The influence of the transverse curvature on free convection heat or mass transfer at vertical cylinders is investigated. Mass transfer coefficient have been determined from limiting current density measurements, using the electroreduction of ferricyanide ions as the model reaction. The evaluation of the dimensionless free convection mass transfer variables for this system leads to reliable results. The data in the laminar region show good agreement with theoretical predictions, based on a Pohlhausen approximation for infinite Schmidt or Prandtl number, and with heat transfer measurements in water. Theory and experiments are increasingly accurate with stronger curvature. The limiting behaviour for very thick and infinitely thin cylinders is discussed. For turbulent flow at thin cylinders, the electrochemical measurements are in close agreement with heat transfer data in air. The combined data lead to the correlation ShR=0.6Ra[...]R. whereas thick cylinders with RaR > 800 behave like a flat plate. Emperical and theoretical evidence points to a critical value of Grx/Sc, corresponding to Rex≈103, as a criterion for the transition from laminar to turbulent flow, with a slightly destabilizing influence of the curvature.