The local mixing-length theory with convective helium flux

The local mixing-length theory is extended to calculate distributions of chemical elements in the convective region. There are two different convective solutions in the convective core of the massive Main-Sequence star where convective flux of helium is positive. The condition for the convection to exist with -gradient differs from the Ledoux-Sakashita-Hayashi condition when the radiative heat loss from the convective element is taken into account.