Two models have been developed for predicting free convection low Reynolds number turbulent flows. The models also apply to mixed convection flows. The first, a k-ε model, is based on the notion of eddy diffusivities for momentum and heat. The second, an algebraic stress model, is based on approximations derived for the anisotropic turbulent fluxes by a suitable truncation of their conservation equations. Both formulations apply to variable property flows with high overheat ratios, ΔT T ∞ , and have not required the definition of new model constants. No attempt has been made to modify previously established values of the constants in order to improve agreement between measurements and predictions of the flow investigated. Such an optimization must await the availability of more detailed and reliable experimental measurements of turbulence-related quantities. Fully elliptic forms of the differential transport equations, subject to appropriately specified boundary conditions, have been solved numerically for two flow configurations. Both are two-dimensional. The first corresponds to free convection along a heated vertical flat plate and is the subject of Part I of this study. The second corresponds to free and mixed convection from a heated cavity of arbitrary rectangular cross-section and variable orientation, and is the subject of Part II. For the case of the vertical plate, a comparison between measurements and predictions shows that both models yield fairly accurate results for the mean flow and heat transfer. Near-wall velocity and temperature distributions predicted by both models reveal the 1 3 power-law dependence derived by George and Capp [ Int. J. Heat Mass Transfer 22, 813–826 (1979)] and confirmed for temperature by Siebers et al [ J. Heat Transfer 107, 124–132 (1985)]. Values of the constants in the power-law relations for velocity and temperature have been obtained here numerically for high and low ΔT T ∞ . Predictions of the anisotropic Reynolds stress and turbulent heat flux distributions are in good qualitative agreement with the measurements of Miyamoto et al. [ Proc. 7th Int. Heat Transfer Conference, Vol. 2, pp. 323–328 (1982)]. In particular, regions of negative buoyant and shear production of turbulent kinetic energy observed experimentally are clearly revealed by the calculations.