The aim of this paper was to present the concept of mathematical models of heat transfer in flow boiling in an annular mini gap between the metal pipe with enhanced exterior surface and the external glass pipe. The one- and two-dimensional mathematical models were proposed to describe stationary heat transfer in the gap. A set of experimental data governed both the form of energy equations in cylindrical coordinates and the boundary conditions. The models were formulated to minimize the number of experimentally determined constants. Known temperature distributions in the enhanced surface and in the fluid helped to determine, from the Robin condition, the local heat transfer coefficients at the enhanced surface – fluid contact. The Trefftz method was used to find two-dimensional temperature distributions for the thermal conductive filler layer, enhanced surface and flowing fluid. The method of temperature calculation depended on whether the area of single-phase convection ended with boiling incipience in the gap or the two-phase flow region prevailed, with either fully developed bubbly flow or bubbly-slug flow. In the two–phase flow, the fluid temperature was calculated by Trefftz method. Trefftz functions for the Laplace equation and for the energy equation were used in the calculations.