CHAPTER
6
Rates of decay and of deterioration in foodstuffs depend on temperature. At suitable low temperatures, changes in the food can be reduced to economically acceptable levels. The growth and metabolism of microorganisms is slowed down and if the temperature is low enough, growth of all microorganisms virtually ceases. Enzyme activity and chemical reaction rates (of fat oxidation, for example) are also very much reduced at these temperatures. To reach temperatures low enough for deterioration virtually to cease, most of the water in the food must be frozen. The effect of chilling is only to slow down deterioration changes. 
In studying chilling and freezing, it is necessary to look first at the methods for obtaining low temperatures, i.e. refrigeration systems, and then at the coupling of these to the food products in chilling and freezing. The basis of mechanical refrigeration is the fact that at different pressures the saturation (or the condensing) temperatures of vapours are different as clearly shown on the appropriate vapourpressure/temperature curve. As the pressure increases condensing temperatures also increase. This fact is applied in a cyclic process, which is illustrated in Fig. 6.8.
To start with the evaporator; in this the pressure above the refrigerant is low enough so that evaporation of the refrigerant liquid to a gas occurs at some suitable low temperature determined by the requirements of the product. This temperature might be, for example 18°C in which case the corresponding pressures would be for ammonia 229 kPa absolute and for tetrafluoroethane (also known as refrigerant 134a) 144 kPa. Evaporation then occurs and this extracts the latent heat of vaporization for the refrigerant from the surroundings of the evaporator and it does this at the appropriate low temperature. This process of heat extraction at low temperature represents the useful part of the refrigerator. On the pressure/enthalpy chart this is represented by ab at constant pressure (the evaporation pressure) in which 1 kg of refrigerant takes in (H_{b}  H_{a}) kJ . The low pressure necessary for the evaporation at the required temperature is maintained by the suction of the compressor. The remainder of the process cycle is included merely so that the refrigerant may be returned to the evaporator to continue the cycle. First, the vapour is sucked into a compressor which is essentially a gas pump and which increases its pressure to exhaust it at the higher pressure to the condensers. This is represented by the line bc which follows an adiabatic compression line, a line of constant entropy (the reasons for this must be sought in a book on refrigeration) and work equivalent to (H_{c}  H_{b}) kJ kg^{1} has to be performed on the refrigerant to effect the compression. The higher pressure might be, for example, 1150 kPa (pressures are absolute pressures) for ammonia, or 772 kPa for refrigerant 134a, and it is determined by the temperature at which cooling water or air is available to cool the condensers. To complete the cycle, the refrigerant must be condensed, giving up its latent heat of vaporization to some cooling medium. This is carried out in a condenser, which is a heat exchanger cooled generally by water or air. Condensation is shown on Fig. 6.9 along the horizontal line (at the constant condenser pressure), at first cd cooling the gas and then continuing along de until the refrigerant is completely condensed at point e. The total heat given out in this from refrigerant to condenser water is (H_{c}  H_{e}) = (H_{c}  H_{a}) kJ kg^{1}. The condensing temperature, corresponding to the above high pressures, is about 30°C and so in this example cooling water at about 20°C, could be used, leaving sufficient temperature difference to accomplish the heat exchange in equipment of economic size. This process of evaporation at a low pressure and corresponding low temperature, followed by compression, followed by condensation at around atmospheric temperature and corresponding high pressure, is the refrigeration cycle. The highpressure liquid then passes through a nozzle from the condenser or highpressure receiver vessel to the evaporator at low pressure, and so the cycle continues. Expansion through the expansion valve nozzle is at constant enthalpy and so it follows the vertical line ea with no enthalpy added to or subtracted from the refrigerant. This line at constant enthalpy from point e explains why the point a is where it is on the pressure line, corresponding to the evaporation (suction) pressure. By adjusting the high and low pressures, the condensing and evaporating temperatures can be selected as required. The high pressure is determined: by the available coolingwater temperature, by the cost of this cooling water and by the cost of condensing equipment. The evaporating pressure is determined by either the low temperature that is required for the product or by the rate of cooling or freezing that has to be provided. Low evaporating temperatures mean higher power requirements for compression and greater volumes of lowpressure vapours to be handled therefore larger compressors, so that the compression is more expensive. It must also be remembered that, in actual operation, temperature differences must be provided to operate both the evaporator and the condenser. There must be lower pressures than those that correspond to the evaporating coil temperature in the compressor suction line, and higher pressures in the compressor discharge than those that correspond to the condenser temperature. Overall,
the energy side of the refrigeration cycle can therefore be summed up:
A
useful measure is the ratio of the heat taken in at the evaporator (the
useful refrigeration), (H_{b}  H_{a}) ,
to the energy put in by the compressor which must be paid for (H_{c}–
H_{b}). This ratio is called the coefficient of performance
(COP).
