What is heat exchanger efficiency?
Many descriptions and articles talk about the efficiency of heat exchangers and often make statements like, the efficiency is 100% or even higher. It is often not explained what the efficiency of a heat exchanger actually is and how it is calculated. We clarify...
The heat exchanger efficiency indicates the relationship between the outlet temperature of a medium to be heated or cooled and the physical possible limit. At an efficiency of 100%, the heat exchanger has its limit performance. Since the heat exchanger efficiency depends heavily on the way the heat exchanger is operated, it is often referred to as the operating characteristic.
To calculate the efficiency, it is important to first consider the operating status of the heat exchanger. The following questions play a role:
1. Should a medium be cooled or heated?
2. Between which media is the heat exchanged?
3. Which medium has the greater mass flow?
To 1
If a medium is to be cooled, it can reach the temperature of the cooling medium if the heating surface of the heat exchanger is infinitely large. The reverse applies if the medium is to be heated.
A temperature coordinate diagram would then look like this:
At the heat exchanger inlet x1, the hot medium has the temperature t11 and the temperature of the medium to be heated has the same temperature t22. When the hot medium has given off its heat to the cold medium at the outlet of the heat exchanger x2, it has the temperature t12 which corresponds to the temperature of the medium to be heated t21.
To 2
If you know which media are in the heat exchanger, you get a statement about the specific heat capacity cp of the two media. This describes the ability of a substance to store thermal energy. If the specific heat capacity of the cold medium is lower than that of the hot medium, it can be heated more poorly under otherwise identical conditions than if the specific heat capacity were the same.
To 3
If you know the mass flows of the two media, you can use this information to calculate the heat capacity flow of the two material flows 1 and 2. If the heat capacity flow of the first medium is less than or equal to that of the second, the following applies:
Furthermore, the ratio of the two heat capacity flows is less than or equal to 1:
This results in the following calculation basis for the heat exchanger efficiency:
EXAMPLE
Hot water with a small mass flow m1 should heat cold water with a large mass flow m2:
It becomes clear that the "little" warm water is not enough to warm up the cold water significantly.
Therefore, the outlet temperature of the larger heat capacity flow plays no role in calculating the efficiency. Only the inlet temperature of the cold mass flow t21 and the outlet temperature of the warm mass flow t12 can approach each other and so the heat exchanger can achieve an efficiency of 100% with a sufficiently large heating surface.
The reverse applies if the mass flow of hot water is greater than that of cold water.
Then the following applies to the ratio of the heat capacity flows:
The heat exchanger efficiency must then also be calculated differently:
EXAMPLE
Since the mass flow of the hot water is significantly larger than that of the cold water, the hot water has hardly lost any temperature, whereas the water to be heated was able to be warmed significantly. You have no problem getting the cold water up to temperature, so to speak. Therefore, the outlet temperature of the cooling water does not play a role in calculating the heat exchanger efficiency in this case.
If the heat capacity flows of both media are the same, the following relationship arises for the heat capacity flows:
This results in the value 1 for both C1 and C2 and both calculation methods can be used to calculate the heat exchanger efficiency.
EXAMPLE
In the following example, both m1 and m2 are water and have the same mass flow. If one ignores the temperature dependence of the specific heat capacity, both heat capacity flows are the same. In this case one can either say that t22 has approached t11 as closely as possible , or t12 has approached t21 as closely as possible. The relationship is the same in both cases.