Turbulent boundary-layer buoyant flow modeling over a wide Prandtl number range

This work is devoted to the free turbulent convection theory applied to a vertical plate under uniform heat flux density conditions by using the integral formalism approach. A fully developed model is derived for a large Prandtl number range over the real distinct boundary layer thicknesses. Comparisons are established with the few data in literature. Of practical interest are the deduced dynamical similarity law and Nusselt number correlations. The transition events are found to be Prandtl number dependent, and the results suggest the thermal transition to be reached in space before the dynamical one up to Pr = 100.