Plank's Freezing Time & Know How Long the Slab Takes to Freeze
Freezes fish fillets
Fast freezing keeps texture and quality — enter the slab thickness, density, latent heat, driving force, surface coefficient and conductivity to get the freezing time in hours and minutes by Plank's equation.
Set the freezing job
Next: allow about 4.2 h (252 min) in the blast freezer for this 50 mm slab — schedule batches and door cycles around that window.
Plank's equation for an infinite slab (P=0.5, R=0.125). It covers only the latent-heat freezing plateau, not the sensible cool-down before or sub-cooling after, so total cabinet time is longer.
Plank's freezing — key facts
- Equation
- t = (ρL ÷ ΔT)(Pa/h + Ra²/k)
- Slab P, R
- 0.5 and 0.125
- Sphere P, R
- 1/6 and 1/24
- Cylinder P, R
- 1/4 and 1/16
- Thickness effect
- conduction term ∝ a²
- Covers
- freezing phase only
- Blast-air h
- ≈ 25–50 W/m²·°C
- Privacy
- Runs in your browser; nothing uploaded
A quick freeze protects texture — a slow one ruins it
When food freezes fast it forms small ice crystals that leave cells intact, so the product thaws firm with little drip; a slow freeze grows large crystals that rupture cells and leave it mushy. Plank's equation tells you the freezing time from the slab thickness, the freezing properties and the cooling conditions. Because the conduction term carries thickness squared, a thinner slab or stronger surface cooling is usually the lever that turns a slow freeze into a quick one.
This tool gives the freezing time in hours and minutes from the thickness, density, latent heat, temperature driving force, surface coefficient and conductivity. Use it to set tray depth and airflow, size a blast freezer, and check that a pack freezes quickly enough for quality. Pair it with the Cold Room Cooling Load and Precooling Time tools to design the whole cold chain.
Protect quality
Hit a freeze fast enough for small ice crystals.
Set tray depth
See how thickness drives the freezing time.
Size the freezer
Plan blast capacity from real cycle times.
Tune airflow
Weigh stronger surface cooling against thinner packs.
Frequently Asked Questions
What is Plank's equation?+
Plank's equation estimates the time to freeze a food once it is at its freezing point: t = (ρ·L / ΔT)·(P·a/h + R·a²/k). Here ρ is density, L the latent heat of freezing, ΔT the temperature driving force, a the slab thickness, h the surface heat-transfer coefficient and k the thermal conductivity. For an infinite slab P = 0.5 and R = 0.125, which is the shape this tool models.
What do the P and R constants mean?+
They are shape factors. P scales the surface-resistance term and R scales the internal-conduction term, and their values depend on geometry. For an infinite slab P = 0.5 and R = 0.125; a sphere uses 1/6 and 1/24, and an infinite cylinder 1/4 and 1/16. This tool uses the slab values, which suit fillets, blocks, trays and flat packs of produce.
Does Plank's equation include cooling the food first?+
No — it estimates only the freezing phase, the time spent removing the latent heat at the freezing plateau. It does not include pre-cooling the food from its starting temperature down to freezing, nor sub-cooling the frozen block further. In practice add time for those phases; Plank's time is the dominant central part of a blast-freeze cycle.
Why does thickness matter so much?+
The conduction term carries thickness squared, so doubling the slab thickness more than doubles the freezing time. That is why thin packs and fillets freeze far faster than thick blocks, and why blast freezers spread product in shallow trays. If your time looks long, the quickest win is usually a thinner slab rather than a colder freezer.
What is the surface heat-transfer coefficient?+
It is how readily heat leaves the food surface into the cold air or plate, in W per m² per °C. Still air is poor (around 5–10), forced-air blast freezing is much better (25–50), and contact plate freezing higher still. A higher coefficient shrinks the surface term, so faster airflow or plate contact cuts freezing time — until the conduction term inside the slab dominates.
What temperature driving force should I use?+
Use the difference between the food's freezing point and the freezer air or plate temperature — for example freezing at −1°C in a −30°C blast freezer gives a driving force of about 29°C. A larger driving force freezes faster, so a colder freezer or a higher-freezing-point food shortens the time. Enter the ΔT that matches your equipment.
Why freeze produce and fish quickly?+
Fast freezing forms small ice crystals that do less damage to cell walls, so the food keeps better texture, drip and quality on thawing. Slow freezing grows large crystals that rupture cells and leave the product mushy and weeping. Knowing the freezing time lets you set tray depth and airflow to hit a quick freeze, not just any freeze.
Are the figures exact?+
They are good engineering estimates. Plank's equation assumes a single freezing point, constant properties and one-dimensional heat flow, while real foods freeze over a range and have changing properties. Treat the result as a sound planning figure for sizing freezers and setting cycle times, and confirm with a probe in the slowest-freezing point of the product.