A similarity solution for heat transfer analysis during progressive freeze-concentration based desalination

A mathematical model was developed to obtain a similarity solution for heat transfer analysis during progressive freeze-concentration-based desalination. The model considered the process as a one-phase Stefan problem. The model is based on the assumption that a local thermodynamic equilibrium exists at the ice-liquid interface. The heat transfer is by diffusion in the ice and by forced convection in the liquid phase. The similarity solution predicted the temperature distributions in the ice, the thickness of the ice, and heat flux. Scheil equation was used to predict the solute redistribution since the freeze-concentration process involves simultaneous heat and mass transfer. The predicted data of thickness of the ice and salinity of thawed ice is compared with the data reported in the previously published experimental study. A reasonable agreement is found between the predicted and experimental data reported in the previously published study. Based on the similarity solution, a parametric study was carried out to investigate the effect of ice-liquid interface speed, the stirrer's circumferential velocity, of the stirrer, and initial salinity of the liquid on heat transfer. For a fixed value of the solid fraction, the temperature distribution in ice was substantially influenced by ice-liquid interface speed and the initial salinity of the liquid. However, the effect of the stirrer's circumferential velocity on the temperature distribution in ice was observed to be insubstantial. For a fixed value of the solid fraction, the heat flux was significantly increased with ice-liquid interface speed. Nevertheless, the effect of the circumferential velocity of the stirrer on heat flux was nonsignificant.