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

Abstract

Purpose – 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. Design/methodology/approach – 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. Findings – The statistical analysis of a large number of calculations leads to reliable results covering laminar, transitional and turbulent natural convection heat transfer zones. Practical implications – The proposed relationships can be applied in several engineering fields such as nuclear technology, solar energy, security and safety electronics, building, domotics or aeronautics. Originality/value – The new relationships proposed in this paper provide important information on the evolution of convective heat transfer during the transient regime.