Nu–Ra–Fo correlations for thermal control of embarked radars contained in tilted hemispherical cavities and subjected to constant heat flux

This work is intended to improve the operation of on-board radar systems contained in the disk of an inclined air-filled hemispherical cavity. When the device is switched on, its thermal behaviour is driven by the transient convection heat transfer that precedes the steady state. The heat flux density imposed on the device, the radius of the disk and its inclination with respect to the horizontal are the most influential parameters on this phenomenon. Nusselt–Rayleigh-Fourier correlations are proposed to calculate the transient convective heat exchanges. These relationships cover a wide range of Rayleigh numbers varying between 104 and 3.2 × 1011 and inclination angles comprised between 0° (horizontal cavity) and 90° (vertical cavity) in steps of 15°. These results are obtained by numerical approach based on the finite volume method and supplement steady state correlations presented in previous works validated experimentally. The large Rayleigh number and inclinations ranges considered in this work allow application of the proposed correlations in several other engineering fields such as solar energy, security of persons, domotics or installation safety.