Abstract For the range 3 × 103 ≤ Grdi ≤ 108 and 1·3 ≤ r 0 r i ≤ 7·5 , it is suggested that Nu δ = 0·181( r 0 r i ) − 0·215 Gr d i 0·25 for the steady-state rate of heat transfer outwards by combined laminar, free convection and conduction through the atmospheric pressure air contained within horizontal concentric annuli. This simple correlation, evolved from an analysis of published, as well as new, experimental information, will enable designers to predict the combined convective/conductive resistance provided by the contained air for the range of concentric pipes likely to be encountered in practice. An optimal eccentricity of 0·24 (the inner cylinder being moved vertically upwards relative to the outer cylinder from the concentric position) corresponds to the maximum combined convective/conductive resistance configuration. For the systems tested in the temperature range 18°C ≤ T ≤ 150°C, this optimal eccentricity is not significantly affected by changes in the surface emissivities.