From
the tabulated data (Appendix 7)
the specific heat of fish is 3.18 kJ kg^{1} °C^{1}
above freezing and 1.67 kJ kg^{1 }°C^{1} below freezing,
and the latent heat is 276 kJ/kg^{1}. If maximum is twice
average Coil rate of heat transfer q = UADT_{m} and so
A = q/UDT_{m} The great advantage of tracing the cycle on the pressure/enthalpy diagram is that from the numerical coordinates of the various cycle points performance parameters can be read off or calculated readily.
From the chart in Appendix 11(b) the boiling temperature of ammonia at a pressure of 120 kPa is 30°C, so this is the evaporator temperature. Also from the chart,
the latent heat of evaporation is: For a heatremoval
rate of 300 watts = 0.3 kJ s^{1} the ammonia evaporation rate
is: The
chart shows at the saturated vapour point for the cycle (b on Fig. 6.8)
that the specific volume of ammonia vapour is: 2.2 x 10^{4} x 0.98 = 2.16 x10^{4} m^{3} s^{1}. So far we have been talking of the theoretical cycle. Real cycles differ by, for example, pressure drops in piping, superheating of vapour to the compressor and nonadiabatic compression, but these are relatively minor. Approximations quite good enough for our purposes can be based on the theoretical cycle. If necessary, allowances can be included for particular inefficiencies. The refrigerant vapour has to be compressed so it can continue round the cycle and be condensed. From the refrigeration demand, the weight of refrigerant required to be circulated can be calculated; each kg s^{1} extracts so many J s^{1} according to the value of (H_{b}  H_{a}). From the volume of this refrigerant, the compressor displacement can be calculated, as the compressor has to handle this volume. Because the compressor piston cannot entirely displace all of the working volume of the cylinder, there must be a clearance volume; and because of inefficiencies in valves and ports, the actual amount of refrigerant vapour taken in is less than the theoretical. The ratio of these, actual amount taken in, to the theoretical compressor displacement, is called the volumetric efficiency of the compressor. Both mechanical and volumetric efficiencies can be measured, or taken from manufacturer's data, and they depend on the actual detail of the equipment used. Consideration of the data from the thermodynamic chart and of the refrigeration cycle enables quite extensive calculations to be made about the operation.
