Transient free convection within air-filled hemispherical enclosures. Nu-Ra-Fo relationships for isothermal and inclined disk with dome oriented upwards

Nusselt-Rayleigh-Fourier type correlations are proposed to quantify the temporal evolution of convective heat transfer occurring within air-filled hemispherical enclosures whose disk, initially at ambient temperature, is suddenly maintained at a higher temperature. The temperature difference imposed between this hot wall and the isothermal cold dome involves Rayleigh number varying between 104 and 2.55×1012. Depending on the application, the disk can be inclined with respect to the horizontal plane by an angle varying between 0° (horizontal disk) and 90° (vertical disk) in steps of 15°. The paper aims to discuss these issues.

The results are obtained by means of a numerical approach based on the finite volume method. The proposed correlations linked to the steady state Nusselt-Rayleigh internships recently published, concerning the same inclination angle and Rayleigh ranges.

The statistical analysis of a large number of calculations leads to reliable results covering laminar, transitional and turbulent natural convection heat transfer zones.

The proposed relationships can be applied in several engineering fields such as nuclear technology, solar energy, security and safety electronics, building, domotics or aeronautics.

The new relationships proposed in this paper provide important information on the evolution of convective heat transfer during the transient regime.