Stability analysis of a Maxwell fluid in a porous medium heated from below

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 360, Issue 3, 2007, Pages 454-460

  Tan, Wenchang ^a   Masuoka, Takashi ^b  

^a Peking University   (China)

^b KYUSHU UNIVERSITY   (Japan)

Author keywords

Maxwell fluid; Modified Darcy Brinkman Maxwell model; Overstability; Porous media; Thermal convection

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; HEAT CONVECTION;

CRITICAL RAYLEIGH NUMBER; DESTABILIZING EFFECT; EIGENVALUE PROBLEM; MAXWELL FLUID; MAXWELL MODELS; OVERSTABILITY; THERMAL CONVECTIONS; VIS-COELASTIC FLUIDS;

POROUS MATERIALS;

EID: 33750737484     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2006.08.054     Document Type: Article

References (34)

1. Benard H. Les tourbillons cellulaires dans une nappe liquide. Revue Gen. Sci. Our. Appl. 11 (1900) 1261
2. Rayleigh L. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Philos. Mag. Ser. 6 32 (1916) 529
3. Jeffreys H. The stability of a layer of fluid heated below. Philos. Mag. Ser. 7 2 (1926) 833
4. Pellow A., and Southwell R.V. On maintained convective motion in a fluid heated from bellow. Proc. R. Soc. A 176 (1940) 312
5. Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability (1961), Clarendon, Oxford
6. Drazin P.G., and Reid W.H. Hydrodynamic Stability (1981), Cambridge Univ. Press, Cambridge
7. Dyko M.P., Vafai K., and Mojtabi A.K. A numerical and experimental investigation of stability of natural convective flows within a horizontal annulus. J. Fluid Mech. 381 (1999) 27
8. Dyko M.P., and Vafai K. Three-dimensional natural convective states in a narrow-gap horizontal annulus. J. Fluid Mech. 445 (2001) 1
9. Bejan A. Convection Heat Transfer. third ed. (2004), John Wiley & Sons, New Jersey
10. Li Z., and Khayat R.E. Finite-amplitude Rayleigh-Benard convection and pattern selection for viscoelastic fluids. J. Fluid Mech. 529 (2005) 221
11. Horton C.W., and Rogers F.T. Convection currents in a porous medium. J. Appl. Phys. 16 (1945) 367
12. Lapwood E.R. Convection of a fluid in a porous medium. Proc. Cambridge Philos. Soc. 44 (1948) 508
13. Katto Y., and Masuoka T. Criterion for the onset of convective flow in a fluid in a porous medium. Int. J. Heat Mass Transfer 10 (1967) 297
14. Jesse O., Lubomira A.D., Hans J., et al. High-Rayleigh-number convection in a fluid-saturated porous layer. J. Fluid Mech. 500 (2004) 263
15. Bejan A. Simple methods for convection in porous media: Scale analysis and the intersection of asymptotes. Int. J. Energy Res. 27 (2003) 859
16. Rudraiah N., Siddhesshwar P.G., and Masuoka T. Nonliear convection in porous media: a review. J. Porous Media 6 (2003) 1
17. Younes A. On modeling the multidimensional coupled fluid flow and heat or mass transport in porous media. Int. J. Heat Mass Transfer 46 (2003) 367
18. Nield D.A., and Bejan A. Convection in Porous Media. second ed. (1999), Springer, Berlin
19. Alisaev G.M., and Mirzadjanzade A.K. For the calculation of delay phenomenon in filtration theory. Izv. Vuzow Neft Gaz. 6 (1975) 71
20. Khuzhayorov B., Auriault J.L., and Royer P. Derivation of macroscopic filtration law for transient linear viscoelastic fluid flow in porous media. Int. J. Eng. Sci. 38 (2000) 487
21. Khaled A.R.A., and Vafai K. The role of porous media in modeling flow and heat transfer in biological tissues. Int. J. Heat Mass Transfer 46 (2003) 4989
22. Malashetty M.S., and Wadi V.S. Rayleigh-Benard convection subject to time dependent wall temperature in a fluid-saturated porous layer. Fluid Dynam. Res. 24 (1999) 293
23. Capuani F., Frenkel D., and Lowe C.P. Velocity fluctuations and dispersion in a simple porous medium. Phys. Rev. E 67 (2003) 056306
24. Rudraiah N., Radhaevi P.V., and Kaloni P.N. Convection in a viscoelastic fluid-saturated sparse packed porous layer. Can. J. Phys. 18 (1990) 1446
25. Kim M.C., Lee S.B., and Kim S. Thermal instability of viscoelastic fluids in porous media. Int. J. Heat Mass Transfer 46 (2003) 5065
26. Tan W.C., and Masuoka T. Stokes' first problem for an Oldroyd-B fluid in a porous half-space. Phys. Fluids 17 (2005) 023101
27. Tan W.C., and Masuoka T. Stokes' first problem for a second grade fluid in porous half-space with a heated plate. Int. J. Nonlinear Mech. 40 (2005) 515
28. Vafai K., and Tien C.L. Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Transfer 24 (1981) 195
29. Slattery J.C. Advance Transport Phenomena (1999), Cambridge Univ. Press, Cambridge
30. Ingham D.B., and Pop I. Transport Phenomena in Porous Media II (2002), Elsevier, Oxford
31. Rosenblat S. Thermal convection in a viscoelastic liquid. J. Non-Newtonian Fluid Mech. 21 (1986) 201
32. Kolkka R.W., and Ierley G.R. On the convected linear stability of a viscoelastic Oldroyd B fluid heated from below. J. Non-Newtonian Fluid Mech. 25 (1987) 209
33. Vest C.M., and Arpaci V.S. Overstability of a viscoelastic fluid layer heated from below. J. Fluid Mech. 36 (1969) 613
34. Banu N., and Rees D.A.S. Onset of Darcy-Benard convection using a thermal nonequilibrium model. Int. J. Heat Mass Transfer 45 (2002) 2221