<p>This research advances the understanding of flow and heat transfer in non-circular ducts, a topic that has received significantly less attention compared to circular ducts. Such understanding is essential for optimizing the design of various industrial applications, including compact heat exchangers and gas-cooled nuclear reactors. This study presents an analytical investigation of fully developed laminar flow in annular corrugated pipes, employing epitrochoid mapping to model transversally corrugated geometries. The research focuses on friction factor, incremental pressure drop, hydrodynamic entry length, and Nusselt number, with corrugation amplitude, radius ratio, and waviness as governing parameters. The study indicates that increasing the corrugation amplitude reduces the friction factor, especially for larger values, while increasing waviness further diminishes it. In contrast, the incremental pressure drop increases with amplitude, particularly at higher radius ratio and waviness. Both amplitude and waviness significantly extend the hydrodynamic entry length, especially for larger radius ratio. In terms of heat transfer, the Nusselt number generally decreases with increasing amplitude and waviness, especially at higher values, highlighting a trade-off between reduced friction and heat transfer performance. Simplified equations are presented to quantify the dependence of these parameters on the amplitude, waviness, and radius ratio of the corrugation. The solution recovers the established results for smooth annular pipes, validating its accuracy.</p>