Heat Exchanger Effectiveness⚠ unverified
Physics / Thermodynamics · Compute the effectiveness of a counterflow heat exchanger
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| NTU | NTU | — | 1.0 | Number of transfer units (dimensionless) |
| Cr | Cr | — | 1.0 | Heat-capacity rate ratio, ``C_m |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | eps | — | Heat-exchanger effectiveness (dimensionless) |
The science & history
Understanding the Parameters
- NTU — $UA$ over the smaller capacity rate; larger NTU → effectiveness approaches 1.
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$C_r$ — should select which $\varepsilon$–NTU formula applies; ignored now (always balanced counterflow formula).
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$\varepsilon$ — actual heat transfer over maximum possible $q_{\max} = C_{\min}(T_{h,\mathrm{in}} - T_{c,\mathrm{in}})$.
Derivation (Approaching a Proof)
Effectiveness–NTU method integrates the local rate equation $dq = U\Delta T\,dA$ for a chosen flow arrangement. For counterflow with $C_r = 1$ ($C_h = C_c$), the closed form is
$$\varepsilon = \frac{\mathrm{NTU}}{1+\mathrm{NTU}}.$$
For $C_r = 0$, $\varepsilon = 1 - \exp(-\mathrm{NTU})$. General $C_r$ uses a different algebraic expression — not implemented here.
History
Kays and London popularised the $\varepsilon$–NTU method for compact heat-exchanger design mid-20th century; it remains standard in HVAC and process equipment.
Related Concepts: Thermal Efficiency, First Law DeltaU, Carnot Efficiency
Notes: Registry calculator heat-exchanger-effectiveness (unverified). Unused input: $C_r$.
Formula is balanced-counterflow only.