In fluid descriptions of the solar wind the heat conductive flux is us
ually determined by the use of the classical Spitzer-Harm expression.
This expression for the heat flux is derived assuming the gas to be st
atic and collision-dominated and is therefore strictly not valid in th
e solar wind. In an effort to improve the treatment of the heat conduc
tive flux and thereby fluid models of the solar wind, we study an eigh
t-moment approximation two-fluid model of the corona-solar wind system
. We assume that an energy flux from the Sun heats the coronal plasma,
and we solve the conservation equations for mass and momentum, the eq
uations for electron and proton temperature, as well as the equations
for heat flux density in the electron and proton fluid. The results ar
e compared with the results of a ''classical'' model featuring the Spi
tzer-Harm expression for the heat conductive flux in the electron and
proton gas. In the present study we discuss models with heating of the
coronal protons; the electrons are only heated by collisional couplin
g to the protons. The electron temperature and heat flux are small in
these cases. The proton temperature is large. In the classical model t
he transfer of thermal energy into flow energy is gradual, and the pro
ton heat flux in the solar wind acceleration region is often too large
to be carried by a reasonable proton velocity distribution function.
In the eight-moment model we find a higher proton temperature and a mo
re rapid transfer of thermal energy flux into flow energy. The heat fl
uxes from the corona are small, and the velocity distribution function
s, for both the electrons and protons, remain close to shifted Maxwell
ians in the acceleration region of the solar wind.