Chaotic convection of viscoelastic fluids in porous media

Chaos, Solitons and Fractals

Volumn 37, Issue 1, 2008, Pages 113-124

  Sheu, Long Jye ^a   Tam, Lap Mou ^b   Chen, Juhn Horng ^a   Chen, Hsien Keng ^c   Lin, Kuang Tai ^d   Kang, Yuan ^d  

^a CHUNG HUA UNIVERSITY   (Taiwan)

^b UNIVERSITY OF MACAU   (Macao)

^c HSIUPING INSTITUTE OF TECHNOLOGY   (Taiwan)

^d CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC ANALYSIS; BUOYANCY; CHAOTIC SYSTEMS; GALERKIN METHODS; HEAT CONVECTION; MOMENTUM; POROUS MATERIALS; STRESS RELAXATION; VISCOELASTICITY;

BUOYANCY INDUCED CONVECTION; CHAOTIC CONVECTION; TRUNCATED GALERKIN EXPANSION; VISCOELASTIC FLUIDS;

FLOW OF FLUIDS;

EID: 39149145877     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.07.050     Document Type: Article

References (28)

1. de Boer R. Theoretical poroelasticity - a new approach. In: Weibel P., Ord G., and Rössler O.E. (Eds). Space time physics and fractality (2005), SpringerWien, New York 189-222
2. de Boer R. Theoretical poroelasticity - a new approach. Chaos Soliton Fract 25 (2005) 861-878
3. Horton C.W., and Logers F.T. Convection currents in a porous medium. J Appl Phys 16 (1945) 367-370
4. Lapwood E.R. Convection of a fluid in a porous medium. Proc Cambridge Phil Soc 44 (1948) 508-521
5. Katto Y., and Masuoka T. Criterion for onset of convection in a saturated porous medium. Int J Heat Mass Transfer 10 (1967) 297-309
6. Straughan B. A sharp non-linear stability threshold in rotating porous convection. Proc R Soc London A 457 (2001) 87-93
7. Yoon D.Y., Kim M.C., and Choi C.K. Oscillatory convection in a horizontal porous layer saturated with a viscoelastic fluid. Korean J Chem Eng 20 (2003) 27-31
8. Yoon D.Y., Kim M.C., and Choi C.K. The onset of oscillatory convection in a horizontal porous layer saturated with viscoelastic liquid. Transport Porous Med 55 (2004) 275-284
9. Kim M.C., Lee S.B., Kim S., and Chung B.J. Thermal instability of viscoelastic fluids in porous media. Int J Heat Mass Transfer 46 (2003) 5065-5072
10. Malashetty M.S., Shivakumara I.S., and Kulkarni S. The onset of convection in an anisotropic porous layer using a thermal non-equilibrium model. Transport Porous Med 60 (2005) 199-215
11. Malashetty M.S., Shivakumara I.S., Kulkarni S., and Swamy M. Convective instability of Oldroyd-B fluid saturated porous layer heated from below using a thermal non-equilibrium model. Transport Porous Med 64 (2006) 123-139
12. Masuoka T., Rudraiah N., and Siddheshwar P.G. Non-linear convection in porous medium: a review. J Porous Media 6 (2003) 1-32
13. Vadasz P. Local and global solutions for transitions to chaos and hysteresis in a porous layer heated from below. Transport Porous Med 37 (1999) 213-245
14. Vadasz P., and Olek S. Weak turbulence and chaos for low Prandtl number gravity driven convection in porous media. Transport Porous Med 37 (1999) 69-91
15. Vadasz P., and Olek S. Route to chaos for moderate Prandtl number convection in a porous layer heated form below. Transport Porous Med 41 (2000) 211-239
16. Vadasz J.J., Roy-Aikens J.E.A., and Vadasz P. Sudden or smooth transition in porous media natural convection. Int J Heat Mass Transfer 48 (2005) 1096-1106
17. Vadasa P. Heat transfer regimes and hysteresis in porous media convection. ASME J Heat Transfer 123 (2001) 145-156
18. Sheu L.J. An autonomous system for chaotic convection in a porous medium using a thermal non-equilibrium model. Chaos Soliton Fract 30 (2006) 672-689
19. Khayat R.E. Chaos and overstability in thermal convection of viscoelastic fluids. J Non-Newton Fluid Mech 53 (1994) 227-255
20. Khayat R.E. Fluid elasticity and the transition to chaos in thermal convection. Phys Rev E 51 (1995) 380-399
21. Khayat R.E. Non-linear overstability in the thermal convection of viscoelastic fluids. J Non-Newton Fluid Mech 58 (1995) 331-356
22. Abu-Ramadan E., Hay J.M., and Khayat R.E. Characterization of chaotic thermal convection of viscoelastic fluids. J Non-Newton Fluid Mech 115 (2003) 79-113
23. Lorenz E.N. Deterministic non-periodic flows. J Atmos Sci 20 (1963) 130-141
24. Akhatov I.S.h., and Chembarisova R.G. The thermoconvective instability in hydrodynamics of relaxational liquids. In: Gouesbet G., and Berlemont A. (Eds). Instabilities in multiphase flows (1993), Plenum Press, New York 277-287
25. Kumar P., Mohan H., and Singh G.J. Rayleigh-Taylor instability of rotating Oldroydian viscoelastic fluids in porous medium in presence of a variable magnetic field. Transport Porous Med 56 (2004) 199-208
26. Oldroyd J.G. Non-newtonian effects in steady motion of some idealized elastico-viscous liquids. Proc Roy Soc (London) A245 (1958) 278-297
27. Khayat RE. Developments in non-Newtonian flows. in: Siginer DA, Van Arsdale WE, Altau MC, Alexandrou AN., editors., ASME AMD 1993;175:7.
28. Wolf A., Swift J.B., Swinney H.L., and Vastano J.A. Determining Lyapunov exponents from a time series. Physica D 16 (1985) 285-317