Abstract: The field synergy principle for incompressible convective heat transfer is extended to high speed compressible laminar and turbulent flows based on theoretical analysis. The result shows the convective heat transfer of compressible laminar and turbulent flows is determined by the synergy between the local momentum per unit volume and the gradient of total enthalpy, different from the field synergy principle for incompressible convective heat transfer. The principle based on the synergy between the local momentum per unit volume and the gradient of total enthalpy can be applied to the problem of heat transfer of the wall. For laminar flows, not only the effect of the change of density for high speed flows is taken into account, but the effect of the gradient of static enthalpy, the pressure gradient and the molecular viscosity near the wall on the heat flux is also considered. For high speed turbulent flows, besides the effect of the change of density, the gradient of static enthalpy, the pressure gradient and the molecular viscosity near the wall on the heat flux, the Reynolds shear stress is also contained. In addition, for the incompressible convective heat transfer flows that the viscous effect cannot be neglected, the result of the present study also indicates that it is more accurate to express the synergy with velocity vector and gradient of total temperature or total enthalpy.

Key words: field synergy principle, heat flux density, compressible flow, total enthalpy, total temperature, laminar flow, turbulent flow