Parallel transport of long mean-free-path plasma along an open magnetic field line is characterized by strong temperature anisotropy, which is driven by two effects. The first is magnetic moment conservation in a non-uniform magnetic field, which can transfer energy between parallel and perpendicular degrees of freedom. The second is decompressional cooling of the parallel temperature due to parallel flow acceleration by conventional presheath electric field which is associated with the sheath condition near the wall surface where the open magnetic field line intercepts the discharge chamber. To the leading order in gyroradius to system gradient length scale expansion, the parallel transport can be understood via the Chew-Goldbeger-Low (CGL) model which retains two components of the parallel heat flux, i.e., qn associated with the parallel thermal energy and qs related to perpendicular thermal energy. It is shown that in addition to the effect of magnetic field strength (B) modulation, the two components (qn and qs) of the parallel heat flux play decisive roles in the parallel variation of the plasma profile, which includes the plasma density (n), parallel flow (u), parallel and perpendicular temperatures (T∥ and T⊥), and the ambipolar potential (ϕ). Both their profile (qn/B and qs/B2) and the upstream values of the ratio of the conductive and convective thermal flux (qn/nuT∥ and qs/nuT⊥) provide the controlling physics, in addition to B modulation. The physics described by the CGL model are contrasted with those of the double-adiabatic laws and further elucidated by comparison with the first-principles kinetic simulation for a specific but representative flux expander case.