Frost behavior on a fin considering the heat conduction of heat exchanger fins

A mathematical model is proposed for predicting frost behavior on a heat exchanger fin under frosting conditions, taking into account fin heat conduction. The change in the three-dimensional airside airflow caused by frost growth is reflected in this model. The numerical estimates of frost thickness are consistent with experimental data, with an error of less than 10%. Due to fin heat conduction, frost thickness decreases exponentially toward the fin tip, while considerable frost growth occurs near the fin base. When a constant fin surface temperature is assumed, the predicted frost thickness was larger by more than 200% at maximum, and the heat flux by more than 10% on average, compared to results obtained with fin heat conduction taken into account. Therefore, fin heat conduction could be an essential factor in accurately predicting frost behavior. To improve prediction accuracy under the assumption of constant fin surface temperature, the equivalent temperature (for predicting frost behavior) is defined to be the temperature at which the heat transfer rate neglecting fin heat conduction is the same as the heat transfer rate with fin heat conduction taken into consideration. Finally, a correlation for predicting the equivalent temperature is suggested.