In this study, a constitutive relation between fluid power flux and pressure gradient was discussed, and a conservative equation of fluid mechanical energy was introduced to describe convectional phenomena that is essential to convective heat and mass transfer. The multi-field synergy relations among velocity, pressure, temperature and component concentration were revealed according to the synergy equations based on the conservations of thermal energy, mechanical energy, component mass and fluid momentum to analyze physical characteristic of enhancing convective heat and mass transfer. A new experimental correlation of Eu number versus Re and Li numbers was obtained for the first time through theoretical derivation and experiment to test hydrodynamic performance of heat transfer tube. A circular tube inserted by longitudinal swirl flow generator with center-connected rectangle rods was investigated through numerical simulation and PIV experiment to validate the synergy relation in convective heat transfer enhancement. (C) 2019 Elsevier Ltd. All rights reserved.