Abstract The steady-state performance of the gravity-assisted, two-phase, closed thermosyphon was modeled from first principles. Liquid-film momentum advection and axial normal stress, typically neglected by previous investigators, were included and shown to be important to the thermosyphon performance. The model presented also expanded previous analyses to include both temperature and heat-flux controlled thermosyphons and thermosyphons with mixed or other external boundary conditions. Numerical techniques were incorporated to solve the nonlinear governing equations and respective boundary conditions. A series of thermosyphon experiments were conducted. Predictions from the model agree well with experimental results. The parametric effects of operating temperatures, geometry, working fluid inventory and condenser thermal capacity were studied. The model presented could be used for optimization studies and design of thermosyphons.