FREZING-TIME CALCULATIONS

NAMA           : ISRA AMANDA SUNOKI

NIM                : 05021381520047

            Freezing times are basic design criteria for freezing systems and represent the residence time for the food product within the freezing system required to achieve the desired level of freezing. The most widely accepted definition of freezing time is the time required to reduce the product temperature from some initial magnitude to an established final temperature at the slowest cooling location. An alternative definition changes the endpoint to the mass average enthalpy equivalent to the desired final temperature for product.

Freezing-Time Equations

            Numerous equations and approaches to freezing-time prediction have been proposed and utilized. The best known and most used of the prediction methods is based on Planck’s equation (1913):

            The limitations to Planck’s equation for estimation of freezing times for foods are numerous and have been discussed by Heldman and Singh (1981) and Ramaswami and Tung (1981). One of the concerns is selection of a latent heat magnitude (L) and an appropriate value for the thermal conductivity (k). In addition, the basic equation does not account for the time required for removal of sensible heat from un frozen product above the initial freezing temperature or for removal of frozen product sensible heat.

            Cleland and Earle (1977, 1979a, 1979b, 1982) developed and presented a modification with sound emprical justification. The authors use Planck’s equation in dimensionless form:

The influence of sensible heat above freezing is incorporated by introducing Plank’s number:

The values of the constants (P and R) are determined by using charts with relationship between Planck’s number and Stefan’s number.

Figure: Chart providing P and R constants for Planck’s equation when applied to a brick or block geometry.

Figure: Chart showing the Plack’s number vs the Stefan number for determinations of different values of the empirical modification P.

Figure: Chart showing the Plack’s number vs the Stefan number for determinations of different values of the empirical modification P.

Product shape is considered by an equivalent heat-transfer dimension (EHTD), as determined by:

Figure: Chart showing the Biot number vs. The shape factor for determination of different values of W.

Numerical Methods

            The evolution of hight-speed computing systems and appropriate numerical methods have provided opportunities to solve camplex partial differential equations with temperature-dependent properties. Equations of the following form for one-dimensional heat transfer during freezing of the product can be solved to predict temperature distribution histories within the Product:

Freezing times are restablished at the point when the temperature history curve passes through the temperature established for the storage of the frozen product. The numerical solutions can be 

Used to compute enthalpy distributions and mass-average enthalpies. Often, mass-average enthalpies equivalent to the desired final temperature are used to establish the end of the freezing process.