Analytical Modeling of Natural Convection in Concentric Spherical Enclosures

A modeling procedure is developed for natural convection heat transfer from an isothermal heated sphere located at the center of an isothermal, cooled, sphericalshaped enclosure. The model is based on the linear superposition of conduction and convection solutions, where the convective component is determined based on a combination of two limiting cases, laminar boundary layer convection and transition flow convection. The model is validated using experimental and numerical data from the literature, including data from an experimental test program performed by the authors in a previous publication for four different enclosure configurations, 1 5 do di 4 8, over the range of Rayleigh number 10 Ra Ai 1 10 7 . The model accurately predicts the experimental data with an RMS difference of 2-4%a nd is ingood agreement with the other data from the literature.