GIFSQ Tools · Module 17 — Food Processing, Thermal Engineering & Utilities · Tool 326 of 500
Estimate the freezing time of a food slab with Plank’s equation, from thickness, freezing point, air temperature, surface heat transfer and thermal conductivity.
Try sample values — fills the form with the worked example below.
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Freezing time (h)
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Freezing time (min)
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Freezing rate (mm/h)
Equation: Plank’s equation (slab): t = (ρ × L / (Tf − Ta)) × (P × a / h + R × a² / k), with P = 1/2 and R = 1/8 for a slab, a = half-thickness in metres, L the latent heat in J/kg.
Method: Plank’s equation (Plank, 1913), the standard first estimate of freezing time in food process engineering (Heldman and Singh; ASHRAE Refrigeration Handbook).
Assumptions: one-dimensional freezing of a slab cooled from both sides; constant properties; sensible heat above and below the freezing point is not included.
Limitations: real freezing times are longer because sensible cooling is ignored; shape factors P and R differ for cylinders and spheres; use measured data for a validated schedule.
Rounding: freezing time to 2 decimal places, freezing rate to 2; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Plank’s equation (Plank, 1913), the standard first estimate of freezing time in food process engineering (Heldman and Singh; ASHRAE Refrigeration Handbook).
Assumptions: one-dimensional freezing of a slab cooled from both sides; constant properties; sensible heat above and below the freezing point is not included.
Limitations: real freezing times are longer because sensible cooling is ignored; shape factors P and R differ for cylinders and spheres; use measured data for a validated schedule.
Rounding: freezing time to 2 decimal places, freezing rate to 2; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: A 50 mm slab, freezing point −1 °C, air at −30 °C, h = 20 W/m²·K, k = 1.5 W/m·K, density 1000 kg/m³, latent heat 250 kJ/kg: freezing time = 1.62 h (97.28 min).
Enter values above to see results.
Typical food values: freezing point −1 to −3 °C, latent heat 230–300 kJ/kg, frozen thermal conductivity 1.0–2.0 W/m·K. Tool 326 of 500 — GIFSQ
