Variables which affect freezing times
5.2 Calculation of freezing time
5.3 Sample freezing times
The freezing time is the time taken to lower the temperature of the product from its initial temperature to a given temperature at its thermal centre. Most freezing codes of practice require that the average or equilibrium temperature of the fish be reduced in the freezer to the intended storage temperature. The final temperature at the thermal centre is therefore selected to ensure that the average fish temperature has been reduced to this storage value. The recommended storage temperature for frozen fish in the UK for a period of 1 year is -30°C and, to ensure that the fish are frozen quickly, the temperature of the freezer must be lower than this.
The surface of the fish in a freezer will be quickly reduced to near the freezer temperature of say -36°C. Thus when the warmest part at the thermal centre is reduced to 20°C, the average temperature of the fish will be close to the required storage temperature of -30°C. The freezing time, in this particular case, will therefore be defined as the time taken for the warmest part of the fish, at the thermal centre, to be reduced to -20°C.
The above factors will determine the overall heat transfer coefficient and hence the freezing time.
Freezer type. The type of freezer will greatly influence the freezing time. For example, due to improved surface heat transfer, a product will normally freeze faster in an immersion freezer than in an air blast freezer operating at the same temperature.
Operating temperature. The colder the freezer, the faster the fish will freeze. However, the cost of freezing increases as the freezer temperature is reduced, and in practice, most freezers are designed to operate only a few degrees below the required storage temperature of the product. For example, plate freezers usually operate at about -40°C and blast freezers at about -35°C when the storage temperature is -30°C.
Air speed in blast freezers. The general relationship between air speed and freezing time is shown in Figure 5 and this shows that freezing time is reduced as the air speed is increased. This, however, is a rather complicated relationship and it depends on a number of factors. If the resistance to heat transfer of the stagnant boundary layer of air is important, changes in air speed will make a significant difference to the freezing time. If, however, the package is large and the resistance of the fish itself is the important factor then changes in air speed will be less significant. Air temperature, air density, air humidity and air turbulence are other factors that have to be taken into account when the effect of air condition on freezing time is considered. Some of these factors however, may only have a minor effect.
Product temperature before freezing. The warmer the product, the longer it will take to freeze. Fish should therefore be kept chilled before freezing both to maintain quality and reduce freezing time and refrigeration requirement. For example, a single tuna 150 mm in diameter frozen in an air blast freezer will take 7h to freeze when the initial temperature is 35°C but, only 5h when the temperature is 5°C.
The initial temperature of the product must therefore be given when quoting a freezing time.
Product thickness. The thicker the product, the longer is the freezing time. For products less than 50 mm thick, doubling the thickness may more than double the freezing time whereas doubling a thickness of 100 mm or more may increase the freezing time fourfold. The rate of change of freezing time with thickness therefore, depends on the relative importance of the resistance of the fish to heat transfer.
Product shape. The shape of a fish or package can have a considerable effect on its freezing time and this is dependent on the ratio of surface area to volume.
Product contact area and density. In a plate freezer, poor contact between product and plate results in increased freezing time. Poor contact may be due to ice on the plates, packs of unequal thickness, partially filled packs or voids at the surface of the block. Surface voids are often accompanied by internal voids and this also results in poor heat transfer. Apart from increasing freezing time, internal voids also reduce the density of the block. The relationship between time, block density and contact area for 100 mm blocks of white fish is shown in Table 6.
Product packaging. The method of wrapping and the type and thickness of the wrapping material can greatly influence the freezing time of a product. Air trapped between wrapper and product has often a greater influence on the freezing time than the resistance of the wrapping material itself. The following example illustrates the point. Smoked fish in a cardboard box with the lid on take 15h to freeze in an air blast freezer. Smoked fish in an aluminium box of the same shape and size and with the lid on take 12h, but if the lid is taken off the cardboard box, the freezing time is only 8h because there is no trapped air acting as an insulation.
Species of fish. The higher the oil content of the fish the lower is the water content. Most of the heat extracted during freezing is to change the water to ice; therefore, if there is less water, then less heat will require to be extracted to freeze the fish. Since the fat content of oily fish is subject to seasonal variations, it is safer to assume the same heat content figure used for lean fish in any calculation. This also ensures that the freezer capacity is adequate whatever the species of fish being frozen.
