An analytical solution to the problem of frost growth and densification on flat surfaces

This paper advances an algebraic first-principles simulation model to predict the frost growth and densification on flat surfaces. The model was put forward based on macroscopic heat and mass balances in the frost layer, which were written according to a dimensionless formulation and solved analytically to obtain an algebraic expression for the time evolution of the frost thickness as a function of the Nusselt number, the supersaturation degree and the air-to-surface temperature difference. The model predictions for the frost thickness were compared with experimental data obtained elsewhere, when a very good agreement between calculated and measured counterparts was observed. The sensitivity of the frost growth rate to key heat and mass transfer parameters is also assessed and reported.