In this paper, an experimental study is reported of variable property mixed convection heat transfer to air flowing through a vertical passage of annular cross-section of diameter ratio 2.1, having a uniformly heated core and a thermally insulated outer casing. This is the first of three related papers each of which is concerned with buoyancy-influenced flow and heat transfer in vertical passages with one surface heated and the opposite one unheated. The second paper also reports mixed convection heat transfer experiments with a vertical passage of annular cross-section. The diameter ratio of 1.9 is similar. However, in that case the working fluid was water rather than air and effects of fluid property variations were negligibly small. The third paper reports mixed convection heat transfer experiments with a vertical plane passage of relatively short length. The working fluid was air. In all three cases the need for the experiments arose in connection with nuclear power plant design and operation. However, the studies are all of a fundamental nature and address an interesting and important aspect of buoyancy-influenced convective heat transfer in vertical passages. The results presented in this first paper show, that with a passage of annular cross-section having a heated inner surface and an adiabatic outer one, the heat transfer behaviour is generally similar to that found with uniformly heated circular tubes but that there are certain important differences. Thermal development is slower and the effects of buoyancy and variable properties are both weaker. As with circular tubes, the mixed convection data for downward flow show systematic enhancement of heat transfer with an increase of buoyancy influence and a fully developed heat transfer situation is readily achieved. The results for such conditions correlate satisfactorily in terms of Nusselt number ratio (mixed to forced) and a buoyancy parameter which combines Grashof number, Reynolds number and Prandtl number in a particular manner designed to characterize the strength of buoyancy influences. The results are fitted satisfactorily by a simple correlation equation based on a semi-empirical model. In the case of mixed convection with upward flow, heat transfer is always less effective than with downward flow. Impairment of heat transfer occurs with the onset of buoyancy influences, but more gradually and at a somewhat higher values of buoyancy parameter than in circular tubes. Non-monotonic axial distributions of Nusselt number are found and the data do not correlate in terms of purely local parameters. A fully developed situation is not readily achieved. With further increase of buoyancy influence, heat transfer recovers and eventually becomes enhanced.