Freezing times can be calculated, but there is usually insufficient information available to make this calculation accurate. Calculated freezing times can be fairly accurate for uniformly shaped products such as blocks of fillets but, for other products with irregular shapes, calculation can only give a rough guide. The presence of wrappers and many other factors can make calculation of the freezing time difficult and unreliable.
Formulae that have been used for quick calculations in the past had to be simplified to make them practical. They also assume that the fish has been chilled before freezing and that all of the heat is extracted at the initial freezing temperature. Calculated freezing times should therefore only be used to give an approximation of the true figure and should not be used for designing freezing equipment. Modern computer techniques have now made it possible to calculate freezing times more precisely.
Plank's formula for calculating the freezing time of fish has been widely used in a variety of forms. It has proved to be particularly valuable in extending the results from experimental studies to cover a wide range of variables. Thus, if an accurately measured freezing time is known, others can be calculated if most of the freezing conditions are similar.
The most general form of Plank's equation for calculing freezing time is:
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 refrigeration medium (°C)
D = Thickness of product in direction of prevailing heat transfer (m)
k = Thermal conductivity of frozen fish (kcal/h m °C)
P and R = Constants which depend on shape
From the above formula, it can be seen that freezing time is inversely proportional to the temperature difference and, depending on other conditions, it may also be nearly proportional to the square of the product thickness. This knowledge can be used to calculate other freezing times as shown in the examples shown in Table 8.
Table 8 Values for shape constants P and R
Measured freezing time. A measured freezing time of 3h 20m (200 min) is known for a 100 mm thik block of whole herring frozen in a VPF with a refrigerant temperature of 35°C.
Calculated freezing time - Example 1. What is the freezing time if all other conditions remain the same but the operating temperature is -25°C?
Fish freezes at about -1°C, therefore in the measured freezing time the effective temperature difference is 34 degC (the difference between -35°C and - 1°C). The effective temperature difference for the freezing time required is 24 degC( the difference between -25°C and -1°C). Freezing time is inversely proportional to the temperature difference, therefore the freezing time with an operating temperature of -25°C will be longer than for a temperature of -35°C and can be calculated as follows:
200 × 34 ÷ 24 = 283 min or 4h 43min
Table 10 Freezing times for fish products
|Product||Freezing method||Product initial temperature (°C)||Operating temperature (°C)||Freezing time|
|Whole cod block 100 mm thick||Vertical plate||5||-40||3||20|
|Whole round fish 125 mm, e.g. cod, salmon, frozen singly||Air blast 5 m/s||5||-35||5||00|
|Cod fillets laminated block 57 mm thick in waxed carton||Horizontal plate||6||-40||1||20|
|Haddock fillets 50 mm thick on metal tray||Air blast 4 m/s||5||-35||2||05|
|Whole lobster 500 g||Liquid nitrogen spray||8||-80/ Variable||0||12|
|Scampi meat 18 mm thick||Air blast 3 m/s||5||-35||0||26|
|Shrimp meat||Liquid nitrogen spray||6||-80/Variable||0||5|
|Single haddock fillets||Air blast||5||-35||0||13|
|Packaged fillets 50 mm thick||Sharp freezer||8||-12 to -30||15||00|
|Packages fillets 50 mm thick||Air blast 2.5 to 5 m/s||5||-35||5||15|
|Single tuna, 50 kg||Sodium chloride immersion||20 to -18°C at centre||-12 to -15||72||00|
|Single tuna, 90 kg||Air blast||20 to -45°C at centre||-50 to -60||26||00|
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 75 mm?
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 × 5625 ÷ 10000 = 112 min (1h 52 min)
The freezing times in Table 9 are observed times for a number of fish products and will give designers and operators some idea of what to expect in practice.
It should be noted that the initial fish temperature for all the examples given in Table 10 is about 5 to 8°C. This temperature is typical if fish are chilled before freezing and makes allowance for the fish warming up during handling prior to freezing.