Empirical Nu–Ra–Fo relationships for natural convection in air-filled hemispherical enclosures. Isothermal and inclined disk with dome oriented downwards

Correlations of Nusselt–Rayleigh–Fourier type proposed in this work allow quantifying of the transient convective heat transfer occurring in air-filled hemispherical cavities. The disk, initially at ambient temperature, is suddenly heated and kept isothermal. Throughout the heating process, the dome is maintained at ambient temperature. The radius of the cavity, associated with the temperature difference imposed between the disk and the dome, involves a large Rayleigh number range, varying between 104 and 5 × 108. The disk can be inclined with respect to the horizontal plane at an angle varying between 90° (vertical disk) and 180° (horizontal disk with dome downwards) by steps of 10°. The numerical approach is based on the finite volume method. The proposed empirical relationships in transient regime are linked to the steady state Nusselt–Rayleigh ones. They are obtained via the analysis of results corresponding to many combinations of the Rayleigh number and the disk inclination angle. The relationships are new since the considered geometry associated with the inclinations of the isothermal disk has not been treated previously. They constitute an important tool for the thermal design of engineering systems involved as they allow determining the convective heat transfer during the transient regime. They can be applied in several fields such as nuclear technology, solar energy, security and safety electronics, building, domotics or aeronautics.