Nu-Ra correlations for natural convection at high Ra numbers in air-filled tilted hemispherical cavities with dome oriented upwards. Disk submitted to constant heat flux

Abstract

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 (-)

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

“…It is complemented by some specific codes developed in the LTIE laboratory. The calculation procedure of the present work is being detailed in [16][17][18][19] so only the essential elements are repeated here. The mesh is not structured, constituted by triangular elements on the walls and tetrahedral ones in the fluid volume.…”

“…Imposed heat flux on the disk (Neumann condition) applied to electronic technologies (Ania) is examined in [16] at steady state for angle inclinations 0 ≤ α ≤ 90°and Rayleigh numbers 10 4 ≤ Ra φ ≤ 5 × 10 7 . Correlations of Nusselt-Rayleigh type contained in [16] are extended in [17] to 5 × 10 7 ≤ Ra φ ≤ 2.55 × 10 12 . The applications of transient natural convection in hemispherical cavities are mostly related to surveillance and security systems.…”

A synthesis of correlations on quantification of free convective heat transfer in inclined air-filled hemispherical enclosures

“…The correlations obtained in studies [1][2][3][4][5][6][7][8][9][10] are presented in the single Table 1.…”

“…The average convective heat transfer on the disk during the transient regime can be calculated by means of Nu φ α Table 1 Steady state correlations: values of Ra φL , Ra φC , k φ (α) and n φ (α) for Nu φ α ð Þ ¼ kφ α ð ÞRa nφ α ð Þ φ [1,2,4]. Values of Ra TL , Ra TC , k T (α) and n T (α) for Nu T α ð Þ ¼ k T α ð ÞRa nT α ð Þ T [6,8,10].…”

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

“…Neumann condition concerning specific applications in electronic technologies has been treated by Baïri and García de María (2013) at steady state for disk angle inclinations 0 ⩽ α ⩽ 90°and Rayleigh numbers 10 4 ⩽ Ra φ ⩽ 5 × 10 7 . Correlations of Nusselt-Rayleigh type contained in their paper are extended by Baïri et al (2014b) to 5×10 7 ⩽ Ra φ ⩽ 2.55 × 10 12 . Influence of the disk inclination angle on the steady state natural convection within hemispherical cavities has been treated by Cabelli (1977) but the convective heat transfer is not quantified.…”