In a heat exchanger, heat energy is transferred from one body or fluid stream to another. In the design of heat exchange equipment, heat transfer equations are applied to calculate this transfer of energy so as to carry it out efficiently and under controlled conditions. The equipment goes under many names, such as boilers, pasteurizers, jacketed pans, freezers, air heaters, cookers, ovens and so on. The range is too great to list completely. Heat exchangers are found widely scattered throughout the food process industry.
Continuous-flow Heat Exchangers
It is very often convenient to use heat exchangers in which one or both of the materials that are exchanging heat are fluids, flowing continuously through the equipment and acquiring or giving up heat in passing.
One of the fluids is usually passed through pipes or tubes, and the other fluid stream is passed round or across these. At any point in the equipment, the local temperature differences and the heat transfer coefficients control the rate of heat exchange.
The fluids can flow in the same direction through the equipment, this is called parallel flow; they can flow in opposite directions, called counter flow; they can flow at right angles to each other, called cross flow. Various combinations of these directions of flow can occur in different parts of the exchanger. Most actual heat exchangers of this type have a mixed flow pattern, but it is often possible to treat them from the point of view of the predominant flow pattern. Examples of these exchangers are illustrated in Figure 6.1.
Applying the basic overall heat-transfer equation for the the heat exchanger heat transfer:
uncertainty at once arises as to the value to be chosen for DT, even knowing the temperatures in the entering and leaving streams.
Consider a heat exchanger in which one fluid is effectively at a constant temperature, Tb as illustrated in Fig. 6.1(d). Constant temperature in one component can result either from a very high flow rate of this component compared with the other component, or from the component being a vapour such as steam or ammonia condensing at a high rate, or from a boiling liquid. The heat-transfer coefficients are assumed to be independent of temperature.
The rate of mass flow of the fluid that is changing temperature is G kg s-1, its specific heat is cp J kg-1 °C-1. Over a small length of path of area dA, the mean temperature of the fluid is T and the temperature drop is dT. The constant temperature fluid has a temperature Tb. The overall heat transfer coefficient is U J m-2 s-1 °C-1.
Therefore the heat balance over the short length is:
Therefore U/)cpG) dA = dT/(T –Tb)
If this is integrated over the length of the tube in which the area changes from A = 0 to A = A, and T changes from T1 to T2, we have:
From the overall equation, the total heat transferred per unit time is given by
but (T1 –T2) can be written (T1 – Tb) - (T2 - Tb)
where DTm is called the log mean temperature difference.
In other words, the rate of heat transfer can be calculated using the heat transfer coefficient, the total area, and the log mean temperature difference. This same result can be shown to hold for parallel flow and counter flow heat exchangers in which both fluids change their temperatures.
The analysis of cross-flow heat exchangers is not so simple, but for these also the use of the log mean temperature difference gives a good approximation to the actual conditions if one stream does not change very much in temperature.
Also q = UADTm
This can be extended to the situation where there are two fluids flowing, one the cooled fluid and the other the heated fluid. Working from the mass flow rates (kg s-1) and the specific heats of the two fluids, the terminal temperatures can normally be calculated and these can then be used to determine DTm and so, from the heat-transfer coefficients, the necessary heat-transfer surface.
DT1 = [32 - 10] = 22°C and DT2 = [7 - (-8)] = 15°C.
In some cases, heat-exchanger problems cannot be solved so easily; for example, if the heat transfer coefficients have to be calculated from the basic equations of heat transfer which depend on flow rates and temperatures of the fluids, and the temperatures themselves depend on the heat-transfer coefficients. The easiest way to proceed then is to make sensible estimates and to go through the calculations. If the final results are coherent, then the estimates were reasonable. If not, then make better estimates, on the basis of the results, and go through a new set of calculations; and if necessary repeat again until consistent results are obtained. For those with multiple heat exchangers to design, computer programmes are available.
In a jacketed pan, the liquid to be heated is contained in a vessel, which may also be provided with an agitator to keep the liquid on the move across the heat-transfer surface, as shown in Fig. 6.3(a).
The action of the agitator and its ability to keep the fluid moved across the heat transfer surface are important. Some overall heat transfer coefficients are shown in Table 6.1. Save for boiling water, which agitates itself, mechanical agitation is assumed. Where there is no agitation, coefficients may be halved.
result applies only to the beginning of heating; as the temperature rises
less steam will be consumed as DT
some food processes, quick heating is required in the pan, for example,
in the boiling of jam. In this case, a helical coil may be fitted inside
the pan and steam admitted to the coil as shown in Fig. 6.3(b). This can
give greater heat transfer rates than jacketed pans, because there can
be a greater heat transfer surface and also the heat transfer coefficients
are higher for coils than for the pan walls. Examples of the overall heat
transfer coefficient U are quoted as:
One type of heat exchanger, that finds considerable use in the food processing industry particularly for products of higher viscosity, consists of a jacketed cylinder with an internal cylinder concentric to the first and fitted with scraper blades, as illustrated in Fig. 6.3(c). The blades rotate, causing the fluid to flow through the annular space between the cylinders with the outer heat transfer surface constantly scraped. Coefficients of heat transfer vary with speeds of rotation but they are of the order of 900-4000 J m-2 s-1 °C-1. These machines are used in the freezing of ice cream and in the cooling of fats during margarine manufacture.
A popular heat exchanger for fluids of low viscosity, such as milk, is the plate heat exchanger, where heating and cooling fluids flow through alternate tortuous passages between vertical plates as illustrated in Fig. 6.3(d). The plates are clamped together, separated by spacing gaskets, and the heating and cooling fluids are arranged so that they flow between alternate plates. Suitable gaskets and channels control the flow and allow parallel or counter current flow in any desired number of passes. A substantial advantage of this type of heat exchanger is that it offers a large transfer surface that is readily accessible for cleaning. The banks of plates are arranged so that they may be taken apart easily. Overall heat transfer coefficients are of the order of 2400-6000 J m-2 s-1 °C-1.
Heat-Transfer Applications > THERMAL PROCESSING
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