Freezing of liquids in turbulent flow inside tubes

The problem of steady-state freezing of liquids in turbulent flow inside a tube with its walls kept at a uniform temperature lower than the freezing temperature of the liquid is solved for a wide range of Reynolds and Prandtl numbers, 10⁴ ≤ Re ≤ 10⁴ and 0 ≤ Pr ≤ 10³. The effects of Prandtl and Reynolds number on the location of the solid-liquid interface and on the heat transfer rate as a function of position along the tube are established.