Predicting the Nusselt Number of Heterogeneous (Porous) Enclosures Using a Generic Form of the Berkovsky–Polevikov Correlations

A well-known set of Berkovsky–Polevikov (BP) correlations have been extremely useful in predicting the wall-averaged Nusselt number of “wide” enclosures heated from the side and filled with a fluid undergoing natural convection. A generic form of these correlations, dependent on only two coefficients, is now proposed for predicting the Nusselt number of a heterogeneous (fluid–solid), porous enclosure, i.e., an enclosure filled not only with a fluid but also with uniformly distributed, disconnected and conducting, homogeneous solid particles. The final correlations, and their overall accuracies, are determined by curve fitting the numerical simulation results of the natural convection process inside the heterogeneous enclosure. Results for several Ra and Pr, and for 1, 4, 9, 16, and 36 solid particles, with the fluid volume-fraction (porosity) maintained constant, indicate the accuracy of these correlations to be detrimentally affected by the interference phenomenon caused by the solid particles onto the vertical boundary layers that develop along the hot and cold walls of the enclosure; the resulting correlations, in this case, present standard deviation varying between 6.5% and 19.7%. An analytical tool is then developed for predicting the interference phenomenon, using geometric parameters and scale analysis results. When used to identify and isolate the interference phenomenon, this tool is shown to yield correlations with much improved accuracies between 2.8% and 9.2%.