Velocity distribution for a gas with steady heat flow

An exact solution to the nonlinear Bhatnagar-Gross-Krook kinetic equation representing heat transport in one direction is obtained. The velocity distribution function is given explicitly and illustrated for both small and large temperature gradients. The Chapman-Enskog expansion for this function is proved to be divergent but asymptotic. Also, the relationship of this solution to infinite hierarchies of moment equations is discussed. In the following paper this special solution is analyzed in the context of more physical boundary-value problems.