A three-dimensional numerical study of the turbulent convective heat transfer of the cryogenic methane flowing inside a square engine cooling channel under supercritical pressures was systematically conducted. Numerical results indicate that increasing the fluid pressure results in enhanced heat transfer of the cryogenic methane under supercritical pressures. At the pseudo-critical temperature under a corresponding supercritical pressure

drastic property variations cause heat transfer deterioration and sharp wall temperature increase at a high wall heat flux of 7MW/m2. A modified Jackson and Hall heat transfer equation

which can be used for supercritical heat transfer calculations of the cryogenic methane

has been successfully established in this paper.