×

On the linear stability analysis of a Maxwell fluid with double-diffusive convection. (English) Zbl 1201.76013

Summary: The problem of double-diffusive convection and cross-diffusion in a Maxwell fluid in a horizontal layer in porous media is re-examined using the modified Darcy-Brinkman model. The effect of Dufour and Soret parameters on the critical Darcy-Rayleigh numbers is investigated. Analytical expressions of the critical Darcy-Rayleigh numbers for the onset of stationary and oscillatory convection are derived. Numerical simulations show that the presence of Dufour and Soret parameters has a significant effect on the critical Darcy-Rayleigh number for over-stability. In the limiting case some previously published results are recovered.

MSC:

76A05 Non-Newtonian fluids
35B35 Stability in context of PDEs
76S05 Flows in porous media; filtration; seepage
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Hayat, T.; Fetecau, C.; Sajid, M., On MHD transient flow of a Maxwell fluid in a porous medium and rotating frame, Phys. lett. A, 372, 1639-1644, (2008) · Zbl 1217.76086
[2] Hayat, T.; Abbas, Z.; Ali, N., MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species, Phys. lett. A, 372, 4698-4704, (2008) · Zbl 1221.76031
[3] Martinez-Mardones, J.; Perez-Garcia, C., Linear instability in viscoelastic fluid convection, J. phys.: condens. matter, 2, 1281-1290, (1990)
[4] Maxwell, J.C., On the dynamical theory of gases, Philos. trans. R. soc. lond. A, 157, 2678, (1866)
[5] Eltayeb, I.A., Nonlinear thermal convection in an elasticoviscous layer heated from below, Proc. R. soc. lond. A, 356, 161-176, (1977) · Zbl 0359.76044
[6] Sokolov, M.; Tanner, R.I., Convective stability of a general viscoelastic fluid heated from below, Phys. fluid, 15, 534-539, (1972) · Zbl 0247.76041
[7] Hayat, T.; Fetecau, C.; Abbas, Z.; Ali, N., Flow of a Maxwell fluid between two sided walls due to suddenly moved plate, Nonlinear anal.: real world appl., 9, 2288-2295, (2008) · Zbl 1156.76347
[8] Hayat, T.; Alvi, N.; Ali, N., Peristaltic mechanism of a Maxwell fluid in an asymmetric channel, Nonlinear anal.: real world appl., 9, 1474-1490, (2008) · Zbl 1154.74334
[9] Hayat, T.; Ali, N.; Asgher, S., Hall effects on peristaltic flow of a Maxwell fluid in a porous medium, Phys. lett. A, 363, 397-403, (2007) · Zbl 1197.76126
[10] Fetecau, C.; Fetecau, C., A new exact solution for the flow of a Maxwell fluid past an infinite plate, Int. J. non-linear mech., 38, 423-427, (2003) · Zbl 1287.76041
[11] Fetecau, C.; Fetecau, C., The rayleigh – stokes-problem for a fluid of Maxwellian type, Int. J. non-linear mech., 38, 603-607, (2003) · Zbl 1287.76042
[12] Fetecau, C.; Fetecau, C., Decay of a potential vortex in a Maxwell fluid, Int. J. non-linear mech., 38, 985-990, (2003) · Zbl 1287.76043
[13] Fetecau, C.; Fetecau, C., On a simple flow of a Maxwell fluid, Rev. roum. sci. techn. mec. appl., 1, 3-11, (2006)
[14] Wang, S.W.; Tan, W.C., Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below, Phys. lett. A, 372, 3046-3050, (2008) · Zbl 1220.76031
[15] Wang, S.W.; Tan, W.C., The onset of darcy – brinkman thermosolutal convection in a horizontal porous media, Phys. lett. A, 373, 776-780, (2009) · Zbl 1227.76060
[16] Sekhar, G.N.; Jayalatha, G., Elastic effects on rayleigh-BĂ©rnard convection in liquids with temperature-dependent viscosity, Int. J. thermal sci., 67-75, (2010)
[17] Brand, H.R.; Zielinska, B.J.A., Tricritical codimension-2 point near the onset of convection in viscoelastic liquids, Phys. rev. lett., 57, 3167-3170, (1986)
[18] Zielinska, B.J.A.; Mukamel, D.; Steinberg, V., Multicriticality in viscoelastic fluids heated from below, Phys. rev. A, 33, 1454-1457, (1986)
[19] Nield, D.A.; Bejan, A., Convection in porous media, (1999), Springer-Verlag New York · Zbl 0924.76001
[20] Pop, I.; Ingham, D.B., Convective heat transfer, (2001), Elsevier · Zbl 0856.76015
[21] Green, T., Oscillating convection in an elastico-viscous liquid, Phys. fluid, 11, 7, 1410-1413, (1968)
[22] Nield, D.A., Onset thermohaline convection in a porous medium, Water resour. res., 11, 553-560, (1968)
[23] Poulikakos, D., Double-diffusive convection in a horizontal sparsely packed porous, Int. commun. heat mass transfer, 13, 587-598, (1986)
[24] Malshetty, M.S.; Wadi, V.S., Rayleigh – bernard convection subject to time dependent wall temperature in a fluid saturated porous layer, Fluid dynam. res., 24, 293, (1999)
[25] Taslim, M.E.; Narusawa, U., Binary fluid convection and double-diffusive convection in porous medium, J. heat transfer, 108, 221-224, (1986)
[26] Capuani, F.; Frankel, D.; Lowe, C.F., Velocity fluctuations and dispersion in a simple porous medium, Phys. rev. E, 67, 056306, (2003)
[27] Masouka, T.; Rudraiah, N.; Siddheshwar, Nonlinear convection in porous media, J. porous media, 6, 1, (2003) · Zbl 1152.76387
[28] Tan, W.C.; Masouka, T., Stability analysis of a Maxwell fluid in a porous medium heated from below, Phys. lett. A, 360, 454-460, (2007)
[29] Vafai, K., Handbook of porous media, (2005), CRC Press
[30] Younes, A., On modeling the multidimensional coupled fluid flow and heat or mass transport in porous media, J. heat transfer, 46, 367-379, (2003) · Zbl 1121.76416
[31] Kafoussias, N.G.; Williams, E.W., Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective and mass transfer boundary layer flow with temperature dependent viscosity, Int. eng. sci., 33, 1369-1384, (1995) · Zbl 0899.76325
[32] Alam, M.S.; Rahman, M.M., Dufour and soret effects on mixed convection flow past a vertical porous flat plate with variable suction, Nonlinear anal.: modell. control, 11, 3-12, (2006) · Zbl 1109.76057
[33] Motsa, S., On the onset of convection in a porous layer in the presence of dufour and soret effects, Sjpam, 3, 58-65, (2008)
[34] Qin, Y.; Kaloni, P.N., Steady convection in a porous medium based upon the brinlkman model, IMA J. appl. math., 48, 85-95, (1992) · Zbl 0765.76085
[35] Subramanian, L.; Patil, P.R., Thermohaline convection with coupled molecular diffusion in an anisotropic porous medium, Indian J. pure appl. math., 22, 2, 169-183, (1991) · Zbl 0734.76069
[36] Siddheshwar, P.G.; Krishna, C.V.S., Rayleigh – bernard convection in a viscoelastic fluid-filled high porosity medium with nonuniform basic temperature gradient, Ijmms, 25, 609-619, (2001) · Zbl 1029.76019
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.