Global stability for thermal convection in a couple-stress fluid with temperature and pressure dependent viscosity

• Autorzy: Choudhary S. S. , Bharti P. K.

Identyfikatory

DOI

10.2478/sgem-2013-0032

• Języki publikacji: EN

Abstrakty

EN

We show that the global nonlinear stability threshold for convection in a couple-stress fluid with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It has also been found that the couplestress fluid is more stable than the ordinary viscous fluid and then the effect of couple-stress parameter (F) and variable dependent viscosity (Γ) on the onset of convection is also analyzed.

Słowa kluczowe

EN

convection; thermal convection; stability; non-Newtonian fluid

PL

konwekcja; konwekcja cieplna; stabilność; płyn nieniutonowski

• Wydawca: De Gruyter
• Czasopismo: Studia Geotechnica et Mechanica
• Rocznik: 2013
• Tom: Vol. 35, nr 3
• Strony: 85--102
• Opis fizyczny: Bibliogr. 52 poz., rys.

Twórcy

autor

Choudhary S. S.

• Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) − 177 005, India

autor

Bharti P. K.

• Department of Mathematics, G. S. S. S. Mandal, Kangra, (H.P.) − 176 001, India

Bibliografia

• [1] REYNOLDS O., Phil. Trans. Roy. Soc. Lond., 1895, A 186, 123.
• [2] ORR W. McF., Proc. Roy. Irish. Acad., 1907, A 2, 9.
• [3] SERRIN J., Arch. Ration. Mech. Analysis, 1959, 3, 1.
• [4] JOSEPH D.D., Arch. Ration. Mech. Analysis, 1965, 20, 59.
• [5] JOSEPH D.D., Arch. Ration. Mech. Analysis, 1966, 22, 163.
• [6] JOSEPH D.D., Stability of Fluid Motions, Springer Verlag, New York, 1976.
• [7] RIONERO S., Ann. Mat. Pur. Appl., 1968, 78, 339.
• [8] GALDI G.P., Arch. Ration. Mech. Analysis, 1985, 87, 167.
• [9] GALDI G.P., STRAUGHAN B., Proc. Roy. Soc. Lond., 1985, A 402, 257.
• [10] GALDI G.P., PADULA M., Arch. Ration. Mech. Analysis, 1990, 110, 187.
• [11] STRAUGHAN B., The Energy Method, Stability, and Nonlinear Convection, Springer Verlag, New York, 2004.
• [12] RIONERO S., MULONE G., Arch. Ration. Mech. Analysis, 1988, 103, 347.
• [13] MULONE G., RIONERO S., J. Math. Anal. Appl., 1989, 144, 109.
• [14] QIN Y., KALONI P.N., Q. J. Appl. Math., 1995, 53, 129.
• [15] GUO J., QIN Y., KALONI P.N., Int. J. Engg. Sci., 1994, 32, 1207.
• [16] GUO J., KALON P.N., J. Math. Analysis Appl., 1995, 190, 373.
• [17] STRAUGHAN B., WALKER D.W., J. Comput. Phys., 1996, 127, 128.
• [18] KALONI P.N., QIAO Z., Int. J. Heat Mass Transfer, 1997, 40, 1611.
• [19] KALONI P.N., QIAO Z., Int. J. Engg. Sci., 1997, 35, 299.
• [20] KALONI P.N., QIAO Z., Int. J. Heat Mass Transfer, 2001, 44, 1585.
• [21] STRAUGHAN B., Explosive Instabilities in Mechanics, Springer, Berlin, Germany, 1998.
• [22] PAYNE L.E., STRAUGHAN B., Stud. Appl. Math., 2000, 105, 59.
• [23] STRAUGHAN B., Roy. Soc. Lond., 2001, A 457, 87.
• [24] SUNIL, MAHAJAN A., Proc. Roy. Soc. Lond., 2008, A 464, 83.
• [25] SUNIL, MAHAJAN A., Appl. Math. Comput., 2008, 204, 299.
• [26] SUNIL, MAHAJAN A., Z. Naturforsch., 2008, A 63a, 797.
• [27] SUNIL, MAHAJAN A., J. Geophys. Engg., 2008, 5 (3), 311.
• [28] SUNIL, MAHAJAN A., Trans. Porous Media, 2009, 76, 327.
• [29] SUNIL, MAHAJAN A., ZAMP, 2009, 60, 344.
• [30] SUNIL, DEVI R., MAHAJAN A., Int. Commun. Heat Mass Transfer, 2011, 38, 938.
• [31] STOKES V.K., Phys. Fluids, 1966, 9, 1709.
• [32] STOKES G.G., Trans. Camb. Phil. Soc., 1845, 8, 287.
• [33] BARUS C., Am. J. Sci., 1893, 45, 87.
• [34] ANDRADE E.C., Nature, 1930, 125, 309.
• [35] LAUN H.M., Rheol. Acta, 2003, 42, 295.
• [36] BAIR S., KOTTKE P., Tribolory Trans., 2003, 46, 289.
• [37] MARTIN-ALFONSO M.J., MARTINEZ-BOZA F.J., PARTAL P., GALLEGOS C., Rheol. Acta, 2006, 45, 357.
• [38] MARTIN-ALFONSO M.J., MARTINEZ-BOZA F.J., NAVARRO F.J., FERNANDEZ M., GALLEGOS C., Fuel, 2007, 86, 227.
• [39] RAMANAIAH G., WEAR, 1979, 52, 27.
• [40] GUPTA R.S., SHARMA L.G., WEAR, 1988, 48, 257.
• [41] SHEHAWEY E.F.E., MEKHEIMER K.S., J. Phys. D. appl. Phys., 1994, 27, 1163.
• [42] DAS N.C., STLE Trib. Trans., 1997, 40, 353.
• [43] DAS N.C., Tribology Int., 1998, 31, 393.
• [44] ABDALLAH A.E., LOTFI H.G., Tribology Int., 2001, 34, 107.
• [45] HSU C.H., LIN J.R. CHIANG H.L., Indus. Lub. Tribology, 2003, 55, 233.
• [46] LAHMAR M., Proc. Instn. Mech. Engrs., Part J: J. Eng. Tribology, 2005, 219, 145.
• [47] RAJAGOPAL K.R., SACCOMANDI G., VERGORI L., Nonlinear Anal. Real Word Appl., 2009, 10 (2), 1139.
• [48] RAJAGOPAL K.R., SACCOMANDI G., VERGORI L., ZAMP, 2009, 60, 739.
• [49] KLOEDEN P., WELL R., Proc. Roy. Soci. Lond., 1983, A 390, 293.
• [50] TEMAM R., Appl. Math. Sci., 68, Springer-Verlag, New York, Berlin, Heidelberg, 1997.
• [51] RIONERO S., Annali di Matematica Pura ed Applicata, 1968, 78, 339.
• [52] CHANDRASEKHAR S., Hydrodynamic and Hydromagnetic Stability, Dover, New York, 1981.