Abo Bibliothek: Guest

ISSN Online: 2377-424X

ISBN Print: 0-89116-130-9

International Heat Transfer Conference 6
August, 7-11, 1978, Toronto, Canada

ONSET OF CONVECTION IN A SEMI-INFINITE LAYER WITH NON-LINEAR DENSITY-TEMPERATURE RELATION

Get access (open in a dialog) DOI: 10.1615/IHTC6.3210
pages 223-228

Abstrakt

In the well known "Bénard-problem" where the density is taken to be inverse proportional to the temperature and the basic temperature distribution is given by the steady linear conduction profile the onset of convection is described by one parameter only, the critical Rayleigh number. Using a parabolic temperature-density relationship the present analysis shows that the influence of the density anomaly of water can be described by two parameters when the basic temperature profile is a steady-state one; and by three parameter when it is a time - dependent one. The two additional parameters are the nonlinearity N which is a measure for the deviation of the real density distribution from the linear one and the startparameter γ which essentialy depends on the initial isothermal temperature. For a semi-infinite water layer the marginal stability limits are calculated for two cases: a) constant temperature and b) constant heat flux at the lower boundary. For a normal fluid the calculate critical Rayleigh numbers, Rac = 213 and Rac = 135, are in excellent agreement with experimental data. For water the theory predicts a strong stabilizing effect of the density anomaly for low and moderate heat flux rates whereas a week destabilizing is observed at very high rates.