Prediction of 3D natural convection heat transfer characteristics in a shallow enclosure with experimental data

This study presents an inverse computational fluid dynamics (CFD) simulation combined with the least-squares method and overdetermined experimental temperature data to predict the unknown heat transfer rate Q_h and three-dimensional (3D) natural convection heat transfer characteristics in a closed shallow enclosure. This novel study belongs to the inverse convection-conduction conjugate heat transfer problem. The results show that the zero-equation turbulence model is more suitable for this study compared to other flow models. Thus, the zero-equation model is chosen as the suitable flow model because its estimates are the closest to the experimental data and existing correlation. An important finding is that, for H/L = 1/15 and Ra = 1820, Bénard convection cells and eight vortices appear in 3D and two-dimensional (2D) temperature contours, respectively. This Ra value is close to the existing critical Rayleigh number of 1708. The arrangement of these cells and vortices can be merged with each other and reorganized as H/L increases. The obtained 2D velocity patterns and air temperature contours agree with existing patterns and isotherms. The obtained h‾_hi values also agree well with the existing correlation. Thus, the present results have good accuracy. A review of the literature indicates that a few studies have been conducted on using the inverse method along with overdetermined experimental temperature data to study the present problem.