2023 Ha Two-phase Stefan problem for the modeling of urea prilling tower

The prilling technique is frequently used to make granular urea and ammonium nitrate.
The generated droplets fall and become solid due to the heat removal by the cooling air, which flows in a counter-current direction. Generally, three sequential thermal intervals for the solidification of urea droplets are considered: cooling of liquid drops, solidification at freezing temperature of the liquid phase, and cooling of complete solid particles. In this study, the solidification of the urea droplets has been considered as a two-phase Stefan problem with convective flux boundary condition rather than dividing the whole process into three sequential steps. The heat transfer problem was solved numerically using the enthalpy method. The particles were assumed to attain the terminal velocity immediately. The convective heat transfer was determined from the terminal velocity.
The temperature distribution of the droplets, and the minimum height for complete solidification
at different particle diameters were investigated.

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