Flames propagating above the surface of n-butanol in mini and microchannels have been investigated experimentally. It was determined that when oxygen is used as an oxidant, the critical channel size is about 0.3 mm, and according to the estimates this corresponds to the critical size for a premixed homogeneous gas mixture. In order to understand the mechanism of flame propagation above the surface of liquid, in this study, we attempted to simulate the processes, occurring in liquid. The problem of "thermal wave" propagation in a horizontal rectangular channel, when the liquid film moves under the action of gas flow, was studied theoretically. The analysis was carried out taking into account evaporation, specific heat release, and radiation and absorption processes in the gas and on the free surface, as well as the formed zone of strong heating above the liquid film surface for low oxidant velocities in the channel. Based on data obtained, it can be concluded that at high concentration of oxygen and low oxidant velocities, the experimental value of velocity coincides with the calculated value with satisfactory accuracy.