This paper is aiming at numerically demonstrating the interrelationship and consistency between field synergy principle (FSP) via the field synergy number (Fc) and the entransy dissipation extremum principle (EDEP). Numerical simulation is conducted by using the FLUENT software and the user defined function programs (UDF) for fin-and-tube surfaces (plain plate and slotted fins) and composite porous materials. The thermal boundary conditions include given heat flux and given surface temperature. The flow includes laminar and turbulent. The air properties may be constant or vary with temperature. Based on the numerical data the analyzed results from the FSP via Fc are totally consistent with the results analyzed by the EDEP for all the cases studied. Such consistency between the FSP and the entransy theory can be regarded as a kind of demonstration of the reliability and correctness of both the FSP and the entransy theory. (C) 2017 Elsevier Ltd. All rights reserved.