On the onset of thermal convection in a layer of Oldroydian visco-elastic fluid saturated by Brinkman–Darcy porous medium

• Autorzy: Chand R.

Identyfikatory

DOI

10.1515/sgem-2015-0039

• Języki publikacji: EN

Abstrakty

EN

Thermal instability in a horizontal layer of Oldroydian visco-elastic fluid in a porous medium is investigated. For porous medium the Brinkman–Darcy model is considered. A linear stability analysis based upon perturbation method and normal mode technique is used to find solution of the fluid layer confined between two free-free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically. The influence of the Brinkman–Darcy, Prandtl–Darcy number, stress relaxation parameter on the stationary and oscillatory convection is studied both analytically and graphically. The sufficient condition for the validity of PES has also been derived.

Słowa kluczowe

EN

thermal instability; Oldroydian viscoelastic fluid; Brinkman–Darcy number; Prandtl–Darcy number

• Wydawca: De Gruyter
• Czasopismo: Studia Geotechnica et Mechanica
• Rocznik: 2015
• Tom: Vol. 37, nr 4
• Strony: 3--10
• Opis fizyczny: Bibliogr. 25 poz., rys.

Twórcy

autor

Chand R.

• Department of Mathematics Government Arya Degree College Nurpur, Nurpur, Himachal Pradesh, India

Bibliografia

• [1] CHANDRASEKHAR S., Hydrodynamic and Hydromagnetic Stability, Dover Publications, New York 1981.
• [2] LAPWOOD E.R., Convections of a fluid in porous medium, Proc. Camb. Phil. Soc., 1948, 44, 508–519.
• [3] WOODING R.A., Rayleigh instability of a thermal boundary layer in flow through a porous medium, J. Fluid Mech., 1960, 9, 183–192.
• [4] MCDONNELL J.A.M., Cosmic Dust, John Wiley and Sons, Toronto 1978.
• [5] VAFAI K.A., HADIM H.A., Hand Book of Porous Media, M. Decker, New York 2000.
• [6] INGHAM D.D., POP L., Transport Phenomena in Porous Media, Elsvier, New York 1981.
• [7] NIELD D.A., BEJAN A., Convection in porous medium, second ed., Springer-Varlag, New York 2013.
• [8] KUZNETSOV AV., NIELD D.A., Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman Model, Transp. Porous Medium, 2010, 81, 409–422.
• [9] CHAND R., RANA G.C., On the onset of thermal convection in rotating nanofluid layer saturating a Darcy-Brinkman porous medium, Int. J. of Heat and Mass Transfer, 2012, 55(21–22), 5417–5424.
• [10] TOMS B.A., STRAWBRIDGE D.J., Elastic and viscous properties of dilute solutions of polymethyl methacrylate in organic liquids, Trans. Faraday Soc., 1953, 49, 1225– 1232.
• [11] OLDROYD J.G., Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids, Proc. Roy. Soc. (London), 1958, A245, 1241, 278–297.
• [12] GREEN T., Convective instability of a visco-elastic fluid heated from below Phy, Fluids, 1968, 11(7), 1410–1412.
• [13] VEST C.M., ARPACI V., Overstability of visco-elastic fluid layer heated from below, Fluid Mech., 1969, 36, 613–623.
• [14] BHATIA P.K., STEINER J.M., Convective instability of rotating fluid, ZAMM, 1972, 52(6), 321–327.
• [15] SHARMA R.C., Effect of rotation on thermal instability of a viscoelastic fluid, Acta Physica Hungrica, 1976, 40, 11–17.
• [16] SHARMA R.C., KUMAR P., Thermal instability of an Oldroydian visco-elastic fluid in porous medium, Engg. Trans, 1996, 44(1), 99–109.
• [17] PRAKESH K., CHAND R., Thermal instability of Oldroydian visco-elastic fluid in the presence of Finite Larmor Radius rotation and variable gravity in porous medium, Proc. Natl. Acad. Sci. India Sect. A Phys. Sci. 2002, 72 (4), 373–386.
• [18] CHAND R., Effect of suspended particles on thermal instability of Maxwell visco-elastic fluid with variable gravity in porous medium, Antarctica Journal of Mathematics, 2011, 8(6), 487–497.
• [19] CHAND R., Thermal Instability of rotating Maxwell viscoelastic fluid with variable gravity in porous medium, Journal of the Indian Math. Soc., 2013, 80(1–2), 23–31.
• [20] CHAND R., KANGO S.K., Thermosolutal instability of dusty rotating Maxwell visco-elastic fluid in porous medium, Advances in Applied Science Research, 2011, 2(6), 541–553.
• [21] CHAND R., RANA G.C., Dufour and Soret effects on the thermosolutal instability of Rivlin-Ericksen elastico-viscous fluid in porous medium, Z. Naturforsch., 2012, 67a, 685–691.
• [22] THAKUR R.C., RANA G.C., Effect of magnetic field on thermal instability of Oldroydian visco-elastic rotating fluid in porous medium, Int. J. of Applied Mechanics and Engineering, 2013, 18(2), 555–569.
• [23] CHAND R., RANA GC., Double diffusive convection in a layer of Maxwell viscoelastic fluid in porous medium in the presence of Soret and Dufour effects, Journal of Fluids, 2014, Article ID 479107, 7 pp., 2014.
• [24] YANG Z., WANG S., ZHAO M., LI S., ZHANG Q., The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer with non equilibrium model, PLoS ONE, 2013, 8(11): e79956. DOI: 10.1371/journal.pone.0079956.
• [25] BALA A., CHAND R., Thermal instability in a horizontal layer of ferrofluid in Brinkman porous medium, Journal of Scientific and Eng. Research, 2014, 1(2), 25–34.