Доступ предоставлен для: Guest

ISSN Online: 2377-424X

ISBN CD: 1-56700-226-9

ISBN Online: 1-56700-225-0

International Heat Transfer Conference 13
August, 13-18, 2006, Sydney, Australia

ONSET OF CONVECTION IN AN UNSTEADY THERMAL BOUNDARY LAYER

Get access (open in a dialog) DOI: 10.1615/IHTC13.p6.140
10 pages

Аннотация

We consider the stability of the thermal boundary layer which is set up by suddenly imposing a relatively high temperature on the lower horizontal surface bounding a semi-infinite region of Newtonian fluid. The basic temperature field is then described by the complementary error function with no flow. We solve the full linearised disturbance equations, which are parabolic in time, to find the critical time for the onset of convection as a function of the disturbance wavelength, and to compare these exact results with criteria based on a quasi-static theory.
Neutral curves based upon different measures of the strength of the disturbance are obtained and these are different from one another. In addition a quasi-static neutral curve is obtained for comparison purposes. It is shown that a stability criterion based upon a thermal energy of the disturbance, a global measure of the disturbance strength, yields a critical time which is substantially earlier than is predicted using approximate theories. This may be explained by appealing to the fact that approximations impose unrealistic constraints upon the disturbance. In addition, an investigation of the effect of changing the time at which the disturbance is introduced shows that there is a preferred evolutionary path to which all disturbances are attracted. Thus, if a disturbance is imposed at a sufficiently early time, then the critical time for growth of the disturbance is independent of the time of introduction.