How to Use Effectiveness-NTU Calculator
The Effectiveness-NTU Calculator estimates how much of the theoretical maximum heat transfer a heat exchanger actually achieves at a given NTU and Cr.
- Pick the flow arrangement — Counter, parallel, shell-and-tube, or three cross-flow options.
- Enter NTU — NTU = UA / Cmin (dimensionless).
- Enter Cr — Cr = Cmin / Cmax, between 0 and 1.
- Read ε — The Effectiveness-NTU Calculator outputs ε (0 to 1) and the percent value.
Formula & Theory - Effectiveness-NTU Calculator
The Effectiveness-NTU Calculator uses the standard correlations:
NTU = UA / Cmin
Cr = Cmin / Cmax
ε = Q / Q_max where Q_max = Cmin (Th_in − Tc_in)Counter-flow:
ε = (1 − exp[−NTU(1 − Cr)]) / (1 − Cr · exp[−NTU(1 − Cr)])
ε = NTU / (1 + NTU) if Cr = 1Parallel-flow:
ε = (1 − exp[−NTU(1 + Cr)]) / (1 + Cr)Shell-and-tube (1 shell, 2,4,… tube passes):
s = √(1 + Cr²)
ε = 2 / { 1 + Cr + s · [(1 + e^(−NTU·s)) / (1 − e^(−NTU·s))] }Cross-flow, both unmixed:
ε = 1 − exp{ (1/Cr) · NTU^0.22 · [exp(−Cr · NTU^0.78) − 1] }| Symbol | Meaning |
|---|---|
| U | Overall heat transfer coefficient |
| A | Heat transfer area |
| Cmin, Cmax | Smaller / larger heat capacity rate (W/K) |
| NTU | Number of transfer units |
| Cr | Capacity ratio |
| ε | Effectiveness (0 to 1) |
Assumptions and Limits
- Constant U over the heat exchanger.
- Negligible heat loss to surroundings.
- Constant specific heats and no phase change unless Cr = 0.
Use Cases for Effectiveness-NTU Calculator
- Heat exchanger sizing — Find ε given NTU and pick UA accordingly.
- Rating analysis — Check whether an existing unit meets duty.
- Education — Compare arrangements side-by-side.
- Thermal design tradeoffs — Quickly explore the effect of Cr on ε.
The Effectiveness-NTU Calculator is the fastest way to compare flow arrangements at a glance.