The inverse heat conduction problem in a two-layer barrier with phase change in a fluid streaming along one of its sides

Flow of freon-11 through a narrow channel is considered. Three sides of the channel are thermally insulated and the fourth one is a barrier consisting of a thin foil, thermochromic liquid crystal layer and a thick glass layer. The foil is also a heater. The problem of temperature field determination in a barrier is an ill-posed one. To solve it the heat polynomials method is used. Then, on the freon-foil surface the position of the saturation point is found and heat transfer coefficient is calculated with the freon-11 phase change taken into consideration.