Linear stability of mixed convection flows in horizontal rectangular channels of finite transversal extension heated from below

International Journal of Heat and Mass Transfer

Volumn 43, Issue 4, 2000, Pages 589-610

  Nicolas, X ^a,c   Luijkx, J M ^b   Platten, J K ^b  

^a IMFT   (France)

^b UNIVERSITY OF MONS   (Belgium)

^c UNIVERSITÉ GUSTAVE EIFFEL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; BOUNDARY CONDITIONS; CHANNEL FLOW; FLOW PATTERNS; HYDRODYNAMICS; MATHEMATICAL MODELS; PRANDTL NUMBER; REYNOLDS NUMBER;

LINEAR HYDRODYNAMIC STABILITY; POISEUILLE FLOW; RAYLEIGH NUMBER;

MIXED CONVECTION;

CHANNEL; CONVECTION; MATHEMATICAL ANALYSIS; POISEUILLE FLOW; STABILITY;

EID: 0345044933     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0017-9310(99)00099-X     Document Type: Article

References (40)

1. H. Bénard, D. Avsec, Travaux récents sur les tourbillons en bandes; applications àl'astrophysique et àla météorologie, J. Phys. et de Radium 9 (1938) 468-500.
2. D. Brunt, Experimental cloud formation, in: Compendium of Meteorology, American Meteorological Society, Boston, 1951, pp. 1255-1262.
3. M.E. Braaten, S.V. Patankar, Analysis of laminar mixed convection in shrouded arrays of heated rectangular blocks, Int. J. Heat Mass Transfer 28 (1985) 1699-1709.
4. M. Hasnaoui, E. Bilgen, P. Vasseur, L. Robillard, Mixed convective heat transfer in a horizontal channel heated periodically from below, Num. Heat Transfer, Part A 20 (1991)297-315.
5. S.Q. Zhang, A.V. Tangborn, Flow regimes in twodimensional mixed convection with spatially periodic lower wall heating, Phys. Fluids 6 (1994) 3285-3293.
6. K.F. Jensen, E.O. Einset, D.I. Fotiadis, Flow phenomena in chemical vapor deposition of thin films, Annu. Rev. Fluid Mech. 23 (1991) 197-233.
7. G. Evans, R. Greif, Thermally unstable convection with applications to chemical vapor deposition channel reactors, Int. J. Heat Mass Transfer 36 (1993) 2769-2781.
8. N.K. Ingle, T.J. Mountziaris, The onset of transverse recirculations during flow of gases in horizontal ducts with differentially heated lower walls, J. Fluid Mech. 277 (1994) 249-269.
9. J.-M. Luijkx, Influence de la présence de parois latérales sur l'apparition de la convection libre, forcée et mixte. Ph.D. thesis, Université d'état de Mons, Belgique, 1983.
10. K.C. Chiu, J. Ouazzani, F. Rosenberger, Mixed convection between horizontal plates-II. Fully developed flow, Int. J. Heat Mass Transfer 30 (1987) 1655-1662.
11. K.C. Chiu, F. Rosenberger, Mixed convection between horizontal plates-I. Entrance effects, Int. J. Heat Mass Transfer 30 (1987) 1645-1654.
12. M.T. Ouazzani, J-P. Caltagirone, G. Meyer, A. Mojtabi, Etude numérique et expérimentale de la convection mixte entre deux plans horizontaux àtempératures différentes, Int. J. Heat Mass Transfer 32 (1989) 261-269.
13. M.T. Ouazzani, J.-K. Platten, A. Mojtabi, Etude expérimentale de la convection mixte entre deux plans horizontaux àtempératures différentes-II, Int. J. Heat Mass Transfer 33 (1990) 1417-1427.
14. M.T. Ouazzani, J.-K. Platten, A. Mojtabi, Intermittent patterns in mixed convection, Applied Scientific Research 51 (1993) 677-685.
15. M.T. Ouazzani, J.-K. Platten, H.W. Müller, M. Lücke, Etude de la convection mixte entre deux plans horizontaux àdes températures différentes-III, Int. J Heat Mass Transfer 38 (1995) 875-886.
16. H.W. Müller, M. Lücke, M. Kamps, Transversal convection patterns in horizontal shear flow, Physical Review A 45 (1992) 3714-3725.
17. W. Veite, Zur Stabilität der Strömung in einem horizontalen Rohr bei ungleichmäßig erwärmter Wand, Z. Angew. Math. Phys. 13 (1962) 591-600.
