The major purpose of this article is to extend the field synergy principle from incompressible fluid flow to compressible fluid flow. Theoretical analysis and numerical simulation are both conducted. Theoretical analysis indicates that for compressible boundary-layer flow, dot production of static pressure gradient and velocity, and viscous dissipation could be involved in energy equation, which are absent in the incompressible boundary-layer energy equation. Therefore, the heat transfer of the compressible flow is determined by the synergy between total enthalpy gradient and velocity, instead by the synergy between static temperature gradient and velocity, thereby extending the FSP from incompressible fluid flow to compressible flow. Detailed numerical analysis is conducted for the compressible boundary-layer flow to numerically verify the above findings. (C) 2015 Elsevier Ltd. All rights reserved.