Lesson 8 - Heat Exchangers

When we refer to sizing a heat exchanger, we are primarily referring to calculating the heat transfer area an exchanger needs to have to achieve the required heat transfer rate. After this is calculated the actual physical size and dimensions of the exchanger can be calculated.

So far in this unit, we have presented three equations that define heat transfer rate in brewing applications:

Single fluid being heated or cooled:

Single fluid changing phase

Overall heat transfer rate across an exchanger

It is worthwhile mentioning that in the equations above, ∆T and ∆T_LM are not the same thing. ∆T_LM is the average temperature difference between the product and utility fluid across the exchanger. ∆T is the increase in temperature of a single fluid as it passes through the exchanger from inlet to outlet.

The principle of heat balance, as defined by the law of conservation of energy, states that the energy gained by one fluid must be equal to the heat loss by the second fluid, assuming no energy losses.

In practical situations, there is always a little loss from the surface of equipment which for the purposes of this lesson, we will assume to be insignificant.

Applying this principle of heat balance means that the heat transfer rates (q) in the above equations can be equated as follows:

When a fluid is being heated or cooled:

When a fluid is changing phase:

We can use these relationships in three ways:

1. To determine characteristics of the heat exchanger, for example, the required heat transfer surface area (A).

2. If we have an existing heat exchanger with a known area, we can use this relationship to determine the outgoing product temperature (To) or the mass of fluid that can be evaporated (M).

3. To determine the characteristics of the utility fluid, for example, if we know the amount of energy to be transferred out of the product fluid (q) and the difference in temperature of the utilities fluid between inlet and outlet (∆T) we can determine the required utilities flowrate (m).

In addition to the exchanger type and fluid properties, to determine the overall heat transfer coefficient one needs to know the size and configuration of the heat exchanger components. But this can only be done once the required heat transfer surface area is known, which, requires U to be known.

To solve this problem, when sizing a heat exchanger, an initial value for U is assumed based on guidelines (examples were given in the table in the previous section). The heat transfer area of the exchanger is then calculated using this value and from that the dimensions of the exchanger components are determined.

The overall heat transfer coefficient is then recalculated based on this final design. If there is a significant difference (> 30%) between the initial U and the new recalculated U, the exchanger sizing is repeated using the new U.

Once the detailed design is known, the pressure drop across the exchanger is calculated. If this is above specification, the heat exchanger dimensions and layout have to be redesigned for a lower pressure drop.

Finally, the exchanger design and sizing are optimised to find the lowest cost exchanger.

Now let’s look at a worked example for sizing a heat exchanger.