Heat Transfer in Pipe and Conduit Flows: From Classical Formulations to Modern Computational Paradigms and Next-Generation Frontiers

Convection in internal pipe flow is an important part of modern thermal engineering that links classical fluid mechanics with high-flux cooling, renewable energy and microfluidic technologies. This review offers an in-depth synthesis of heat transfer in internal pipe flow across fluid dynamics, structural configurations and computational modeling paradigms. Beginning with foundational physics, the coupled Navier–Stokes and energy equations are revisited, along with temperature-dependent variations of fluid properties and the dynamics of thermal development in hydrodynamic and thermal entrance regions. Canonical Nusselt number (Nu) and friction factor (f) correlations are used to perform a systematic assessment of flow regimes from laminar to transitional to fully turbulent conditions. Emphasis is placed on conjugate heat transfer mechanisms across complex, non-circular and curved geometries where Dean vortices and secondary swirl flows significantly enhance convective transport. We also review modern heat transfer enhancement paradigms such as surface micro-texturing, nanofluids, supercritical fluids and passive swirl inserts. Finally, we compare state-of-the-art computational methods and high-resolution non-intrusive diagnostic techniques highlighting key challenges in multiphase and multiscale thermal transport. This review identifies key knowledge gaps and suggests future directions for artificial intelligence and data-driven thermal management strategies, bridging fundamental principles and the latest technological frontiers.