Reference ID: MET-FF11 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
The thawing of frozen food products is a critical unit operation in food process engineering, requiring a balance between processing speed and product quality. This calculation utilizes Plank's equation to model the phase‑change process, treating the product as a moving‑boundary problem. It is primarily used to estimate the thawing time required for a frozen slab to reach its melting point under various convective boundary conditions, such as air, water, or refrigerated environments. By quantifying the convective and conductive resistances, engineers can optimize thawing protocols to minimize microbial growth and prevent surface degradation.
Methodology & Formulas
The thawing time is determined by calculating the total thermal resistance of the system, which consists of a convective component (external) and a conductive component (internal). In the Plank formulation for thawing, heat must conduct through the already‑thawed (unfrozen) outer layer to reach the melting front; the conductive term therefore uses the thermal conductivity of the unfrozen phase. The governing physics are defined by the following algebraic expressions:
1. Temperature Gradient:
\[ \Delta T = T_{\infty} - T_{m} \]
2. Dimensionless Biot Number (Validity Check):
\[ \text{Bi} = \frac{h \cdot L}{k} \]
3. Thermal Resistance Terms:
\[ C = \frac{0.5 \cdot L}{h} \]
\[ D = \frac{0.125 \cdot L^{2}}{k} \]
4. Scaling Factor:
\[ F = \frac{\rho \cdot L_{h}}{\Delta T} \]
5. Total Thawing Time:
\[ t = F \cdot (C + D) \]
Regime/Condition
Criteria
Thawing Feasibility
\(\Delta T > 0\)
Plank Equation Validity
\(0.1 < \text{Bi} < 10.0\)
Lumped Analysis Threshold
\(\text{Bi} < 0.1\)
Interior Resistance Dominance
\(\text{Bi} > 10.0\)
To select the most efficient thawing method, process engineers should evaluate the following criteria:
Thermal sensitivity of the product components.
Required throughput volume and cycle time constraints.
Energy consumption profiles of the equipment.
Consistency of the final temperature distribution.
Transitioning to forced convection increases heat transfer rates but introduces specific operational risks:
Potential for localized overheating if airflow is not uniform.
Increased risk of surface dehydration or quality degradation.
Higher mechanical maintenance requirements for blower systems.
Need for tighter control loops on temperature setpoints.
Dielectric thawing offers superior scalability for high-throughput lines compared to water baths:
Dielectric systems provide volumetric heating, which significantly reduces total process time.
Water baths often face sanitation challenges and high water usage costs at scale.
Dielectric units occupy a smaller physical footprint relative to the volume of product processed.
Automated integration is more seamless with dielectric systems than with batch-based immersion tanks.
Worked Example: Refrigeration Thawing of a Frozen Slab
Scenario: A 5 cm thick frozen food slab (modelled as pure water ice) is thawed in a refrigerator. The refrigerator air is maintained at 4 °C with a convective heat transfer coefficient of 10 W/m²·K. The initial product temperature is uniform at –18 °C, and the melting point is 0 °C. Using Plank's equation, compute the thawing time.
Knowns (Input Parameters):
Density, \(\rho = 1000\ \text{kg/m}^3\)
Latent heat of fusion, \(L_h = 334\,000\ \text{J/kg}\)
Thermal conductivity of unfrozen product, \(k = 0.6\ \text{W/m·K}\)
Total slab thickness, \(L = 0.05\ \text{m}\)
Melting temperature, \(T_{m} = 0\ \text{°C}\)
Refrigerator air temperature, \(T_{\infty} = 4\ \text{°C}\)
Temperature driving force:
\[
\Delta T = T_{\infty} - T_{m} = 4.0 - 0.0 = 4.0\ \text{K}
\]
Biot number (validity check):
\[
\text{Bi} = \frac{h\,L}{k} = \frac{10.0 \times 0.05}{0.6} = 0.833
\]
The value lies within the empirical range \(0.1 < \text{Bi} < 10\); Plank's equation is applicable.
