A refutation of King’s rule for multi-dimensional external natural convection

Abstract Experiments have been carried out to test the validity of King’s widely quoted rule for evaluating a characteristic length for problems of multi-dimensional external natural convection. A more recent rule set forth by Lienhard was also tested. Both rules are intended to enable standard textbook-type correlations to be employed to predict natural convection heat transfer from complex bodies. The experiments were performed using a heated vertical cylinder of equal height and diameter, with heat being transferred to the ambient air from all three faces of the body (top, side, and bottom). The use of King’s rule led to 40–50% overpredictions of the experimental data, so that its continued citation in textbooks appears inappropriate. Although Lienhard’s rule yielded predictions that were somewhat closer to the data than those of King, the level of agreement does not appear to warrant its adoption as the link between multi-dimensional natural convection and the established literature correlations.