3.5.1.2. Calculation of freezing times

3.5.1.2. Calculation of freezing times

The more general from of Plank’s equation for calculation freezing time is:

                            L     PD   RD2

Freezing time = -----{------ + ------}

                           V      D        f k

Where

L = Heat to be extracted between the initial freezing point and final temperature (kcal/kg).

V = Specific volume of fish (m3/kg)

D = Temperature difference between the initial freezing point of the

fish and the refrigerating medium (oC)

D = Thickness of product in direction or prevailing heat transfer (m)

f = Surface coefficient of heat transfer (including effect of

packaging) (kcal/h.m oC)

k = Thermal conductivity of frozen fish (kcal/h moC)

P and R= Constants which depend on shape

Values for shape constants P and R

Shape

P

R

Sphere

0.167

0.042

Infinite Cylinder

0.167

0.042

Infinite Slab

0.500

0.250

Calculated freezing time – Example 1: What is the freezing time if all other conditions remain the same but the operating temperature is –25oC.

Fish freezers at about –1oC, therefore in the measured freezing time, the effective temperature difference is 34ºC (the difference between –35oC and –1oC). The effective temperature difference for the freezing time required is 24ºC (the difference between 25oC and –1oC). Freezing time is inversely proportional to the temperature difference, therefore the freezing time with an operating temperature of –25oC will be longer than for a temperature of –35oC and can be calculated as follows:

200 x 34 % 24 = 283 min or 4h 43min

Calculated freezing time – Example 2 What is the approximate freezing time if all other conditions remain the same and the block thickness is reduced to 75mm?

Freezing time is directly proportional to the square of the thickness since in this case the surface heat transfer coefficient is high and the factor relating to the thickness of the block, PD/f, will be small. The new freezing time will therefore be calculated as follows:

200 x 752 ¸ 1002 = 200 x 5625 ¸ 10000 = 112 min (1h 52 min)

Last modified: Saturday, 24 December 2011, 11:26 AM