From the chart Appendix 11(b), the heat extracted by ammonia at the evaporating temperature of 15°C is (1.740.63) = 1.11 MJ kg^{1 = 1.11x 103}J kg^{1}
Under cycle conditions,
from chart, the coefficient of performance Variations in load and in the evaporating or condensing temperatures are often encountered when considering refrigeration systems. Their effects can be predicted by relating them to the basic cycle. If the heat load increases in the cold store, then the temperature tends to rise and this increases the amount of refrigerant boiling off. If the compressor cannot move this, then the pressure on the suction side of the compressor increases and so the evaporating temperature increases tending to reduce the evaporation rate and correct the situation. However, the effect is to lift the temperature in the cold space and if this is to be prevented additional compressor capacity is required. As the evaporating pressure, and resultant temperature, change, so the volume of vapour per kilogram of refrigerant changes. If the pressure decreases, this volume increases, and therefore the refrigerating effect, which is substantially determined by the rate of circulation of refrigerant, must also decrease. Therefore if a compressor is required to work from a lower suction pressure its capacity is reduced, and conversely. So at high suction pressures giving high circulation rates, the driving motors may become overloaded because of the substantial increase in quantity of refrigerant circulated in unit time. Changes in the condenser pressure have relatively little effect on the quantity of refrigerant circulated. However, changes in the condenser pressure and also decreases in suction pressure, have quite a substantial effect on the power consumed per ton of refrigeration. Therefore for an economical plant, it is important to keep the suction pressure as high as possible, compatible with the product requirement for low temperature or rapid freezing, and the condenser pressure as low as possible compatible with the available cooling water or air temperature.
Although in theory a considerable number of fluids might be used in mechanical
refrigeration, and historically quite a number including cold air and
carbon dioxide have been, those actually in use today are only a very
small number. Substantially they include only ammonia, which is used in
many large industrial systems, and approved members of a family of halogenated
hydrocarbons containing differing proportions of fluorine and chosen according
to the particular refrigeration duty required. The reasons for this very
small group of practical refrigerants are many. Ammonia
is in most ways the best refrigerant from the mechanical point of view,
but its great problem is its toxicity. The thermodynamic chart for ammonia,
refrigerant 717 is given in Appendix 11(b).
Compressors are just basically vapour pumps and much the same types as shown in Fig. 4.3 for liquid pumps are encountered. Their design is highly specialized, particular problems arising from the lower density and viscosity of vapours when compared with liquids. The earliest designs were reciprocating machines with pistons moving horizontally or vertically, at first in large cylinders and at modest speeds, and then increasingly at higher speeds in smaller cylinders. An important aspect in compressor choice is the compression ratio, being the ratio of the absolute pressure of discharge from the compressor, to the inlet suction pressure. Reciprocating compressors can work effectively at quite high compression ratios (up to 6 or 7 to 1). Higher overall compression ratios are best handled by putting two or more compressors in series and so sharing the overall compression ratio between them. For smaller compression ratios and for handling the large volumes of vapours encountered at low temperatures and pressures, rotary vane compressors are often used, and for even larger volumes, centrifugal compressors, often with many stages, can be used. A recent popular development is the screw compressor, analogous to a gear pump, which has considerable flexibility. Small systems are often "hermetic", implying that the motor and compressor are sealed into one casing with the refrigerant circulating through both. This avoids rotating seals through which refrigerant can leak. The familiar and very dependable units in household refrigerators are almost universally of this type.
The evaporator is the only part of the refrigeration equipment that enters directly into food processing operations. Heat passes from the food to the heattransfer medium, which may be air or liquid, thence to the evaporator and so to the refrigerant. Thermal coupling is in some cases direct, as in a plate freezer. In this, the food to be frozen is placed directly on or between plates, within which the refrigerant circulates. Another familiar example of direct thermal coupling is the chilled slab in a shop display. Generally, however, the heat transfer medium is air, which moves either by forced or natural circulation between the heat source, the food and the walls warmed by outside air, and the heat sink which is the evaporator. Sometimes the medium is liquid such as in the case of immersion freezing in propylene glycol or in alcoholwater mixtures. Then there are some cases in which the refrigerant is, in effect, the medium such as immersion or spray with liquid nitrogen. Sometimes there is also a further intermediate heattransfer medium, so as to provide better control, or convenience, or safety. An example is in some milk chillers, where the basic refrigerant is ammonia; this cools glycol, which is pumped through a heat exchanger where it cools the milk. A sketch of some types of evaporator system is given in Fig. 6.10.
