Quantification of natural convective heat transfer within air-filled hemispherical cavities. Isothermal tilted disk with dome oriented upwards and wide Ra range

This work quantifies the natural convective heat transfer occurring in hemispherical air-filled cavities whose disk is inclined at an angle varying between 0° and 90°. This active hot disk as well as the dome are maintained isothermal at different temperatures. The numerical approach by means of the control volume method allows the examination of the dynamical phenomena that occurs in many configurations obtained by varying the temperature difference between the two active walls and the radius of the hemisphere. Convective heat transfer at the hot wall is represented by the average Nusselt number associated to Rayleigh numbers varying between 104 and 2.55 × 1012. By taking into account all the studied configurations, correlations between these two dimensionless numbers are established for the set of considered inclination angles. Comparisons with results from other studies for the case of horizontal cavity show a good agreement. The relationships presented here cover the laminar, transitional and turbulent heat transfer regimes. They complement previous studies with the condition of heat flux imposed on the disk. The wide range of Rayleigh numbers considered in this survey and its association with the large inclination angle range allow the application of the correlations to various engineering fields such as nuclear technology, solar energy, building, embarked electronics, architecture, safety or domotics.