Sterilization Process Thermal Analysis
Theory: accumulating lethality from temperature history
Overview
Cans are sterilised at 121 °C, but how is the heating time decided?
By finding how temperature evolves at the slowest-heating point in the can and accumulating lethality from that history. Microbial death rate changes exponentially with temperature, so it's expressed as F0 — equivalent minutes at 121.1 °C. Viscous foods heat by conduction only, so the can centre lags well behind the wall; even after steam-off the centre stays hot during cooling and sterilisation continues. Let's calculate the can's centre temperature and F0.
F0 and cook value
z is the temperature change for a tenfold change in kill rate. Microbes have z ≈ 10 °C, while quality losses such as colour and nutrients have z around 30 °C, so higher temperatures for shorter times protect quality better. Quality loss is expressed as cook value C₁₀₀.
Can centre temperature
The centre temperature of a finite cylinder is the product of infinite-cylinder and slab solutions (with surface at retort temperature). Cooling is added by superposing the step change of surface temperature to cooling-water temperature.
Canning and Ball's method
Canning began around 1810 with Appert's bottled foods for Napoleon's army in France. Why they didn't spoil remained unknown until Pasteur showed the role of microbes half a century later. In the 1920s Ball and Bigelow in the US developed methods to compute lethality from measured can-centre temperatures, laying the basis of the F-value concept. Today such calculations are done numerically to optimise can shapes and heating methods.
Worked example: conduction-heated cans
Diffusivity 1.7×10⁻⁷ m²/s, initial 40 °C, retort 121.1 °C, cooling water 20 °C; can surface taken equal to retort temperature. Heating time found for a centre F0 of 3 min.
| Can size | Heating time | Centre at steam-off | Max centre temperature | F0 (heating + cooling) | Centre cook value |
|---|---|---|---|---|---|
| 75 × 110 mm | 59.4 min | 112.8 °C | 114.4 °C | 1.11 + 1.89 | 79 min |
| 52 × 60 mm | 30.1 min | 115.9 °C | 117.0 °C | 1.41 + 1.59 | 50 min |
Temperature and lethal rate
| Temperature | F0 per minute |
|---|---|
| 110 °C | 0.078 |
| 115 °C | 0.245 |
| 121.1 °C | 1.000 |
| 125 °C | 2.455 |
| 130 °C | 7.762 |
In the large can, F0 is only about a third of the target when the steam goes off.
The centre heats by conduction alone and lags far behind. After steam-off, heat stored in the outer layers keeps flowing inward, so the centre temperature continues rising to 114 °C. Because F0 is very sensitive to temperature, this hot spell during cooling provides over 60% of the total. Trying to secure F0 3 min during heating alone would lengthen heating greatly and overcook the outer food. A small can heats through quickly, halving heating time and cutting centre quality loss to about two-thirds.
Analysis and design tips
- Find the slowest-heating point (centre for conduction, below centre for convection).
- Include F0 during cooling to avoid over-processing.
- Use measured thermal properties of the food (varying with temperature and composition).
- Evaluate both lethality (F0) and quality (cook value).
- Always confirm calculations with thermocouple trials (a safety matter).
“Rotating halved the time”
At a food plant, sterilising thick soup cans took over an hour and the outer ingredients broke down. Switching to rotating the cans in the retort mixed the contents, so heat reached the centre by convection rather than conduction. Sterilisation time fell by more than half and quality improved. Changing how heat is transported can be the most effective way to shorten a process.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| F0 from surface temperature | Under-processing | Use slowest point |
| Ignoring cooling F0 | Over-processing | Include cooling |
| Water properties for food | Wrong times | Measured food data |
| Wrong z-value | Large F0 error | Target organism's z |
| No validation trials | Safety risk | Validate with trials |
I'd like to learn related topics.
Try the food pasteurization D-value tool and milk pasteurization z-value tool. Related pages include transient conduction with heat generation, Heisler charts and drying processes.
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