Heat Exchanger Effectiveness–NTU Calculator
Find the thermal effectiveness of a heat exchanger from NTU and Cr using the ε–NTU method — the standard engineering approach when outlet temperatures are unknown.
Flow arrangement
Fraction of maximum possible heat transfer actually achieved
- 1
Exponent = −NTU × (1 − Cr)
−2 × (1 − 0.5) = -1 - 2
Exponential term = e^(exponent)
e^(-1) = 0.367879 - 3
Numerator = 1 − exp term
1 − 0.367879 = 0.632121 - 4
Denominator = 1 − Cr × exp term
1 − 0.5 × 0.367879 = 0.81606 - 5
Effectiveness ε = numerator ÷ denominator
0.632121 ÷ 0.81606 = 0.7746
How does this calculator work?
Heat exchanger effectiveness ε = Q_actual / Q_max. Counter-flow: ε = (1 − e^(−NTU(1−Cr))) / (1 − Cr·e^(−NTU(1−Cr))). Enter NTU = U·A/C_min and Cr = C_min/C_max. Counter-flow always outperforms parallel-flow at the same NTU and Cr; ε → 1 as NTU → ∞ for counter-flow with Cr < 1.
Formula
How this is calculated
The ε–NTU (effectiveness–Number of Transfer Units) method analyses heat exchangers when outlet temperatures of the two fluid streams are not known in advance. NTU = U·A / C_min quantifies the thermal size of the exchanger: U is the overall heat transfer coefficient (W/m²·K), A is the heat-transfer area (m²), and C_min = ṁ·c_p is the smaller heat capacity rate (W/K) of the two fluid streams. The capacity ratio Cr = C_min / C_max (always 0–1) measures how well-matched the streams are; Cr = 0 occurs when one stream condenses or evaporates at constant temperature.
Effectiveness ε = Q_actual / Q_max, where Q_max = C_min·(T_hot,in − T_cold,in) is the heat transfer an infinitely long exchanger would achieve. For counter-flow (hot and cold streams travelling in opposite directions) the formula is ε = (1 − e^(−NTU·(1−Cr))) / (1 − Cr·e^(−NTU·(1−Cr))), with the special case ε = NTU/(1+NTU) when Cr = 1. For parallel-flow (streams in the same direction), ε = (1 − e^(−NTU·(1+Cr))) / (1 + Cr). The plot shows how ε grows with NTU at the chosen Cr and arrangement, illustrating the diminishing returns of adding more surface area.
Limitations: the method assumes steady-state operation, uniform flow distribution, constant fluid properties, no heat loss to surroundings, and purely axial flow. It does not account for fouling, variable U along the exchanger, or multi-pass shell-and-tube geometries requiring extended correction factors.
Frequently asked questions
NTU (Number of Transfer Units) is a dimensionless measure of the thermal "size" of a heat exchanger relative to C_min. NTU → ∞ means infinite area, giving the maximum possible effectiveness for the given arrangement and Cr. An NTU of 1–3 covers most practical designs.
In counter-flow the temperature difference driving heat transfer remains more uniform along the exchanger length. In parallel-flow both streams enter at the same end, creating a large initial difference that collapses toward the exit — this caps maximum effectiveness at 1/(1+Cr) regardless of NTU.
Use ε–NTU when outlet temperatures are unknown and you need to find them without iteration — which is the design case. Use the Log-Mean Temperature Difference (LMTD) method when all four temperatures are known and you want to determine the required heat-transfer area.
Also known as
TG we-Calculate Editorial Team. (2026). Heat Exchanger Effectiveness–NTU Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/effectiveness-ntu-calculator
TG we-Calculate Editorial Team. "Heat Exchanger Effectiveness–NTU Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/effectiveness-ntu-calculator.
TG we-Calculate Editorial Team, "Heat Exchanger Effectiveness–NTU Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/effectiveness-ntu-calculator
@misc{wecalculate_effectiveness_ntu_calculator, title = {Heat Exchanger Effectiveness–NTU Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/effectiveness-ntu-calculator}}, year = {2026}, note = {TG we-Calculate} }
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