A numerical study, using the finite-difference method (FDM) has been carried out to obtain fluid flow and heat transfer characteristics in respect of rectangular and elliptical ducts, rotating about a parallel axis situated parallel to and away from their axes. The study encompasses many geometries for the rotating as well as stationary duct sections under laminar developed flow conditions for various Prandtl numbers and aspect ratios. The investigation is made for the parameters Nu/Nu0, Ra Re, (f Re)/(f Re)0 and Pr. Correlations for heat transfer in the cases of rotating rectangular and elliptical ducts have been presented. From the study, it has been concluded that elliptical geometry is superior to others that are frequently used as coolant channels in rotating machinery.