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Effectiveness compares actual heat-transfer rate with the maximum possible for the inlet states.
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Formula
ε dimensionless; heat rate in W
| Symbol | Meaning | Unit |
|---|---|---|
| Thermal effectiveness | dimensionless | |
| Q̇ | Actual heat-transfer rate | W |
| Q̇max | Maximum rate based on inlet temperatures and the smaller heat-capacity rate | W |
\varepsilon=\frac{\dot Q}{\dot Q_{max}}This is the basis of the ε-NTU method. Qmax=Cmin(Th,in−Tc,in); the ε-NTU relation depends on parallel-flow, counterflow or other arrangement. Ambient losses and phase change require adjusted models.
This is the basis of the ε-NTU method. Qmax=Cmin(Th,in−Tc,in); the ε-NTU relation depends on parallel-flow, counterflow or other arrangement. Ambient losses and phase change require adjusted models.
Effectiveness compares actual heat-transfer rate with the maximum possible for the inlet states.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Heat-exchanger effectiveness” and check its unit and magnitude.
If an exchanger transfers 60 kW when Qmax=100 kW, ε=0.60.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: ε dimensionless; heat rate in W.
Formula cluster
Effectiveness compares actual heat-transfer rate with the maximum possible for the inlet states.
If an exchanger transfers 60 kW when Qmax=100 kW, ε=0.60.
Compare exchangers without relying on one measured temperature difference.
Here is how to work through a typical Heat-exchanger effectiveness (ε = Q̇/Q̇max) task step by step:
Task
Work through the numerical example for “Heat-exchanger effectiveness” and check its unit and magnitude.
Solution path
If an exchanger transfers 60 kW when Qmax=100 kW, ε=0.60.
Qmax is Cmin times the inlet-temperature difference, where Cmin is the smaller stream heat-capacity rate ṁcp. It represents the limit where the lower-capacity stream could reach the other inlet temperature. Ambient losses change the balance. Use the smaller heat-capacity rate and actual exchanger arrangement. Application: Compare exchangers without relying on one measured temperature difference. The numerical example If an exchanger transfers 60 kW when Qmax=100 kW, ε=0.60 anchors the idea in a concrete measurement case. The corresponding units are ε dimensionless; heat rate in W. If an exchanger transfers 60 kW when Qmax=100 kW, ε=0.60. This checks that the reference quantities are compatible.
ε-NTU is useful when outlet temperatures are unknown; it relates effectiveness, NTU and capacity-rate ratio. LMTD uses logarithmic mean temperature difference and is convenient when terminal temperatures are known. Both require heat balances and defined flow arrangement. Use the smaller heat-capacity rate and actual exchanger arrangement. The corresponding units are ε dimensionless; heat rate in W. If an exchanger transfers 60 kW when Qmax=100 kW, ε=0.60. This checks that the reference quantities are compatible. Scope: This is the basis of the ε-NTU method. Qmax=Cmin(Th,in−Tc,in); the ε-NTU relation depends on parallel-flow, counterflow or other arrangement. Ambient losses and phase change require adjusted models. A practical application is Compare exchangers without relying on one measured temperature difference.
For a conventional exchanger between finite inlet temperatures, ε lies between zero and one when Qmax is defined consistently and no extra energy source exists. Values outside often indicate swapped streams, unit errors or an unsuitable balance boundary. Use the smaller heat-capacity rate and actual exchanger arrangement. Scope: This is the basis of the ε-NTU method. Qmax=Cmin(Th,in−Tc,in); the ε-NTU relation depends on parallel-flow, counterflow or other arrangement. Ambient losses and phase change require adjusted models. A practical application is Compare exchangers without relying on one measured temperature difference.
Write the quantity and unit from the variable list next to every value: ε dimensionless; heat rate in W. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example If an exchanger transfers 60 kW when Qmax=100 kW, ε=0.60. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Use the smaller heat-capacity rate and actual exchanger arrangement.
The background states this starting condition: This is the basis of the ε-NTU method. Qmax=Cmin(Th,in−Tc,in); the ε-NTU relation depends on parallel-flow, counterflow or other. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Use the smaller heat-capacity rate and actual exchanger arrangement.
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Curated exam set for "Heat-exchanger effectiveness":
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Which formula describes Heat-exchanger effectiveness?
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How do you rearrange Heat-exchanger effectiveness for Base equation for the target quantity?
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Which common mistake happens with Heat-exchanger effectiveness?
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