Freezing Time (Plank) Calculator

Work out freezing time (plank) instantly with clear inputs, formula shown and shareable results.

About Freezing Time (Plank) Calculator

Plank's equation gives freezing time for a slab as (rho x L / deltaT) x (a/2h + a^2/8k), where the first term is surface heat transfer resistance and the second internal conduction. Only latent heat is considered, so it underestimates total time; it is nonetheless the standard first estimate for freezer sizing.

Formula

Plank's equation for a slab

t = (rho x L / deltaT) x (a / (2h) + a^2 / (8k))

Worked example

With the default values below, Freezing Time (Plank) Calculator returns Freezing Time of 2.9053. Change any input above and every figure here is recalculated in your browser.

Inputs used

Product Thicknessminimum 0.01 mm: 50 mm
Latent Heat Of Fusionminimum 0.01 kJ/kg: 250 kJ/kg
Product Densityminimum 0.01 kg/m3: 1,050 kg/m3
Freezing Point Minus Medium Temperatureminimum 0.01 degrees C: 30 degrees C

Results

Freezing Time: 2.9053
Freezing Time In Minutes: 174.32
Time Due To Surface Resistance: 2.4306
Time Due To Internal Conduction: 0.4747

Step by step

1Values used
2Plank's equation for a slab
3Freezing Time= 2.9053
4Freezing Time In Minutes= 174.32
5Time Due To Surface Resistance= 2.4306
6Time Due To Internal Conduction= 0.4747

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does Plank's equation underestimate?

It ignores sensible heat removed above and below the freezing point, and assumes a sharp freezing front at a single temperature. Corrections such as Cleland and Earle's method address both.

Which term usually dominates?

For thin products and low air velocity, surface resistance dominates and increasing air speed helps. For thick products, internal conduction dominates and only reducing thickness helps.