The theorem of a constant heat flux ratio at the phase boundary of a geometric one-dimensional freezing or melting problem

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Freezing or melting processes taking place in different bodies with variable cross-sectional areas are considered. The processes have a constant temperature at the surface through which heat is removed or supplied. By using the transformations of the position and time coordinates and the dimensional analysis, the result of a constant ratio of the heat flux from the liquid phase to the phase boundary, to the heat flux from the phase boundary to the solid phase, is established.