A circulating two-phase Taylor flow in a microchannel was considered to be more efficient for overall heat transfer in a heat pipe compared to the pulsating (oscillating) heat pipe. A mathematical model describing the main parameters of a two-phase flow is constructed. The experimental study of hydrodynamics and heat transfer of a circulating two-phase (liquid-vapor) Taylor flow in a glass microchannel was performed. The experimental studies confirmed a microchannel heat pipe operability with a two-phase flow in a circulating mode. Various combinations of heater and cooler disposition have been examined. Minimal heating power to establish Taylor flow was found experimentally for each combination. An optimal configuration of heaters and coolers disposition was defined. The advantages of circulating two-phase Taylor flow related to the pulsating heat pipes are discussed on the proposed mathematical model basis. It is planned to compare the proposed mathematical model results with experimental data in the next paper.