Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions

Physics of Fluids

Volumn 17, Issue 8, 2005, Pages 1-15

  Ennis King, Jonathan ^a   Preston, Ian ^a   Paterson, Lincoln ^a  

^a Department of Civil and Environmental Engineering   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; APPROXIMATION THEORY; BOUNDARY CONDITIONS; GALERKIN METHODS; INTEGRAL EQUATIONS; MATRIX ALGEBRA; MECHANICAL PERMEABILITY; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; POROUS MATERIALS; STABILITY; VECTORS;

ANISOTROPIC POROUS MEDIA; FLUID CONVECTION; SEDIMENTARY FORMATIONS; STABILITY ANALYSIS;

FLUID DYNAMICS;

POROUS MEDIUM;

EID: 24144495580     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2033911     Document Type: Article

References (50)

1. G. Andersen, A. Probst, L. Murray, and S. Butler, in Proceedings of the Seventeenth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA, 29-31 January 1991 (Stanford University, Stanford, CA, 1992), pp. 239-248.
2. J. P. Ennis-King and L. Paterson, "Role of convective mixing in the long-term storage of carbon dioxide in deep saline formations," SPEJ SPJRFW 1086-055X (in press).
3. L. Hnědovský, R. H. Wood, and V. Majer, "Volumes of aqueous solutions of CH4, CO2, H2S, and NH3 at temperatures from 298.15Kto705K and pressures to 35MPa," J. Chem. Thermodyn. JCTDAF 0021-9614 28, 125 (1996).
4. 2," Energy Convers. Manage. ECMADL 0196-8904 38, S229 (1997).
5. J. Ennis-King and L. Paterson, in Proceedings of the Sixth International Conference on Greenhouse Gas Control Technologies, Kyoto, Japan, 1-4 October 2002, edited by J. Gale and Y. Kaya (Pergamon, New York, 2003), Vol. I, pp. 567-570.
6. C. W. Horton and F. T. Rogers, Jr., "Convection currents in a porous media," J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1707601 16, 367 (1945).
7. E. R. Lapwood, "Convection of a fluid in a porous medium," Proc. Cambridge Philos. Soc. PCPSA4 0068-6735 44, 508 (1948).
8. D. A. Nield and A. Bejan, Convection in Porous Media, 2nd ed. (Springer, New York, 1999).
9. K. B. Haugen and P. A. Tyvand, "Onset of thermal convection in a vertical porous cylinder with conducting wall," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1597452 15, 2661 (2003).
10. C. Y. Wang, "Onset of natural convection in a sector-shaped box containing a fluid-saturated porous medium," Phys. Fluids PHFLE6 1070-6631 10.1063/1.869465 9, 3570 (1997).
11. M. Karimi-Fard, M. C. Charrier-Mojtabi, and A. Mojtabi, "Onset of stationary and oscillatory convection in a tilted porous cavity saturated with a binary fluid: Linear stability analysis," Phys. Fluids PHFLE6 1070-6631 10.1063/1.870000 11, 1346 (1999).
12. M. Mamou, "Stability analysis of thermosolutal convection in a vertical packed porous enclosure," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1518996 14, 4302 (2002).
13. A. A. Mohamad, R. Bennacer, and J. Azaiez, "Double diffusion natural convection in a rectangular enclosure filled with binary fluid saturated porous media: The effect of lateral aspect ratio," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1630798 16, 184 (2004).
14. F. T. Rogers, Jr. and H. L. Morrison, "Convection currents in porous media. III. Extended theory of the critical gradient," J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1699561 21, 1177 (1950).
15. T. D. Foster, "Stability of a homogeneous fluid cooled uniformly from above," Phys. Fluids PFLDAS 0031-9171 10.1063/1.1761393 8, 1249 (1965).
16. P. M. Gresho and R. L. Sani, "The stability of a fluid layer subjected to a step change in temperature: Transient vs. frozen time analyses," Int. J. Heat Mass Transfer IJHMAK 0017-9310 14, 207 (1971).
17. B. S. Jhaveri and G. M. Homsy, "The onset of convection in fluid layers heated rapidly in a time-dependent manner," J. Fluid Mech. JFLSA7 0022-1120 114, 251 (1982).
18. T. Green, "The momentary instability of a saturated porous layer with a time-dependent temperature distribution, and the most unstable disturbance," Water Resour. Res. WRERAQ 0043-1397 26, 2015 (1990).
19. D. D. Joseph and C. C. Shir, "Subcritical convective instability. I. Fluid layers," J. Fluid Mech. JFLSA7 0022-1120 26, 753 (1966).
20. B. Straughan, The Energy Method, Stability, and Nonlinear Convection (Springer, New York, 1992).
21. J.-P. Caltagirone, "Stability of a saturated porous layer subject to a sudden rise in surface temperature: Comparison between the linear and energy methods," Q. J. Mech. Appl. Math. QJMMAV 0033-5614 33, 47 (1980).
22. K.-K. Tan, T. Sam, and H. Jamaludin, "The onset of transient convection in bottom heated porous media," Int. J. Heat Mass Transfer IJHMAK 0017-9310 46, 2857 (2003).
