**Related Resources: heat transfer**

### Freezing Times for Food Using Plank’s Equation

Heat Transfer and Engineering

HVAC Systems Components and Engineering

Freezing Times for Food Using Plank’s Equation

One of the most widely known simple methods for estimating freezing times of foods and beverages was developed by Plank (1913, 1941). Convective heat transfer is assumed to occur between the food and the surrounding cooling medium. The temperature of the food is assumed to be at its initial freezing temperature, which is constant throughout the freezing process. Furthermore, constant thermal conductivity for the frozen region is assumed. Plank’s freezing time estimation is as follows:

*θ = L _{f} / ( T_{f} - T_{m} ) [ PD / h + RD^{2} / k_{s} ]*

Where

L_{f} = volumetric latent heat of fusion

T_{f} = initial freezing temperature of the food

T_{m} = freezing medium temperature

D = thickness of the slab or diameter of the sphere or infinite cylinder

h = convective heat transfer coefficient

*k _{s}* = thermal conductivity of the fully frozen food,

P and R = geometric factors.

For an infinite slab, P = 1/2 and R = 1/8. For a sphere, P = 1/6 and R = 1/24; for an infinite cylinder, P = 1/4 and R = 1/16.

Plank’s geometric factors indicate that an infinite slab of thickness D, an infinite cylinder of diameter D, and a sphere of diameter D, if exposed to the same conditions, would have freezing times in the ratio of 6:3:2. Hence, a cylinder freezes in half the time of a slab and a sphere freezes in one-third the time of a slab.

For more information see ASHRAE 2018 Refrigeration, SI Edition

Related:

- Freezing Point and Properties of FoodsThe following is the Unfrozen Composition Data, Initial Freezing Point, and Specific Heats of Foods
- Heat Transfer, A Practical Approach - Heat transfer is a basic science that deals with the rate of transfer of thermal energy.
- Heat Loss or Gain From Pipe Excel Spreadsheet Calculator
- Heat Loss through a Double-Pane Window Equation and Calculator A double-pane window is considered. The rate of heat transfer through the window and the inner surface temperature are to be determined.
- Fan And Ventilation Requirements Procedure, Equations and Calculator . This webpage describes basic methods of selecting typical ventilation and cooling products based on their use and provides and example calculation and calculator.
- Time to Freeze Outdoor / Indoor Piping Formulas and Calculator It is important to recognize that insulation reduces heat flow however it does not stop it completely.
- Anti Freeze Ethylene Glycol Freezing and Boil Temperatures
- Thermal Conductivity of Aqueous Solutions of Propylene Glycol
- Radiant heat exchange for two perpendicular surfaces same size equation and calculator