Many descriptions and articles talk about the efficiency of heat exchangers. Often they do not explain what the efficiency of a heat exchanger actually is and how to calculate it. Let us clarify.
Reviewed by Dipl.-Ing. Wolfgang Buschmeier and M.Sc. Marius Buschmeier
Heat exchanger efficiency states the ratio between the outlet temperature achieved by a medium being heated or cooled and the physically possible limit. At an efficiency of 100 % the heat exchanger reaches its limiting performance. Since efficiency strongly depends on how the heat exchanger is operated, it is often called the operating characteristic.
Before calculating the efficiency, it is important to look at the operating state of the heat exchanger. The following questions matter:
Is a medium to be cooled or heated?
Between which media is heat exchanged?
Which medium has the larger mass flow?
If a medium is to be cooled, it can reach the temperature of the cooling medium given an infinitely large heating surface. The reverse applies if the medium is to be heated.
At the inlet x₁ the hot medium has the temperature t₁₁, and the medium being heated reaches t₂₂ = t₁₁ there. At the outlet x₂ the hot medium has given up its heat: t₁₂ = t₂₁.
Knowing which media are in the heat exchanger tells you the specific heat capacity cp of both media. It describes a substance's ability to store thermal energy. If the specific heat capacity of the cold medium is lower than that of the hot medium, it heats up less readily under otherwise equal conditions than if both specific heat capacities were equal.
Knowing the mass flows of both media, the heat capacity rate Ẇ of the two streams 1 and 2 can be calculated. Which of the two is smaller decides the calculation path. Three cases are to be distinguished:
Hot water with a small mass flow ṁ₁ is to heat cold water with a large mass flow ṁ₂. The "little" hot water is not enough to heat the cold water significantly. The outlet temperature of the larger heat capacity rate therefore plays no role. Only t₂₁ and t₁₂ can approach each other – with a sufficiently large heating surface the heat exchanger thus reaches 100 % efficiency.
Since the mass flow of the hot water is much larger, it hardly loses any temperature while the cold water heats up considerably. Bringing the cold water up to temperature is no problem. For the efficiency, only the approach of t₂₂ to t₁₁ counts – the outlet temperature of the cooling water plays no role.
Both media are water with the same mass flow. Neglecting the temperature dependence of cp, both heat capacity rates are equal; C₁ and C₂ have the value 1 and both calculation paths are valid. Either t₂₂ has approached t₁₁ as closely as possible, or t₁₂ has approached t₂₁ as closely as possible – the ratio is the same in both cases.
