Influence of inertia and drag terms on the stability of mixed convection in a vertical porous-medium channel

International Journal of Heat and Mass Transfer

Volumn 53, Issue 23-24, 2010, Pages 5261-5273

  Kumar, J ^a   Bera, P ^a   Khalili, A ^b,c  

^a INDIAN INSTITUTE OF TECHNOLOGY ROORKEE   (India)

^b MAX PLANCK INSTITUTE FOR MARINE MICROBIOLOGY   (Germany)

^c JACOBS UNIVERSITY BREMEN   (Germany)

Author keywords

Buoyancy assisted flow; Energy norm; Linear stability; Mixed convection; Non Darcy models; Porous medium

Indexed keywords

COMBINED EFFECT; COMPARATIVE STUDIES; DARCY MODEL; DARCY NUMBER; DARCY-BRINKMAN; DESTABILIZING EFFECT; ENERGY NORM; FLUID VISCOSITY; FLUID-FILLED; FORM DRAG; INERTIA FORCE; INSTABILITY BOUNDARIES; LINEAR STABILITY; MOMENTUM EQUATION; ORDER OF MAGNITUDE; POROUS MEDIUM; VERTICAL CHANNELS;

BUOYANCY; DRAG; MIXED CONVECTION; POROUS MATERIALS;

LINEAR STABILITY ANALYSIS;

EID: 77956060291     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2010.07.033     Document Type: Article

References (49)

