Introduction to Food Engineering

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Freezing Time - Plank's Equation and Pham's Method

Learning Outcomes

At the end of this module, you will be able to:

  1. describe the assumptions used in deriving Plank's equation
  2. calculate freezing time using Plank's equation
  3. calculate freezing time using Pham's method

The food freezing process involves phase change of water into ice, the concentration of solutes, and the lowering of the freezing point. In operating food freezers, the time required to freeze foods is necessary to ensure that a product temperature has reached a desired sub-freezing temperature. In this module, we will first consider the freezing diagram of water to gain a basic understanding of the freezing process.

In the next video, we will consider a widely used equation, namely, Plank’s equation, to determine the time required for the phase change to occur. In the next video, you will learn the assumptions and the steps used to derive this equation.

Although Plank’s equation is simple to use, its assumptions lack its ability to determine the freezing time of foods accurately. Numerous studies have involved developing an improved method for this purpose. In the next video, you will learn the application of Pham’s method to predict freezing time. Based on the comparisons with results from experiments, this method gives more accurate estimates of freezing times than other published methods.


In this module, you learned how Plank’s equation is derived and used to assess the influence of various freezing conditions on the freezing time. As an alternative to using Plank’s equation, you also learned how to use Pham’s method.