Conservation equations of sensible entarnsy and latent entransy are established for flue gas convective heat transfer with condensation in a rectangular channel and the entransy dissipation expression is deduced.The field synergy equation is obtained on the basis of the extremum entransy dissipation principle for flue gas convective heat transfer with condensation.The optimal velocity field is numerically obtained by solving the field synergy equation.The results show that the optimal velocity field has multiple longitudinal vortices,which improve the synergy not only between the veloctiy and temperature fields but also between the velocity and vapor concentration fields.Therefore,the convective heat and mass transfers are significantly enhanced.Flow with multiple longitudinal vortices close to the optimal velocity field can be generated by discrete double-inclined ribs set in the rectangular channel.The numerical results show that the total heat transfer rate in the discrete double-inclined rib channel increases by 29.02% and the condensing heat transfer rate increases by 27.46% for Re = 600 compared with the plain channel. Conservation equations of sensible entarnsy and latent entransy are established for flue gas convective heat transfer with condensation in a rectangular channel and the entransy dissipation expression is deduced. The field synergy equation is obtained on the basis of the extremum entransy dissipation principle for flue gas convective heat transfer with condensation. The optimal velocity field is numerically obtained by solving the field synergy equation. The results show that the optimal velocity field has multiple longitudinal vortices, which improve the synergy not only between the veloctiy and temperature fields but also between the velocity and vapor concentration fields. Wherefore, the convective heat and mass transfers are significantly enhanced. Flow with multiple longitudinal vortices close to the optimal velocity field can be generated by discrete double-inclined ribs set in the rectangular channel. Numerical results show that the total heat transfer rate in the discrete double-in clined rib channel increases by 29.02% and the condensing heat transfer rate increase by 27.46% for Re = 600 compared with the plain channel.