.K., Natural Convection from a Horizontal Annulus Filled with Porous Medium of Variable Permeability, J. Porous Media, vol. 12, no. 7, pp. 715-724,2009.
-
Alves, L.S. de B., Cotta, R.M., and Pontes, J., Stability Analysis of Natural Convection in Porous Cavities through Integral Transforms, Int. J. Heat Mass Transf., vol. 45, no. 6, pp. 1185-1195,2002.
-
Backus, G., Poloidal and Toroidal Fields in Geomagnetic Field Modeling, Rev. Geophys., vol. 24, pp. 75-109, 1986.
-
Bhatta, D., Riahi, D.N., and Muddamallappa, M.S., On Nonlinear Evolution of Convective Flow in an Active Mushy Layer, J. Eng. Math, vol. 74, pp. 73-89,2010.
-
Bhatta, D., Muddamallappa, M.S., and Riahi, D.N., Magnetic and Permeability Effects on a Weakly Nonlinear Magneto-Convective Flow in an Active Mushy Layer, Int. J. Fluid Mech. Res., vol. 39, no. 6, pp. 494-520, 2012.
-
Bhatta, D. and Riahi, D.N., Convective Flow in an Aquifer Layer, Fluids, vol. 52, pp. 1-19, 2017.
-
Chandrasekhar, S., Hydrodynamic andHydromagnetic Stability, Oxford, U.K.: Oxford University Press, 1961.
-
Das, S. and Morsi, Y., Natural Convection in Domed Porous Enclosures: Non-Darcian Flow, J. Porous Media, vol. 6, no. 3, pp. 159-175,2003.
-
Drazin, P.G. and Reid, W.H., Hydrodynamic Stability, Second Ed., Cambridge, U.K.: Cambridge University Press, 2004.
-
Fowler, A.C., Mathematical Models in the Applied Sciences, Cambridge, U.K.: Cambridge University Press, 1997.
-
Hassanien, I.A. and Omer, G.M., Mixed-Convection Flow Adjacent to a Horizontal Surface in a Porous Medium with Variable Permeability and Surface Heat Flux, J. Porous Media, vol. 8, no. 2, pp. 225-235, 2005.
-
Hassinet, L. and Si-Ameur, M., Numerical Study on Natural Convection in a Porous Cavity that is Partially Heated and Cooled by Sinusoidal Temperature at Vertical Walls, J. Porous Media, vol. 22, no. 1, pp. 73-85, 2019.
-
Horton, C.W. and Rogers, F.T., Convection Currents in a Porous Medium, J. Appl. Phys., vol. 16, no. 6, pp. 367-370,1945.
-
Hsiao, S.W., Natural Convection in an Inclined Porous Cavity with Variable Porosity and Thermal Dispersion Effects, Int. J. Num. Methods Heat Fluid Flow, vol. 8, pp. 97-117, 1998.
-
Kaviany, M., Thermal Convective Instabilities in a Porous Medium, ASMEJ. Heat Transf., vol. 106, pp. 137-142, 1984.
-
Kim, S.J. and Vafai, K., Analysis of Natural Convection about a Vertical Plate Embedded in a Porous Medium, Int. J. Heat Mass Transf, vol. 32, pp. 665-677, 1989.
-
Lai, F.C. and Kulacki, F.A., Natural Convection across a Vertical Layered Porous Cavity, Int. J. Heat Mass Transf, vol. 31, pp. 1247-1260, 1988.
-
Landau, L.D., On the Problem of Turbulence, C.R. Acd. Sci. URSS, vol. 44, pp. 311-314, 1944.
-
Landau, L.D. and Lifshitz, E.M., Fluid Mechanics, London: Pergamon Press, 1959.
-
Lapwood, E.R., Convection of a Fluid in a Porous Media, Proc. Cambridge Philos. Soc., vol. 44, pp. 508-521, 1948.
-
Muddamallappa, M., Bhatta, D., and Riahi, D.N., Numerical Investigation on Marginal Stability and Convection with and without Magnetic Field in a Mushy Layer, Trans. Porous Media, vol. 79, pp. 301-317, 2009.
-
Muddamallappa, M., Bhatta, D., and Riahi, D.N., Linear Stability Analysis of Convective Flow in a Mushy Layer with a Non-Uniform Magnetic Field and Permeable Mush-Liquid Interface, J. Porous Media, vol. 13, no. 10, pp. 925-929, 2010.
