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Heat Transfer

Number of transfer units of a heat exchanger

Size of an exchanger relative to the smaller heat-capacity rate: the overall conductance divided by Cmin.

Ref
HTR-18
Rev
v1
Field
Heat Transfer
Result
NTU

The number of transfer units, NTU = UA/Cmin, compares the size of the exchanger (overall conductance UA, in W/K) with the smaller heat-capacity rate. A large NTU means the exchanger is big enough to bring the streams close to the same temperature; a small NTU means the stream passes too quickly for much heat to cross. NTU is the quantity that goes into the effectiveness formula, together with Cr = Cmin/Cmax.

Size of an exchanger relative to the smaller heat-capacity rate: the overall conductance divided by Cmin. A larger NTU means more of the available heat transfer can be achieved.

Calculator

Solve for
W/K
10100,000
W/K
10100,000
  • Counterflow effectiveness at Cr = 0.50.5647
  • Counterflow effectiveness at Cr = 10.5
  • Effectiveness at Cr = 0 (boiling or condensing)0.6321

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Number of transfer units () current value 1
UAOverall conductanceKey driver
0.01100
CminSmaller heat-capacity rate
0.01100
  • An exchanger with UA = 1,000 W/K serving a stream with Cmin = 1,000 W/K has NTU = 1. A counterflow unit with balanced flows would reach only 50 % effectiveness.
  • At balanced flow (Cr = 1) an NTU of 3 gives only 75 % effectiveness and an NTU of 9 gives 90 %, so each further gain in effectiveness needs a much larger exchanger.
Chart data as tables

Ranked variables

VariableTypical rangeLowest resultHighest resultSwing ()Local stepChange in result
UA Overall conductance10 to 100,000 W/K0.0110099.99+10%+10 %
Cmin Smaller heat-capacity rate10 to 100,000 W/K0.0110099.99+10%−9.09 %

Sweep of Overall conductance

Overall conductance (W/K)Number of transfer units
100.01
31.620.03162
1000.1
316.20.3162
1,0001
3,1623.162
10,00010
31,62031.62
100,000100

Sweep one variable

Number of transfer units ()Hover, touch, or use the arrow keys on the chart
020406080100 10100100010k100k Overall conductance (W/K), log scale now 1

Variables and how each one contributes

NTU

Number of transfer units

Result ·

What the equation gives you. Everything else feeds it.

UA

Overall conductance

W/K · typical 10 to 100,000

The overall heat-transfer conductance of the exchanger, in W/K: the overall coefficient U times the area A. Raises NTU in direct proportion: a larger exchanger has more transfer capacity. Raising it by 100 W/K (to 1,100 W/K) moves the result by +10 %, from 1 to 1.1.

Cmin

Smaller heat-capacity rate

W/K · typical 10 to 100,000

The smaller of the two heat-capacity rates, in W/K. Lowers NTU in inverse proportion: a larger flow gives the heat less time to cross. Raising it by 100 W/K (to 1,100 W/K) moves the result by −9.09 %, from 1 to 0.9091.

Worked example with the values above

  1. Ratio of the two quantities: UA / Cmin = 1,000 / 1,000.
  2. The units W/K cancel, leaving a pure number.
  3. NTU = 1.

Assumptions and limits

  • A steady exchanger with constant UA and constant specific heats.
  • Cmin being the smaller of the two heat-capacity rates.

Common mistakes

  • Using the larger heat-capacity rate in the denominator.
  • Using UA in W/m² K (the overall coefficient alone) without the area.

Statistics and uncertainty

UA is rarely known better than ±10 % because the overall coefficient depends on fouling, and Cmin to a few per cent, so NTU is uncertain by about 10 %. Fouling reduces UA over time; allow for it with a margin.

Where it is used

  • Sizing an exchanger by the effectiveness–NTU method.
  • Checking how much effectiveness is gained from a larger exchanger.

Maths you need

  • Overall heat-transfer coefficient: U, in W/(m² K)
  • Heat-capacity rate: mass flow times specific heat, in W/K

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