Similitude criteria for free convective transfers and their corresponding dimensionless parameters are established. A need for distinction between the correctly designed parameters (to assure similitude) and standard non-dimensional ones is emphasized. An illustrative example of transient free convection points out the difficulties which may arise through the use of unsuitable dimensionless parameters; so we show that the dimensionless thermal boundary layer thickness does not vary with the Prandtl number, in the same way as the true dimensioned thickness does. Copyright (C) 2002 John Wiley Sons, Ltd.