-
Nield, D.A. and Barletta, A., The Horton-Rogers-Lapwood Problem Revisited: The Effect of Pressure Work Porous Layer, Transp. Porous Media, vol. 77, pp. 143-158, 2009.
-
Nield, D.A. and Bejan, A., Convection in a Porous Media, Fifth Edition, New York: Springer, 2017.
-
Nield, D.A. and Kuznetsov, A.V., The Effect of a Transition Layer between a Fluid and a Porous Medium: Shear Flow in a Channel, Transp. Porous Media, vol. 78, pp. 477-487, 2009.
-
Nithiarasu, P., Seetharamu, K.N., and Sundararajan, T., Effect of Porosity onNatural Convective Heat Transfer in a Fluid Saturated Porous Medium, Int. J. Heat Fluid Flow, vol. 19, pp. 56-58, 1998.
-
Oliveski, R.D.C. and Macrczak, L.D.F., Natural Convection in a Cavity Filled with Porous Medium with Variable Porosity and Dacry Number, J. Porous Media, vol. 11, no. 7, pp. 655-667, 2008.
-
Philips, J.R., Desperately Seeking Darcy in Dijon, Soil.Sci. Soc. Am. J, vol. 59, pp. 319-324,1995.
-
Prakash, J., On Arresting the Complex Growth Rates in Ferromagnetic Convection in a Ferrofluid Saturated Porous Layer, J. Porous Media, vol. 16, no. 3, pp. 217-226,2013.
-
Prakash, J., Kumar, K., and Kumar, R., Triple Diffusive Convection in a Maxwell Fluid Saturated Porous Layer: Darcy-Brinkman-Maxwell Model, J. Porous Media, vol. 19, no. 10, pp. 871-883, 2016.
-
Rahman, H., Thermomagnetic Convection in a Layer of Ferrofluid Placed in a Uniform Oblique External Magnetic Field, J. Fluid Mech., vol. 764, pp. 316-348, 2015.
-
Rao, A.S., Prasad, V.R., Beg, O.A., and Rashidi, M., Free Convection Heat and Mass Transfer of a Nanofluid past a Horizontal Cylinder Embedded in a Non-Darcy Porous Medium, J. Porous Media, vol. 21, no. 3, pp. 279-294, 2018.
-
Rees, D.A.S. and Barletta, A., Linear Instability of the Isoflux Darcy-Benard Problem in an Inclined Porous Layer, Transp. Porous Media, vol. 87, pp. 665-675, 2011.
-
Rees, D.A.S. and Pop, I., Vertical Free Convection in a Porous Medium with Variable Permeability Effects, Int. J. Heat Mass Transf, vol. 43, pp. 2565-2571,2000.
-
Riahi, D.N., Nonlinear Convection in a Porous Layer with Finite Conducting Boundaries, J. Fluid Mech., vol. 129, pp. 153-171, 1983.
-
Riahi, D.N., Nonlinear Convection in a Porous Layer with Permeable Boundaries, Int. J. Non-Linear Mech, vol. 24, pp. 459-463, 1989.
-
Riahi, D.N., Modal Package Convection in a Porous Layer with Boundary Imperfections, J. Fluid Mech., vol. 318, pp. 107-128, 1996.
-
Riahi, D.N., On Oscillatory Modes of Nonlinear Compositional Convection in Mushy Layers, Nonlin. Anal.: Real World Appl, vol. 10, pp. 209-226, 2009.
-
Rubin, H., Onset of Thermohaline Convection in Heterogeneous Porous Media, Israel J. Tech, vol. 19, pp. 110-117, 1981. Rubin, H., Thermal Convection in a Nonhomogeneous Aquifer, J. Hydrol., vol. 50, pp. 317-331, 1982.
-
Saleh, H., Natural Convection from a Cylinder in Square Porous Enclosure Filled with Nanofluids, J. Porous Media, vol. 18, no. 6, pp. 559-567,2015.
-
Umavathi, J.C. and Sasso, M., Free Convection Flow in a Duct Filled with Nanofluid and Saturated with Porous Medium: Variable Properties, J. Porous Media, vol. 21, no. 1, pp. 1-33,2018.
-
Vafai, K., Convective Flow and Heat Transfer in Variable-Porosity Media, J. FluidMech, vol. 147, pp. 233-259, 1984.
-
Vafai, K., Handbook of Porous Media, Second Ed., Edited, Boca Raton, FL: Taylor & Francis, 2005.