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In the dry friction between two solids in imperfect contact, the determination of temperature distribution within solids needs the knowledge of: (1) heat flux generated by friction, (2) thermal contact conductance, and (3) intrinsic heat partition coefficient. In this article, numerical study is conducted in order to estimate the values of these parameters from simulated temperatures. Numerical investigations and a sensitivity analysis are performed in order to show the feasibility and the needed conditions for an accurate estimation. In order to take into account the measurements noise, statistical investigations using a stochastic approach and Monte Carlo method are also performed.

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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