On Thermal Control of Devices Contained in Inclined Hemispherical Cavities with Dome Oriented Downwards and Subjected to Transient Natural Convection

Abstract : In this study, relationships of Nusselt–Rayleigh–Fourier type are proposed for the case of air-filled hemispherical cavity whose dome is oriented downwards and maintained isothermal. Its disk is subjected to a constant heat flux and inclined at an angle varying between 90° (vertical position) and 180° (disk horizontal with dome oriented downwards). The numerical approach is performed in transient regime by means of the finite volume method for Rayleigh numbers in the range of 104 − 5 × 108. These results are confirmed at steady state by measurements done for some configurations in a previous study for the same Rayleigh and inclination ranges. Otherwise, they complete other surveys considering inclination angles varying between 0° (horizontal cavity with dome oriented upwards) and 90° (vertical cavity) for a wider range of Rayleigh numbers. The correlations allow thermal control of devices submitted to natural convection in hemispherical cavities during the time preceding the steady state after their switch on.