Global stability for penetrative convection with throughflow in a porous material

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 72, Issue 5, 2007, Pages 635-643

  Hill, A A ^a   Rionero, S ^b   Straughan, B ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Energy method; Penetrative convection; Throughflow

Indexed keywords

BOUNDARY CONDITIONS; DENSITY (SPECIFIC GRAVITY); HEAT CONVECTION; POROUS MATERIALS; TEMPERATURE DISTRIBUTION;

NON-LINEAR ENERGY STABILITY ANALYSIS; PENETRATIVE CONVECTION;

LINEAR STABILITY ANALYSIS;

EID: 35348932260     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxm036     Document Type: Article

References (31)

1. CAPONE, F., GENTILE, M. & RIONERO, S. (2005a) Influence of linear concentration heat source and parabolic density on penetrative convection onset. Proceedings of the 13th Conference on Waves and Stability in Continuous Media (R. Monaco, G. Mulone, S. Rionero & T. Ruggeri eds). Singapore: World Scientific, pp. 77-82.
2. CAPONE, F., GENTILE, M. & RIONERO, S. (2005b) On penetrative convection in porous media driven by quadratic heat sources. Proceedings of the 13th Conference on Waves and Stability in Continuous Media (R. Monaco, G. Mulone, S. Rionero & T. Ruggeri eds). Singapore: World Scientific, pp. 83-88.
3. CAPONE, F. & RIONERO, S. (2003) Nonlinear stability of a convective motion in a porous layer driven by a horizontally periodic temperature gradient. Continuum Mech. Thermodyn., 15, 529-538.
4. CHRISTOPHERSON, D. G. (1940) Note on the vibration of membranes. Q. J. Math., 11, 63-65.
5. DONGARRA, J. J., STRAUGHAN, B. & WALKER, D. W. (1996) Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems. Appl. Numer. Math., 22, 399-434.
6. FLAVIN, J. N. & RIONERO, S. (1996) Qualitative Estimates for Partial Differential Equations. Boca Raton: CRC Press.
7. FLAVIN, J. N. & RIONERO, S. (1999) The Bérnard problem for nonlinear heat conduction: Unconditional stability. Q. J. Mech. Appl. Math., 52, 441-452.
8. FLAVIN, J. N. & RIONERO, S. (2002) Note on a versatile Liapunov functional: Applicability to an elliptic equation. Math. Methods Appl. Sci., 25, 1299-1305.
9. FLAVIN, J. N. & RIONERO, S. (2003) Stability properties for nonlinear diffusion in porous and other media. J. Math. Anal. Appl. 281, 221-232.
10. KRISHNAMURTI R. (1975) On cellular cloud patterns. Part 1: mathematical model. J. Atmos. Sci., 32, 1353-1363.
11. LOMBARDO, S., MULONE, G. & RIONERO, S. (2000) Global stability in the Bérnard problem for a mixture with superimposed plane parallel shear flows. Math. Methods Appl. Sci., 23, 1447-1465.
12. LOMBARDO, S., MULONE, G. & RIONERO, S. (2001) Global nonlinear exponential stability of the conduction-diffusion solution for Schmidt numbers greater than Prandtl numbers. J. Math. Anal. Appl., 262 191-207.
13. MOLER, C. B. & STEWART, G. W. (1973) An algorithm for generalized matrix eigenproblems. SIAM J. Numer. Anal., 10, 241-256.
14. NIELD, D. A. (1987a) Convective instability in porous media with throughflow. AIChE J., 33, 1222-1224.
15. NIELD, D. A. (1987b) Throughflow effects in the Rayleigh-Bénard convective instability problem. J. Fluid Mech., 185, 353-360.
16. NIELD, D. A. (1998) Instability and turbulence in convective flows in porous media. Nonlinear Instability, Chaos and Turbulence (L. Debnath & D. N. Riahi eds). Boston: WIT Press, pp. 225-276.
17. NIELD, D. A. & BEJAN, A. (1999) Convection in Porous Media, 2nd edn. New York: Springer.
18. PAYNE, L. E., SONG, J. C. & STRAUGHAN, B. (1999) Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity. Proc. R. Soc. Lond A, 455, 2173-2190.
19. PAYNE, L. E. & STRAUGHAN, B. (1987) Unconditional nonlinear stability in penetrative convection. Geophys. Astrophys. Fluid Dyn. 39, 57-63.
20. PAYNE, L. E. & STRAUGHAN, B. (1998) Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modeling questions. J. Math. Pures Appl., 77, 317-354.
21. PAYNE, L. E. & STRAUGHAN, B. (2000) Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium. Stud. Appl. Math., 105, 59-81.
22. QIAO, Z. & KALONI, P. (1998) Nonlinear convection in a porous medium with inclined temperature gradient and vertical throughfow. Int. J. Heat Mass Transf., 41, 2549-2552.
23. RIONERO, S. (2005) Functionals for the coincidence between linear and nonlinear stability with applications to spatial ecology and double diffusive convection. Proceedings of the 13th Conference on Waves and Stability in Continuous Media (R. Monaco, G. Mulone, S. Rionero & T. Ruggeri eds). World Scientific, pp. 461-474.
24. ROSENSWEIG, R. (1985) Ferrohydrodynamics. Cambridge: Cambridge University Press.
25. SOMERVILLE, R. C. J. & GAL-CHEN, T. (1979) Numerical simulation of convection with mean vertical motion. J. Atmos. Sci., 36, 805-815.
26. STRAUGHAN, B. (2001) A sharp nonlinear stability threshold in rotating porous convection. Proc. R. Soc. Lond. A, 457, 87-93.
27. STRAUGHAN, B. (2002) Sharp global nonlinear stability for temperature dependent viscosity convection. Proc. R. Soc. Lond. A, 458, 1773-1782.
28. STRAUGHAN, B. (2004a) Resonant porous penetrative convection. Proc. R. Soc. Lond. A, 460, 2913-2927.
29. STRAUGHAN, B. (2004b) The Energy Method, Stability and Nonlinear Convection. New York: Springer.
30. STRAUGHAN, B. (2006) Global nonlinear stability in porous convection with a thermal non-equilibrium model. Proc. R. Soc. Lond. A, 462, 409-418.
31. STRAUGHAN, B. & WALKER, D. W. (1996) Two very accurate and efficient methods for computing eigenvalues and eigenfunctions in porous convection problems. J. Comput. Phys., 127, 128-141.