Number of Transfer Units (NTU)

Also known as NTU method

\mathrm{NTU} = \frac{U A}{\dot{m} \, c_p}

Fluid

Worked example: UA 4000 W/K against 1.5 kg/s of water → NTU 0.637 — press Try an example to run it live, then adjust anything.

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Number of Transfer Units (NTU) explained

NTU is an exchanger's size measured in the only currency that matters — conductance compared with the thermal inertia of the fluid flowing through it. UA is how well the machine can transfer; ṁcₚ is how much heat the limiting stream can carry per degree. Their ratio is dimensionless and tells you immediately what class of equipment you are holding: NTU below 0.5 is a trim heater that barely touches the fluid, 1–3 is normal process duty, 3–5 is a close-approach unit, and above 5 you are in regenerator and cryogenic territory where surface becomes very expensive per degree gained.

The effectiveness-NTU method was developed by W. M. Kays and A. L. London for the compact heat exchangers of gas-turbine regenerators and published in Compact Heat Exchangers (1955) — a book still on working desks seventy years later. Their motivation was practical: LMTD design demands all four terminal temperatures, but a regenerator problem usually gives you the two inlets and asks what comes out, which drives LMTD into iteration and NTU straight to an answer. Worked example: U = 500 W/(m²·K) on 8 m² against 1.5 kg/s of water gives NTU = 4000/6279 = 0.64, a small unit. Trap: ṁcₚ must be the minimum stream's, not whichever stream you measured first.

Number of Transfer Units (NTU) formula

\mathrm{NTU} = \frac{U A}{\dot{m} \, c_p}

Where

$\mathrm{NTU}$ = Number of transfer units
$U$ = Overall coefficient (W/(m²·K))
$A$ = Heat transfer area (m²)
$\dot{m}$ = Minimum stream mass flow (kg/h)
$c_p$ = Minimum stream specific heat (J/(kg·K))

Missing one of these? Work it out first, then come back

Number of transfer units — Effectiveness from NTU (Counterflow), Packed Column Height from HTU and NTU
Overall coefficient — Overall Heat Transfer Coefficient (U), Overall U from Total Resistance
Heat transfer area — Heat Exchanger Duty (Q = U·A·F·LMTD), Newton's Law of Cooling (Q = hAΔT)
Minimum stream mass flow — Capacity Rate Ratio (Cr), Maximum Possible Heat Transfer (Qmax)
Minimum stream specific heat — Maximum Possible Heat Transfer (Qmax), Stream Duty from Mass Flow (Q = ṁcΔT)

Part of this formula set

The effectiveness-NTU method

5 formulasSizing or rating a heat exchanger without knowing the outlet temperatures — capacity rates, NTU, effectiveness and the maximum possible duty.