18. R. Sani, Note on flow instabilities in heated ducts, Z. Angew. Math. Phys. 15 (1964) 381-387.
19. Y. Mori, Y. Uchida, Forced convective heat transfer between horizontal flat plates, Int. J. Heat Mass Transfer 9 (1966) 803-817.
20. K.S. Gage, W.H. Reid, The stability of thermally stratified plane Poiseuille flow, J. Fluid Mech. 33 (1968) 2132.
21. J.-K. Platten, A variational formulation for the stability of flows with temperature gradients, Int. J. Engng Sci. 9 (1971) 855-869.
22. H.B. Squire, On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls, Proc. Roy. Soc. London, A 42 (1933) 621-628.
23. J.-K. Platten, J.-C. Legros, Convection in Liquids, Springer Verlag, Berlin, Heidelberg, 1984 Chaps 6 and 8.
24. J.-M. Luijkx, J.-K. Platten, J.-C. Legros, On the existence of thermoconvective rolls, transverse to a superimposed mean Poiseuille flow, Int. J. Heat Mass Transfer 24 (1981) 803-817.
25. C.H. Yu, M.Y. Chang, T.F. Lin, Structures of moving transverse and mixed rolls in mixed convection of air in a horizontal plane channel, Int. J. Heat Mass Transfer 40 (1997) 333-346.
26. H.R. Brand, R.J. Deissler, G. Ahlers, Simple model for the Bénard instability with horizontal flow near threshold, Physical Review A 43 (1991) 4262-4268.
27. H.W. Müller, M. Tveitereid, S. Trainoff, RayleighBénard problem with imposed weak through-flow: two coupled Ginzburg-Landau equations, Physical Review E 48 (1993) 263-272.
28. E. Schröder, K. Bühler, Three-dimensional convection in rectangular domains with horizontal throughflow, Int. J. Heat Mass Transfer 38 (1995) 1249-1259.
29. M.Y. Chang, C.H. Yu, T.F. Lin, Flow visualization and numerical simulation of transverse and mixed vortex roll formation in mixed convection of air in a horizontal flat duct, Int. J. Heat Mass Transfer 40 (1997) 1907-1922.
30. C.H. Yu, M.Y. Chang, C.C. Huang, T.F. Lin, Unsteady vortex roll structures in a mixed convective air flow through a horizontal plane channel: a numerical study, Int. J. Heat Mass Transfer 40 (1997) 505-518.
31. D. Roth, P. Büchel, M. Lücke, H.W. Müller, M. Kamps, R. Schmilz, Influence of boundaries on pattern selection in through-flow, Physica D 97 (1996) 253-263.
32. X. Nicolas, P. Traore, A. Mojtabi, J.-P. Caltagirone, Augmented Lagrangian method and open boundary conditions in 2-D simulation of Poiseuille-Bénard channel flow, Int. J. Number. Meth. Fluids 25 (1997) 265-283.
33. X. Nicolas, A. Mojtabi, J.-K. Platten, Two dimensional numerical analysis of the Poiseuille-Bénard flow in a rectangular channel heated from below, Physics of Fluids 9 (1997) 337-348.
34. J.-M. Luijkx, J.-K. Platten, On the onset of free convection in a rectangular channel, J. Non-Equilibrium Thermodyn. 6 (1981) 141-158.
35. B.T. Smith, J.M. Boyle, J.J. Dongarra, B.S. Garbow, Y. Ikebe, V.C. Klema, C.B. Moler, Matrix eigensystem routines-Eispack Guide, Lecture Notes in Computer Sciences, Springer-Verlag, vol. 6, 1976.
36. I. Catton, The effect of insulating vertical walls on the onset of motion in a fluid heated from below, Int. J. Heat Mass Transfer 15 (1972) 665-672.
37. C.S. Yi, Thermal instability of viscous fluids, Quart. J. Appl. Math. 17 (1959)25-42.
38. R.J. Deissler, Spatially growing waves, intermittency, and convective chaos in an open-flow system, Physica D 25 (1987) 233-260.
39. P. Huerre, Spatio-temporal instabilities in closed and open flows, in: E. Tirapegui, D. Villaroel (Eds.), Instabilities and Nonequilibrium Structures, Reidel, Dordrecht, 1987, pp. 141-177.
40. S.S. Chen, A.S. Lavine, Laminar, buoyancy induced flow structures in a bottom heated, aspect ratio 2 duct with throughflow, Int. J. Heat Mass Transfer 39 (1996) 1-11.