What Is the Plank Equation Food Freezing Time Calculator?
Plank’s equation (1913) is the fundamental relationship used by food engineers to calculate the duration required to freeze foods from initial freezing point to complete phase change at the center.
Accurate freezing time estimates prevent under-freezing during transport and optimize energy consumption in industrial refrigeration plants.
How Does the Plank Equation Food Freezing Time Calculator Work?
Freezing assumes three successive periods: sensible precooling, latent phase-change freezing, and sensible subcooling.
Plank models the dominant latent heat phase by tracking the propagation of an ice-water interface inward.
Shape factors P and R account for 1D planar (slab), 2D radial (cylinder), or 3D radial (sphere) heat flow.
Plank Equation Food Freezing Time Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Computes latent heat removal time balancing surface convective resistance (P·a/h) and internal conductive ice crust resistance (R·a²/k).
How to Use the Plank Equation Food Freezing Time Calculator
- Select product geometry (slab for fillets/cartons, cylinder for sausages, sphere for fruits).
- Enter product thickness/diameter, moisture fraction, and density.
- Specify cooling medium temperature and heat transfer coefficient h.
Step-by-Step Example Calculation
50 mm Meat Patty in -25°C Air Blast Freezer
Input Values:
Understanding Your Result
Output freezing time represents hours needed to reach complete freezing at the thermal center.
Percentage breakdown reveals whether external air convection or internal ice conduction bottlenecks heat extraction.
Factors That Affect the Result
- Air velocity: Higher fan speeds increase h, cutting freezing time up to the point where internal ice conductivity becomes the bottleneck.
- Product thickness: Doubling slab thickness roughly quadruples freezing time because internal resistance scales as a².
When Should You Use This Calculator?
- Sizing commercial spiral freezers, plate freezers, and blast tunnels.
- Calculating refrigeration plant compressor loads.
Assumptions & Limitations
- Assumes all water freezes at a single constant temperature Tf and ignores sensible heat pre-cooling.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Typically predicts freezing times within ±10% to ±15% compared to numerical enthalpy methods.