The main object of this thesis is to attempt to derive an adequate description of the origin and nature of thermal oscillations induced in fluids of low Prandtl number. Chapter One reviews the hydrodynamic stability of a fluid layer heated from below (results which are equally applicable to a fluid heated from the side) and surveys the current state of theory which is pertinent and linked to the Rayleigh-Benard convection. The next section examines the current state of crystal growth especially problems focusing attention on the induced thermal oscillations. Chapter Two commences with an introduction to the basic flow state. If we are going to consider the salient features of thermal oscillations in an annular configuration, a model should be developed and this is the main area of concentration in this chapter. However, certain approximations are introduced to reduce the complexity of the proposed model and still obtain meaningful results. Turning now to Chapter Three we examine the stability characteristics and transformation of the basic eighth order differential equation describing the fundamental flow pattern into non-dimensional form. The final section of the chapter is concentrated on allowing the converted basic equation of flow be truncated to the small Prandtl number limit. The final Chapter concentrates on the experimental apparatus: five different annular boats were employed with both mercury and gallium as the working fluid. The final section comprises the experimental results and the comparison between theory and experiment. The main conclusions are as follows:- The structural state is a pre-requisite for the existence of large amplitude temperature oscillations, to be initiated and sustained. Furthermore, this links both high and low Prandtl number fluids that together, for specific Rayleigh numbers, exhibit rolls, hexagons et sequ. The square rolls are certainly prominent for liquids whose cell length is greater than its depth. There is a critical temperature which must be exceeded before oscillations can commence. A comparison between the Lorentz model and the wave lengths in the structured state is good. Finally, an estimate of the velocities in a range of fluids is compared. The essential conclusion is that for high Prandtl numbers the magnitude of the t velocity, induced in the fluid by Rayleigh-Benard convection, is not large enough to provide a suitably large vertical shear. Likewise, the stabilizing effect of the vertical temperature gradient becomes too large for oscillations to occur.
|Date of Award||1978|