PMID- 12241475
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20021002
LR  - 20031103
IS  - 1539-3755 (Print)
IS  - 1539-3755 (Linking)
VI  - 66
IP  - 1 Pt 2
DP  - 2002 Jul
TI  - Effects of thermal boundary conditions and cavity tilt on hydrothermal waves: 
      suppression of oscillations.
PG  - 016301
AB  - Hydrothermal waves are longitudinal modes responsible for the onset of 
      oscillations of low-Prandtl number flows inside end-heated cavities. We consider 
      the flow induced by the hydrothermal wave in a rectangular enclosure whose 
      differentially-heated side is tilted alpha degrees from the vertical position. An 
      analytical approximation to the neutral curve and dispersion relation obtained by 
      the Galerkin procedure is shown to quantitatively agree with the exact numerical 
      solution of the stability problem. The analytical expressions are then used to 
      dissect the effect of the Prandtl and Biot numbers and the inclination on the 
      wave stability. In conducting walls the critical Rayleigh R(cr) and wave number 
      m(cr) tend to a constant value at low Pr, while the critical frequency f(cr) 
      approximately Pr(-1/12). In adiabatic walls all these critical parameters 
      increase like Pr(1/2). The boundaries can be considered to be poorly insulated if 
      Bi>Pr, and in this case the critical parameters increase like Bi(1/2). On the 
      other hand, R(cr) and m(cr) reach a minimum value at intermediate inclinations, 
      while the critical frequency steadily increases with alpha. A closed equation for 
      the frequency is also derived. This equation correctly forecasts the critical 
      frequency in the unbounded domain and also the fundamental frequency measured in 
      confined flows, as revealed by comparison with previous experiments and hereby 
      presented numerical calculations for varying alpha. An important conclusion of 
      the study is that for any arbitrarily small value of Pr the hydrothermal wave can 
      be suppressed by heating the cavity above a theoretically predicted 
      (Pr-dependent) angle. This prediction is of great relevance in the application 
      domain (viz. the crystal growth from melts by the Bridgman technique).
FAU - Delgado-Buscalioni, R
AU  - Delgado-Buscalioni R
AD  - Departamento de Fisica Fundamental, UNED, Apartado 60141, Madrid 28080, Spain. 
      R.Delgado-Buscalioni@qmul.ac.uk
LA  - eng
PT  - Journal Article
DEP - 20020712
PL  - United States
TA  - Phys Rev E Stat Nonlin Soft Matter Phys
JT  - Physical review. E, Statistical, nonlinear, and soft matter physics
JID - 101136452
EDAT- 2002/09/21 10:00
MHDA- 2002/09/21 10:01
CRDT- 2002/09/21 10:00
PHST- 2001/10/10 00:00 [received]
PHST- 2002/03/13 00:00 [revised]
PHST- 2002/09/21 10:00 [pubmed]
PHST- 2002/09/21 10:01 [medline]
PHST- 2002/09/21 10:00 [entrez]
AID - 10.1103/PhysRevE.66.016301 [doi]
PST - ppublish
SO  - Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Jul;66(1 Pt 2):016301. doi: 
      10.1103/PhysRevE.66.016301. Epub 2002 Jul 12.