The evaporator surfaces are often extended by the use of metal fins that are bonded to the evaporator pipe surface. The reason for this construction is that the relatively high metal conductance, compared with the much lower surface conductance from the metal surface to the air, maintains the fin surface substantially at the coil temperature. A slight rise in temperature along the fin can be accounted for by including in calculations a fin efficiency factor. The effective evaporator area is then calculated by the relationship
where
A is the equivalent total evaporator surface area, A_{p}
is the coil surface area, called the primary surface, A_{s}
is the fin surface area, called the secondary surface and f
(phi) is the fin efficiency. Chilling of foods is a process by which their temperature is reduced to the desired holding temperature just above the freezing point of food, usually in the region of 2 to 2°C Many commercial chillers operate at higher temperatures, up to 1012°C. The effect of chilling is only to slow down deterioration changes and the reactions are temperature dependent. So the time and temperature of holding the chilled food determine the storage life of the food. Rates of chilling are governed by the laws of heat transfer which have been described in previous sections. It is an example of unsteadystate heat transfer by convection to the surface of the food and by conduction within the food itself. The medium of heat exchange is generally air, which extracts heat from the food and then gives it up to refrigerant in the evaporator. As explained in the heattransfer section, rates of convection heat transfer from the surface of food and to the evaporator are much greater if the air is in movement, being roughly proportional to v^{0.8}. To
calculate chilling rates it is therefore necessary to evaluate: Although the shapes of most foodstuffs are not regular, they often approximate the shapes of slabs, bricks, spheres and cylinders.
This is an example of unsteadystate cooling and can be solved by application of Fig. 5.3,
so
t = [0.46x 3600 x 930 x (0.035)^{2}]/0.5 A full analysis of chilling must, in addition to heat transfer, take mass transfer into account if the food surfaces are moist and the air is unsaturated. This is a common situation and complicates chilling analysis. Water makes up a substantial proportion of almost all foodstuffs and so freezing has a marked physical effect on the food. Because of the presence of substances dissolved in the water, food does not freeze at one temperature but rather over a range of temperatures. At temperatures just below the freezing point of water, crystals that are almost pure ice form in the food and so the remaining solutions become more concentrated. Even at low temperatures some water remains unfrozen, in very concentrated solutions. In the freezing process, added to chilling is the removal of the latent heat of freezing. This latent heat has to be removed from any water that is present. Since the latent heat of freezing of water is 335 kJ kg^{1}, this represents the most substantial thermal quantity entering into the process. There may be other latent heats, for example the heats of solidification of fats which may be present, and heats of solution of salts, but these are of smaller magnitude than the latent heat of freezing of water. Also the fats themselves are seldom present in foods in as great a proportion as water. Because of the latentheatremoval requirement, the normal unsteadystate equations cannot be applied to the freezing of foodstuffs. The coefficients of heat transfer can be estimated by the following equation:
where h_{s} is the total surface heattransfer coefficient, h_{c} is the convection heat transfer coefficient, x is the thickness of packing material, k is the thermal conductivity of the packing material and h_{r} is the radiation heattransfer coefficient. A
full analytical solution of the rate of freezing of food cannot be obtained.
However, an approximate solution, due to Plank, is sufficient for
many practical purposes. Plank assumed that the freezing process: Making these assumptions, freezing rates for bodies of simple shapes can be calculated. As an example of the method, the time taken to freeze to the centre of a slab whose length and breadth are large compared with the thickness, will be calculated. Rates of heat transfer are equal from either side of the slab. Assume that at time t a thickness x of the slab of area A has been frozen as shown in Fig. 6.11. The temperature of the freezing medium is T_{a}. The freezing temperature of the foodstuff is T, and the surface temperature of the food is T_{s}. The thermal conductivity of the frozen food is k, l is the latent heat of the foodstuff and r is its density.
