Periodic growth and decay of a frozen crust over a heat generating liquid layer

A theoretical investigation is made of thermal oscillations in a horizontal layer of liquid heated at high Rayleigh number from within and cooled to freezing from above. The processes of turbulent thermal convection in the liquid layer and transient heat conduction in the solidified layer are modeled and the conditions leading to periodic self-sustained oscillations are identified. The results of this study indicate that there are five independent parameters that control the oscillatory behavior of the system. Effects of these parameters on the behavior of the transient liquid temperature and the instantaneous crust thickness are obtained and discussed. Validity of the present approach is justified based upon the higher-order solutions.