23. D. A. Nield, "Comment on 'the onset of transient convection in bottom heated porous media' [Int. J. Heat Mass Transfer 46, 2857 (2003)]: Rayleigh and Biot numbers," Int. J. Heat Mass Transfer IJHMAK 0017-9310 47, 641 (2004).
24. M. C. Kim, K. Y. Kim, and S. Kim, "The onset of transient convection in fluid-saturated porous layer heated uniformly from below," Int. Commun. Heat Mass Transfer IHMTDL 0735-1933 31, 53 (2004).
25. G. Castinel and M. Combarnous, "Natural convection in an anisotropic porous layer," Int. Chem. Eng. INCEAX 0020-6318 17, 605 (1977).
26. R. A. Wooding, "Large-scale geothermal field parameters and convection theory," New Zeal. J. Sci 21, 219 (1978).
27. O. Kvernvold and P. A. Tyvand, "Nonlinear thermal convection in anisotropic porous media," J. Fluid Mech. JFLSA7 0022-1120 90, 609 (1979).
28. R. McKibbin, in Convective Flows in Porous Media, edited by R. A. Wooding and I. White (DSIR Science Information, Wellington, New Zealand, 1985), pp. 113-127.
29. D. A. Nield, "Notes on convection in a porous medium: (i) An effective Rayleigh number for an anisotropic layer, (ii) the Malkus hypothesis and wavenumber selection," Transp. Porous Media TPMEEI 0169-3913 27, 135 (1997).
30. P. Bera and A. Khalili, "Stability of mixed convection in an anisotropic vertical porous channel," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1460879 14, 1617 (2002).
31. J.-F. Epherre, "Criterion for the appearance of natural convection in an anisotropic porous layer," Int. Chem. Eng. INCEAX 0020-6318 17, 615 (1977).
32. P. A. Tyvand and L. Storsletten, "Onset of convection in an anisotropic porous medium with oblique principal axes," J. Fluid Mech. JFLSA7 0022-1120 226, 371 (1991).
33. G. Degan and P. Vasseur, "Influence of anisotropy on convection in porous media with nonuniform thermal gradient," Int. J. Heat Mass Transfer IJHMAK 0017-9310 46, 781 (2003).
34. D. A. S. Rees and A. Postelnicu, "The onset of convection in an inclined anisotropic porous layer," Int. J. Heat Mass Transfer IJHMAK 0017-9310 44, 4127 (2001).
35. P. A. Tyvand, "Thermohaline instability in anisotropic porous media," Water Resour. Res. WRERAQ 0043-1397 16, 325 (1980).
36. R. Bennacer, A. Tobbal, H. Beji, and P. Vasseur, "Double diffusive convection in a vertical enclosure filled with anisotropic porous media," Int. J. Therm. Sci. IJTSFZ 1290-0729 40, 30 (2001).
37. R. McKibbin and M. J. O'Sullivan, "Onset of convection in a layered porous medium heated from below," J. Fluid Mech. JFLSA7 0022-1120 96, 375 (1980).
38. T. Masuoka, T. Katsuhara, Y. Nakazono, and S. Isozaki, "Onset of convection and flow patterns in a porous layer of two different media," Heat Transfer-Jpn. Res. HTJPAU 0096-0802 7, 39 (1978).
39. D. A. Nield, "Estimation of an effective Rayleigh number for convection in a vertically inhomogenous medium or clear fluid," Int. J. Heat Fluid Flow IJHFD2 0142-727X 15, 337 (1994).
40. R. A. Wooding, S. W. Tyler, and I. White, "Convection in groundwater below an evaporating salt lake. 1. Onset of instability," Water Resour. Res. WRERAQ 0043-1397 10.1029/97WR03533 33, 1199 (1997).
41. N. Joly and D. Bernard, "Critère d'apparition de la convection naturelle dans une couche poreuse horizontale limitée par des frontières conductricies de la chaleur: Effet des anisotropies," C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. CMCAEK 1251-8069 320, 573 (1995).
42. M. R. Gustafson II and L. E. Howle, "Effects of anisotropy and boundary plates on the critical values of a porous medium heated from below," Int. J. Heat Mass Transfer IJHMAK 0017-9310 42, 3419 (1999).
43. J. W. Elder, "Transient convection in a porous medium," J. Fluid Mech. JFLSA7 0022-1120 27, 609 (1967).
44. J. W. Elder, "The unstable thermal interface," J. Fluid Mech. JFLSA7 0022-1120 32, 69 (1968).
45. D. D. Joseph, Stability of Fluid Motions I, Springer Tracts in Natural Philosophy Vol. 27 (Springer, Berlin, 1976).
46. G. M. Homsy, "Global stability of time-dependent flows: Impulsively heated or cooled fluid layers," J. Fluid Mech. JFLSA7 0022-1120 60, 129 (1973).
47. G. P. Neitzel, "Onset of convection in impulsively heated or cooled fluid layers," Phys. Fluids PFLDAS 0031-9171 10.1063/1.863620 25, 210 (1982).
48. T. D. Foster, "Effect of boundary conditions on the onset of convection," Phys. Fluids PFLDAS 0031-9171 10.1063/1.1692095 11, 1257 (1968).
49. H. Masamoto and S. Honda, "Anisotropic modelings of the hydrothermal convection in layered porous media," J. Phys. Earth JPHEAF 0022-3743 40, 555 (1992).
50. C.-Y. Chen, L. Wang, and Y. Kurosaki, "Numerical simulations of heat transfer in porous media with effect of heterogeneities," JSME Int. J., Ser. B JIJEEE 1340-8054 10.1299/jsmeb.45.315 45, 315 (2002).