Now, all of the heat removed at the freezing boundary must be transmitted to the surface through the frozen layer; if the frozen layer is in the steadystate condition we have:
Similarly, this quantity
of heat must be transferred to the cooling medium from the food surface,
so: where h_{s} is the surface heattransfer coefficient. Eliminating T_{s} between the two equations gives:
Since the same heat flow passing through the surface also passes through the frozen layer and is removed from the water as it freezes in the centre of the block:
Now, if the thickness of the slab is a, the time taken for the centre of the slab at x = a/2 to freeze can be obtained by integrating from x = 0, to x = a/2 during which time t goes from t to t_{f} .
In his papers Plank (1913, 1941) derived his equation in more general terms and found that for brickshaped solids the change is in numerical terms, called shape factors, only.
where P = 1/2, R = 1/8 for a slab; P = 1/4, R = 1/16 for an infinitely long cylinder, and P = 1/6, R = 1/24 for a cube or a sphere. Brickshaped solids have values of P and R lying between those for slabs and those for cubes. Appropriate values of P and R for a brickshaped solid can be obtained from the graph in Fig. 6.12. In this figure, b_{1} and b_{2} are the ratios of the two longest sides to the shortest. It does not matter in what order they are taken.
Conductance of cardboard packing = x/k = 0.001/0.06 = 0.017.
In a plate freezer, the thickness of the slab is the only dimension that is significant. The case can be treated as equivalent to an infinite slab, and therefore the constants in Plank's equation are 1/2 and 1/8.
And with no packing h_{s} = 600 so that
This estimate can be improved by adding to the latent heat of freezing, the enthalpy change above the freezing temperature and below the freezing temperature. Above freezing, assume the meat with a specific heat of 3.22 x 10^{3} J kg^{1}°C^{1} starts at +10°C and goes to 2°C, needing 3.9 x 10^{4} J kg^{1}. Below the freezing temperature assume the meat goes from 2°C to the mean of 2°C and 34°C, that is 18°C, with a specific heat of 1.67 x 10^{3} J kg^{1}°C^{1}, needing 2.8 x 10^{4} J kg^{1}. This, with the latent heat of 2.56 x 10^{5 } Jkg, gives a total of 3.23 x 10^{5} J kg^{1} and amended freezing times of
If instead of a slab, cylinder, or cube, the food were closer to a brick shape then an additional 20% should be added. Thus, with a knowledge of the thermal constants of a foodstuff, required freezing times can be estimated by the use of Plank's equation. Appendix 7 gives values for the thermal conductivities, and the latent heats and densities, of some common foods. The analysis using Plank's equation separates the total freezing time effectively into two terms, one intrinsic to the food material to be frozen, and the other containing the surface heat transfer coefficient which can be influenced by the process equipment. Therefore for a sensitivity analysis, it can be helpful to write Plank's equation in dimensionless form, substituting DH for lr:
This leads to defining an efficiency term:
in
which h
(eta) can be regarded as an efficiency of coupling of the freezing medium
to the food varying from 1 for Bi ®
¥,
to 0 for Bi ®
0. Taking an intrinsic freezing time t_{f}’ for
the case of unit driving force, DT
= 1; then for general DT
: and (6.9) can be used very readily to examine the influence of freezing medium temperature, and of surface heat transfer coefficient through the Biot number, on the actual freezing time. Thus the sensitivity of freezing time to process variations can be taken quickly into account.
P/R = 4, and so h
= 3.3/7.3 = 0.45
for (c) 1/ h_{s}
becomes 0.017 + 0.01 = 0.027, For cold storage,
the requirement for refrigeration comes from the need to remove the heat:
Heat
penetrating the walls can be estimated, knowing the overall heattransfer
coefficients including the surface terms and the conductances of the insulation,
which may include several different materials. The other heat sources
require to be considered and summed. Detailed calculations can be quite
complicated but for many purposes simple methods give a reasonable estimate.
HeatTransfer Applications > SUMMARY, PROBLEMS Back to the top 
