The effects of conjugate heat transfer, vapor compressibility, and viscous dissipation in heat pipes are discussed. The accuracy of the partially parabolic versus the elliptic presentation of the governing equations is also examined. The results show that the axial wall conduction has a tendency to make the temperature distribution more uniform for heat pipes with large ratios of pipe wall to effective liquid-wick thermal conductivity. The compressible and incompressible models show very close agreement for the total pressure drop, white the local pressure variations along the heat pipe are quite different for these two models when the radial Reynolds number at the interface is high.