This article examines the unique fluid flow characteristics and associated forced convection in curved ducts where the flow behavior is typified by counterrotating secondary flow vortices arising from the centrifugal forces due to flow curvature. For laminar developing fluid flow through curved heated ducts, the study formulates a novel three-dimensional computational fluid dynamics model based on vortex structures (or helicity). The fluid and thermal characteristics are examined using the helicity contours in duct cross sections for a range of flow rates, wall heat fluxes, and duct aspect ratios at selected duct curvatures. Curved ducts of rectangular and elliptical cross section are analyzed to identify and compare the fundamental differences in flow characteristics for each duct type. The study also presents a new technique using dimensionless helicity for detecting the onset of hydrodynamic instability in curved ducts. Numerical predictions are validated with the available experimental data. It is observed that with increased duct flow rate, the secondary flow intensifies and beyond a certain critical flow condition leads to hydrodynamic instability in both types of ducts. However, the overall fluid flow structure, hydrodynamic instability, and forced convection are significantly dependent on the type of duct, while these aspects are also significantly influenced by the duct aspect ratio and wall heating.