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

Recent works have examined the thermal and dynamical aspects of natural convection occurring in tilted hemispherical cavities whose disk constitutes the hot active wall. The influence of some important aspects on the natural flows have been considered such as the Rayleigh Number, the disk inclination angle with respect to the horizontal plane and the thermal boundary condition on the disk (Dirichlet, Neumann). Combinations of these parameters have been treated in steady state as well as is transient regime. Correlations of Nusselt–Rayleigh type (steady state) and Nusselt–Rayleigh–Fourier type (transient regime) that allow quantifying the heat transfer are proposed in these surveys. The objective of this paper is to synthesize and summarize these works in order to facilitate their implementation in engineering applications.