1. D.A. Nield, and A. Bejan Convection in Porous Media 2006 Springer-Verlag New York
2. K. Vafai, and C.L. Tien Boundary and inertia effects on flow and heat transfer in porous media Int. J. Heat Mass Transfer 24 1981 195 203
3. C.T. Hsu, and P. Cheng Thermal dispersion in a porous medium Int. J. Heat Mass Transfer 33 1990 1587 1597
4. M. Kaviany Principles of Heat Transfer in Porous Media 1985 Springer-Verlag New York
5. P. Bera, and A. Khalili Stability of mixed-convection in an anisotropic porous channel Phys. Fluids 14 2002 1617 1630
6. Y.C. Chen Non-Darcy flow stability of mixed-convection in a vertical channel filled with a porous medium Int. J. Heat Mass Transfer 47 2004 1257 1266
7. P. Bera, and A. Khalili Influence of Prandtl number on stability of mixed convective flow in a vertical channel filled with a porous medium Phys. Fluids 18 2006 124103-1 124103-10
8. H.E. Rose On the resistance coefficient-Reynolds number relationship for fluid flow through a bed of granular materials Proc. Lond. Inst. Mech. Eng. 153 1945 154 161
9. A.E. Scheidegger The Physics of Flow Through Porous Media 1974 University of Toronto Press Toronto
10. A.A. Hannoura, and F. Barends Non-Darcy flow; a state of the art A. Veruijt, F.B.J. Banrends, Flow and Transport in Porous Media 1981 Balkema
11. C.C. Mei, and J.L. Auriault The effect of weak inertia on flow through a porous medium J. Fluid Mech. 222 1991 647 663
12. T. Giorgi Derivation of the Forchheimer law via matched asymptotic expansions Transp. Porous Media 29 1997 191 206
13. M. Firdaouss, J.L. Guermond, and P.L. Quéré Nonlinear corrections to Darcy's law at low Reynolds numbers J. Fluid Mech. 343 1997 331 350
14. E. Skjetne, and J.L. Auriault High-velocity laminar and turbulent flow in porous media Transp. Porous Media 36 1999 131 147
15. H.C. Brinkman On the permeability of media consisting of closely packed porous particles Appl. Sci. Res. 1 1949 81 86
16. T.S. Lundgren Slow flow through stationary random beds and suspensions of spheres J. Fluid Mech. 51 1972 273 299
17. R.C. Givler, and S.A. Altobelli A determination of the effective viscosity for the Brinkman-Forchheimer flow model J. Fluid Mech. 258 1994 355 370
18. N. Martys, D.P. Bentz, and E.J. Garboczi Computer simulation study of the effective viscosity in Brinkman's equation Phys. Fluids 6 1994 1434 1439
19. F.J. Valdes-Parada, J.A. Ochoa-Tapia, and J. Alvarez-Ramirez On the effective viscosity for the Darcy-Brinkman equation Physica A 385 2007 69 79
20. W.P. Breugem The effective viscosity of a channel-type porous medium Phys. Fluids 19 2007 103104-1 103104-8
21. A.A. Hill, and B. Straughan Poiseuille flow in a fluid overlying a porous medium J. Fluid Mech. 603 2008 137 149
22. S. Whitaker The Method of Volume Averaging 1999 Kluwer Academic Publishers
23. N. Tilton, and L. Cortelezzi Linear stability analysis of pressure-driven flows in channels with porous walls J. Fluid Mech. 604 2008 411 445
24. M. Muskat The Flow of Homogeneous Fluids Through Porous Media 1946 The Mapple Press Company New York
25. J.C. Ward Turbulent flow in porous media J. Hydr. Div. ASCE 90 1964 1 12
26. F.A.L. Dullien, and M.I.S. Azzam Flow rate-pressure gradient measurements in periodically nonuniform capillary tubes AIChE J. 19 1973 222 229
27. N. Ahmed, and D.K. Sunada Nonlinear flow in porous media J. Hydr. Div. ASCE 95 1969 1847 1857
28. D.W. Ruth, and H. Ma On the derivation of the Forchheimer equation by means of the averaging theorem Transp. Porous Media 7 1992 255 264
29. S.M. Hassanizadeh, and W.G. Gray High-velocity flow in porous media Transp. Porous Media 2 1987 521 531
30. S. Whitaker The Forchheimer equation: a theoretical development Transp. Porous Media 25 1996 27 61
31. G.S. Beavers, and E.M. Sparrow Non-Darcy flow through fibrous porous media J. Appl. Mech. 36 1969 711 714
32. G.S. Beavers, E.M. Sparrow, and D.E. Rodenz Influence of bed size on the flow characteristics and porosity of randomly packed beds of spheres J. Appl. Mech. 40 1973 655 660
33. O. Coulaud, P. Morel, and J.P. Caltagirone Numerical modeling of nonlinear effects in laminar flow through a porous medium J. Fluid Mech. 190 1988 393 407
34. D. Poulikakos Buoyancy-driven convection in a horizontal fluid layer extending over a porous substrate Phys. Fluids 29 1986 3949 3957
35. K. Vafai, and S.J. Kim On the limitations of the Brinkman-Forchheimer- extended Darcy equation Int. J. Heat Fluid Flow 16 1995 11 15
36. D.A. Nield, S.L.M. Junqueira, and J.L. Lage Forced convection in a fluid-saturated porous-medium channel with isothermal or iso-flux boundaries J. Fluid Mech. 322 1996 201 214
37. A. Delache, M.N. Ouarzazi, and M. Combarnous Spatio-temporal stability analysis of mixed-convection flows in porous media heated from below: comparison with experiments Int. J. Heat Mass Transfer 50 2007 1485 1499
38. R.A. Wooding Steady state free thermal convection of liquid in a saturated permeable medium J. Fluid Mech. 2 1957 273 285
39. J.C. Slattery Single-phase flow through porous media AIChE J. 15 1969 866 872
40. V. Prasad, F.A. Kulacki, and M. Keyhani Natural convection in porous media J. Fluid Mech. 150 1985 89 119
41. P. Nithiarasu, K.N. Seetharamu, and T. Sundararajan Numerical investigation of buoyancy driven flow in a fluid-saturated non-Darcian porous medium Int. J. Heat Mass Transfer 42 1999 1205 1215
42. A. Khalili, A.J. Basu, U. Pietrzyk, and M. Raffel An experimental study of recirculating flow through fluid-sediment interfaces J. Fluid Mech. 383 1999 229 247
43. B. Alazmi, and K. Vafai Analysis of variants within the porous media transport models ASME J. Heat Transfer 122 2000 303 326
44. T. Desaive, G. Lebon, and M. Hennenberg Coupled capillary and gravity-driven instability in a liquid film overlying a porous layer Phys. Rev. E 64 2001 066304-1 066304-1-8
45. Z. Guo, and T.S. Zhao Lattice Boltzmann model for incompressible flows through porous media Phys. Rev. E 66 2002 036304-1 036304-9
46. A.J. Basu, and A. Khalili Computation of flow through a fluid-sediment interface in a benthic chamber Phys. Fluids 11 1999 1395 1405
47. P.G. Drazin, and W.H. Reid Hydrodynamic Stability 2004 Cambridge University Press Cambridge
48. Y.C. Chen, and J.N. Chung The linear stability of mixed-convection in a vertical channel flow J. Fluid Mech. 325 1996 29 51
49. Y.C. Su, and J.N. Chung Linear stability analysis of mixed-convection flow in a vertical pipe J. Fluid Mech. 422 2000 141 166