Effect of heat transfer coefficient error on freezing time estimation methods

The freezing of food is one of the most significant applications of refrigeration. In order for freezing operations to be cost-effective, it is necessary to optimally design the refrigeration equipment. This requires estimation of the freezing times of foods. Numerous semi-analytical/empirical methods for predicting food freezing times have been proposed, all of which require knowledge of the surface heat transfer coefficient. The empirical nature of the surface heat transfer coefficient can introduce significant error in the freezing time calculation. Therefore, a sensitivity analysis was performed on various freezing time estimation methods to determine the impact of errors in the heat transfer coefficient upon the calculated freezing times. A condition number was defined which allows for the quantification of the error in the calculated freezing time due to error in the heat transfer coefficient. Condition numbers were determined for seven common freezing time estimation methods applicable to regularly shaped food items. For these freezing time estimation methods, the sensitivity to errors in the heat transfer coefficient decreases as the Biot number increases. In addition, for Biot numbers greater than one half, these seven freezing time estimation methods were found to attenuate error in the heat transfer coefficient, thus resulting in smaller error in the calculated freezing time.