In 1998 Guo et al. integrated the boundary-layer energy equation along the thermal boundary layer thickness, and noted that at outside boundary the temperature gradient is zero and the convection term is actually the inner production of vector velocity and temperature gradient, they found that for a fixed flow rate and temperature difference, the smaller the intersection angle between velocity and temperature gradient the larger the heat transfer rate. This idea is called field synergy principle (FSP). Later it has been shown that FSP can unify all mechanisms for enhancing single phase heat transfer. In 2007 Guo and his co-workers proposed a new concept: entransy to describe the potential of a body to transfer thermal energy and the entransy dissipation extreme principle (EDEP). It is indicated that for any heat transfer process the entransy of the system is always dissipated, which can be regarded as the indication of the irreversibility of the transport process. For a heat transfer process with given boundary temperature condition the best one has the maximum entransy dissipation, while for that with given boundary heat flux condition the best one has minimum entransy dissipation. The combination of the two cases is called the entransy dissipation extremum principle. The purpose of this paper is to reveal the inherent interrelationship between the ideas of field synergy principle and the entransy extremum principle. Numerical simulations are conducted for five examples of convective heat transfer. All the numerical results demonstrate the inherent consistency between FSP and EDEP. (C) 2014 Elsevier Ltd. All rights reserved.