Introduction & Context

The latent heat of freezing is a critical thermodynamic property in food process engineering, representing the energy that must be removed from a food product to undergo a phase change from liquid water to ice at a constant freezing temperature. Accurate determination of this value is essential for the design and sizing of refrigeration systems, blast freezers, and cold storage facilities. By quantifying the energy load associated with the phase transition, engineers can optimize compressor capacity, cooling rates, and energy consumption, ensuring product quality and safety during the freezing process.

Methodology & Formulas

The calculation of the latent heat of freezing for food products is based on the principle that only the freezable portion of the water content undergoes a phase change. The total water content is adjusted by subtracting the bound water fraction, which remains unfrozen at typical commercial freezing temperatures.

First, the freezable water mass fraction is determined by subtracting the bound water fraction from the total water content:

\[ w_{\text{freezable}} = \max(w_{\text{total}} - w_{\text{bound}}, 0) \]

The latent heat of the food is then calculated by multiplying the freezable water mass fraction by the latent heat of pure water:

\[ \lambda_{\text{food}} = w_{\text{freezable}} \cdot \lambda_{\text{water}} \]

To facilitate integration into industrial energy balance models, the result is often converted from kilojoules per kilogram to megajoules per kilogram:

\[ \lambda_{\text{food, MJ}} = \frac{\lambda_{\text{food}}}{1000} \]

Parameter	Description	Typical Range / Value
w_total	Total water mass fraction	0.50 to 0.95
w_bound	Bound water mass fraction	0.05 to 0.15 (for meats/fish)
λ_water	Latent heat of pure water	334 kJ/kg
λ_food	Calculated latent heat of food	160 to 317 kJ/kg

The latent heat of freezing represents the significant energy removal required to transition water into ice without changing the product temperature. Process engineers must account for this phase change to:

Calculate the total refrigeration load required to cross the phase transition zone.
Determine the residence time necessary for the product core to reach the target storage temperature.
Size compressors and evaporators to handle the peak thermal demand during the freezing plateau.

The latent heat of freezing is primarily a function of the water content within the food matrix. Because the latent heat of fusion for pure water is 334 kJ/kg, the total latent heat for a food product is calculated based on its moisture fraction. Factors influencing this include:

Total water content percentage.
Presence of dissolved solids like sugars and salts, which depress the freezing point and alter the effective latent heat.
The structural composition of the food, which affects how much water is bound versus free.

For complex mixtures, you should first determine the total water mass fraction through laboratory moisture analysis. The latent heat of freezing is not simply the total water fraction multiplied by 334 kJ/kg, because a portion of water is bound to the food matrix and does not freeze at typical commercial freezing temperatures. The recommended approach involves:

Determining the mass fraction of total water and evaluating the bound water fraction (typically 0.05–0.15 for meats/fish, but may vary).
Calculating the freezable water fraction: \(w_{\text{freezable}} = w_{\text{total}} - w_{\text{bound}}\).
Applying the latent heat formula: \(\lambda_{\text{food}} = w_{\text{freezable}} \times 334 \, \text{kJ/kg}\).
If the product has a high concentration of soluble solids (e.g., sugars, salts), consider the effect of freezing point depression on the phase‑change behavior; more advanced models such as the Plank equation can then be used for precise freezing-time predictions.

Worked Example: Latent Heat of Freezing for Lean Fish Fillet

A frozen food engineer needs to estimate the latent heat of freezing for a lean fish fillet (cod). The food is treated as a water–solid mixture where only the water component undergoes phase change. The bound water fraction is accounted for to avoid overestimation.

Knowns

Total water mass fraction, \(w_{\text{total}} = 0.7\)
Bound water mass fraction, \(w_{\text{bound}} = 0.1\)
Latent heat of pure water, \(\lambda_{\text{water}} = 334.0 \, \text{kJ/kg}\)

Step-by-Step Calculation

Determine the freezable water mass fraction:
\(w_{\text{freezable}} = \max(w_{\text{total}} - w_{\text{bound}}, 0) = 0.6\)
Calculate the latent heat of the food (in kJ/kg):
\(\lambda_{\text{food}} = w_{\text{freezable}} \cdot \lambda_{\text{water}} = 200.4 \, \text{kJ/kg}\)
Convert the result to MJ/kg:
\(\lambda_{\text{food}} = 0.2004 \, \text{MJ/kg}\)

Final Answer

The latent heat of freezing for the lean fish fillet is 200.4 kJ/kg (or 0.2004 MJ/kg). This value indicates the energy that must be removed per kilogram of fish at its freezing point.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle