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Purpose -The purpose of this paper is to propose correlations between Nusselt and Rayleigh numbers for the case of inclined and closed air-filled hemispherical cavities. The disk of such cavities is subjected to a constant heat flux. The study covers a wide range of Rayleigh numbers from 5 × 10 7 to 2.55 × 10 12 . Design/methodology/approach -Correlations are obtained from numerical approach validated by experimental measurements on some configurations, valid for several angles of inclination of the cavity between 0°(horizontal disk) and 90°(vertical disk) in steps of 15°. 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 correlations provide solutions for applications in several fields of engineering such as solar energy, aerospace, building, safety and security. Originality/value -The new relations proposed are the first published for high Rayleigh numbers for this type of geometry. They supplement the knowledge of natural convection in hemispherical inclined cavities and constitute a useful tool for application in various engineering areas as solar energy (thermal collector, still, pyranometer, albedometer, pyrgeometer), aerospace (embarked electronics), building, safety and security (controlling and recording sensors). Nomenclature a thermal diffusivity of the air (m 2 s −1 ) C p specific heat at constant pressure ( J kg −1 K −1 ) g acceleration due to the gravity (m s −2 ) k(α) coefficient of the correlations Nu a ¼ kðaÞRa nðaÞ (-) n(α) exponent of Ra φ in the correlations Nu a ¼ kðaÞRa nðaÞ (-)

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Purpose The main purpose of this work is to quantify the convective heat transfer occurring between two inclined and concentric hemispheres. Design/methodology/approach The inner one is an electronic assembly generating a constant heat flux during operation. The outer hemisphere is maintained isothermal at cold temperature. The interstitial space is air-filled. The base of the equipment can be inclined with respect to the horizontal plane by an angle ranging from 0° (horizontal position with dome faced upwards) to 180° (horizontal position with dome faced downwards). Findings Nusselt–Rayleigh correlations are proposed for several configurations obtained by varying the generated power and the base inclination. The large resulting Rayleigh number ranging between 2.4 × 105 and 1.7 × 107 allows using these new and original correlations in various engineering fields, such as electronics in the present work. The calculations are realized by means of a 3D numerical approach based on the finite volume method. Originality/value The geometry and the thermal boundary conditions considered in the present survey are suitable for applications in many engineering areas.