Surface-Tension-Driven Convection in a Fluid Overlying a Porous Layer

Journal of Computational Physics

Volumn 170, Issue 1, 2001, Pages 320-337

  Straughan, B ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Chebyshev tau method; Marangoni effect; Multilayer convection; Superposed porous fluid convection; Surface tension

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; HEAT CONVECTION; POROUS MATERIALS;

CHEBYSHEV TAU METHODS; EIGENVALUE AND EIGENFUNCTIONS; FLUID SURFACE; MARANGONI EFFECTS; MULTILAYER CONVECTION; POROUS LAYERS; POROUS MEDIUM; SUPERPOSED POROUS-FLUID CONVECTION; SURFACE TENSION-DRIVEN CONVECTION; THERMAL CONVECTIONS;

SURFACE TENSION;

EID: 0013389023     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2001.6739     Document Type: Article

References (22)

1. Beavers G. S., Joseph D. D. Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30:1967;197.
2. Blest D. C., Duffy B. R., McKee S., Zulkifle A. K. Curing simulation of thermoset composites. Composites: Part A. 30:1999;1289.
3. Blest D. C., McKee S., Zulkifle A. K., Marshall P. Curing simulation by autoclave resin infusion. Composites Sci. Technol. 59:1999;2297.
4. Chen F., Chen C. F. Onset of finger convection in a horizontal porous layer underlying a fluid layer. J. Heat Transfer. 110:1988;403.
5. Davis S. H. Buoyancy-surface tension instability by the method of energy. J. Fluid Mech. 39:1969;347.
6. Dongarra J. J., Straughan B., Walker D. W. Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems. Appl. Numer. Math. 22:1996;399.
7. Gardner D. R., Trogdon S. A., Douglas R. W. A modified tau spectral method that eliminates spurious eigenvalues. J. Comput. Phys. 80:1989;137.
8. Lebon G., Cloot A. Effects of non-uniform temperature gradients in Bénard-Marangoni's instability. J. Non-Equilib. Thermodyn. 6:1981;15.
9. McFadden G. B., Murray B. T., Boisvert R. F. Elimination of spurious eigenvalues in the Chebyshev tau spectral method. J. Comput. Phys. 91:1990;228.
10. McKay G. Onset of buoyancy-driven convection in superposed reacting fluid and porous layers. J. Eng. Math. 33:1998;31.
11. Nield D. A. Onset of convection in a fluid layer overlying a layer of a porous medium. J. Fluid Mech. 81:1977;513.
12. Nield D. A. The boundary correction for the Rayleigh-Darcy problem: Limitations of the Brinkman equation. J. Fluid Mech. 128:1983;37.
13. Nield D. A. The limitations of the Brinkman-Forchheimer equation in modelling flow in a saturated porous medium and at an interface. Int. J. Heat Fluid Flow. 12:1991;269.
14. Nield D. A. Modelling the effect of surface tension on the onset of natural convection in a saturated porous medium. Transp. Porous Media. 31:1998;365.
15. D. A. Nield, Instability and turbulence in convective flows in porous media, in Nonlinear Instability, Chaos and Turbulence, edited by L. Debnath and D. N. RiahiWIT Press, Boston, Southampton, 1998, pp. 225-276.
16. Nield D. A., Bejan A. Convection in Porous Media. 1999.
17. Payne L. E., Straughan B. Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modeling questions. J. Math. Pures Appl. 77:1998;317.
18. Qin Y., Kaloni P. N. Creeping flow past a porous spherical shell. Z. Angew. Math. Mech. 73:1993;77.
19. Straughan B., Walker D. W. Two very accurate and efficient methods for computing eigenvalues and eigenfunctions in porous convection problems. J. Comput. Phys. 127:1996;128.
20. Straughan B., Walker D. W. Multi component diffusion and penetrative convection. Fluid Dyn. Res. 19:1997;77.
21. Tracey J. Stability Analyses of Multicomponent Convection-Diffusion Problems. 1997.
22. Zebib A. Removal of spurious modes encountered in solving stability problems by spectral methods. J. Comput. Phys. 70:1987;521.