A numerical analysis of transient heat pipe performance including nonconventional heat pipes with nonuniform heat distributions is presented. A body-fitted grid system was applied to a three-dimensional wall and wick model which was coupled with a transient compressible quasi - one-dimensional vapor flow model. The numerical results were first compared with experimental data from cylindrical heat pipes with good agreement. Numerical calculations were then made for a leading edge heat pipe with localized high heat fluxes. Performance characteristics different from conventional heat pipes are illustrated.