Cooling Stop Temperature Determination

Reference ID: MET-75D4 | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

The Cooling Stop Temperature Determination is a critical process engineering calculation used in the food and beverage packaging industry. Following thermal sterilization, cans are subjected to water cooling to reduce the internal product temperature. However, removing cans from the cooling bath while they are too cold can lead to insufficient surface drying, resulting in external corrosion, compromised label adhesion, and potential microbial ingress. Conversely, removing them while too hot may cause thermal degradation of the product or damage to packaging materials.

This calculation determines the optimal T_stop—the surface temperature at which active cooling should cease. By balancing the sensible heat stored in the can against the latent heat required to evaporate the residual water film, this method ensures the can surface dries rapidly in ambient air conditions, maintaining both product integrity and packaging quality.

Methodology & Formulas

The calculation relies on a mass and energy balance approach. First, the mass of the residual water film is determined based on the surface area and film thickness:

\[ m_{water} = A_{surface} \cdot \delta_{film} \cdot \rho_{water} \]

The energy required to evaporate this film is calculated using the latent heat of vaporization:

\[ Q_{evap} = m_{water} \cdot h_{fg} \]

To ensure the surface dries, the sensible heat available from the can as it cools from the stop temperature to a final target temperature must be sufficient to provide the required evaporative energy. The stop temperature is derived as follows:

\[ T_{stop} = T_{final} + \frac{Q_{evap}}{m_{can} \cdot c_{p,can}} \]

The drying efficiency is governed by the vapor pressure driving force, calculated using the saturation pressure at the surface temperature and the partial pressure of water vapor in the ambient air:

\[ P_{sat} = 0.611 \cdot \exp\left(\frac{17.27 \cdot T}{T + 237.3}\right) \] \[ P_{vapor,air} = RH \cdot P_{sat}(T_{air}) \] \[ \Delta P = P_{sat}(T_{stop}) - P_{vapor,air} \]

Parameter	Constraint/Regime	Justification
T_stop	35.0°C ≤ T_stop ≤ 55.0°C	Prevents condensation (low end) and thermophilic spoilage (high end).
h_air	5.0 W/m²K ≤ h_air ≤ 25.0 W/m²K	Valid range for natural convection in ambient air.
ΔP	ΔP ≥ 2.0 kPa	Minimum driving force required for effective moisture evaporation.

To determine the optimal cooling stop temperature for can drying, process engineers should follow this methodology:

Calculate the mass of residual water film on the can surface using the film thickness, surface area, and water density.
Determine the energy required to evaporate this film using the latent heat of vaporization.
Compute the required stop temperature by balancing the sensible heat available from the can as it cools to the target final temperature against the evaporation energy.
Verify that the vapor pressure driving force (ΔP) at the stop temperature exceeds 2.0 kPa to ensure adequate drying rate.
Confirm that the calculated stop temperature lies within the recommended bounds of 35–55 °C to avoid condensation or thermophilic spoilage risks.

Setting the cooling stop temperature above the recommended threshold (55 °C) can lead to several issues:

Increased risk of thermophilic spoilage if the product core remains in the danger zone for too long.
Thermal degradation of heat-sensitive product components, affecting flavor, color, or nutritional value.
Potential damage to packaging materials (e.g., seal integrity, label adhesive failure) due to prolonged exposure to elevated temperatures.
Insufficient surface drying if the can cools too quickly in ambient air, leaving residual moisture that promotes corrosion.

Ambient conditions influence the drying driving force and the energy balance:

Higher ambient temperatures increase the saturation pressure of water vapor in the air, which raises the partial pressure (P_air,vap) for a given relative humidity, thereby reducing the vapor pressure difference ΔP.
A reduced ΔP may slow evaporation, potentially requiring a higher stop temperature to maintain the minimum 2.0 kPa driving force.
Seasonal or daily variations in facility temperature should be monitored; the cooling stop setpoint may need to be adjusted dynamically to ensure consistent drying performance.
Conversely, lower ambient temperatures can enhance ΔP, allowing for a slightly lower stop temperature while still achieving effective drying.

Worked Example: Cooling Stop Temperature Determination

Scenario: A cylindrical can of mass m_can = 0.5 kg and surface area A_surface = 0.05 m² exits a sterilizer at high temperature. It is spray-cooled with water, then removed from the water to air-dry. The objective is to determine the surface temperature at which active cooling should stop so that residual water film evaporates quickly, preventing corrosion.

Knowns (Input Parameters)

Mass of can: m_can = 0.5 kg
Surface area: A_surface = 0.05 m²
Film thickness: δ = 0.0002 m
Density of water: ρ_water = 1000.0 kg/m³
Latent heat of vaporization: h_fg = 2.4 × 10⁶ J/kg
Specific heat of can: c_p = 4000.0 J/(kg·K)
Ambient air temperature: T_air = 25.0 °C
Relative humidity: RH = 0.6
Air convective coefficient: h_air = 10.0 W/(m²·K)
Target final temperature: T_final = 30.0 °C

Step-by-Step Calculation

Mass of water film: The film is assumed uniform over the surface. \[ m_{water} = A_{surface} \cdot \delta \cdot \rho_{water} = 0.05 \cdot 0.0002 \cdot 1000.0 = 0.01 \, \text{kg} \]
Energy required to evaporate the film: \[ Q_{evap,req} = m_{water} \cdot h_{fg} = 0.01 \cdot 2.4 \times 10^6 = 24000.0 \, \text{J} \]
Saturation pressure at final target temperature: Using the Antoine-like approximation for water: \[ P_{sat,final} = 4.244 \, \text{kPa} \] (This value is taken directly from the numerical output.)
Partial pressure of water vapor in ambient air: \[ P_{air,vap} = RH \cdot P_{sat}(T_{air}) = 1.901 \, \text{kPa} \] where P_sat(25°C) is computed via the same Antoine expression.
Required stop temperature: The sensible heat from the can cooling from T_stop to T_final must cover the evaporation load: \[ T_{stop} = T_{final} + \frac{Q_{evap,req}}{m_{can} \cdot c_p} = 30.0 + \frac{24000.0}{0.5 \cdot 4000.0} = 30.0 + 12.0 = 42.0 \, \text{°C} \]
Driving force for drying: The vapor pressure difference at the stop temperature: \[ \Delta P = P_{sat}(T_{stop}) - P_{air,vap} = 6.3 \, \text{kPa} \] This value exceeds the minimum required threshold of 2 kPa, ensuring rapid evaporation.
Validity checks:
- T_stop = 42.0 °C lies within the empirical bounds (35–55 °C).
- h_air = 10.0 W/(m²·K) is within the natural convection range (5–25 W/(m²·K)).

Final Answer

The active cooling should be stopped when the can surface reaches 42.0 °C. At this temperature, the residual water film evaporates with a vapor pressure driving force of 6.3 kPa, and the can core is expected to remain above microbiological safety limits for an acceptable duration.

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

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