Freezing time formulas for foods with low moisture content, low freezing point and for cryogenic freezing

• Approximate methods for freezing time are compared with results of numerical methods.
• The comparison included low moisture content, low freezing point foods and cryogenic temperatures.
• Pham’s (1984) method was most accurate, followed by Pham’s (1986) method.
• Correction factors are found to allow Pham’s methods to be used in all cases.
• Mascheroni and Calvelo’s three-stage approach is vindicated.

Existing food freezing time formulas have not been tested on low moisture, low freezing point foods or cryogenic temperatures. A systematic numerical experiment was therefore performed to generate freezing times over a wide range of parameters, never before covered in the literature, yet still within industrial practice. The results were used to evaluate four well-known freezing time formulas. Pham’s first (three-stage) method has the best theoretical basis and fewest empirical parameters, and agrees best with numerical predictions. By applying simple correction factors, this method agrees with numerical predictions to within ±10% while Pham’s second (two-stage) method is almost as accurate. For the freezing time of fresh foods (Tf ⩾ −1.5 °C), Pham’s first method can be used without modification. The corrected formulas remain accurate under cryogenic freezing conditions.