A numerical study of heat transfer in 90 deg, constant cross section curved duct, steady, laminar, flow is presented. The work is aimed primarily at characterizing the effects on heat transfer of duct geometry and entrance conditions of velocity and temperature by considering, especially, the role of secondary motions during the developing period of the flow. Calculations are based on fully elliptic forms of the transport equations governing the flow. They are of engineering value and are limited in accuracy only by the degree of computational mesh refinement. A comparison with calculations based on parabolic equations shows how the latter can lead to erroneous results for strongly curved flows. Buoyant effects are excluded from the present study so that, strictly, the results apply to heat transfer flows in the absence of gravitational forces such as arise in spacecraft.