Library / Heat Transfer / HTR-18
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
- 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.
- 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
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| UA Overall conductance | 10 to 100,000 W/K | 0.01 | 100 | 99.99 | +10% | +10 % |
| Cmin Smaller heat-capacity rate | 10 to 100,000 W/K | 0.01 | 100 | 99.99 | +10% | −9.09 % |
Sweep of Overall conductance
| Overall conductance (W/K) | Number of transfer units |
|---|---|
| 10 | 0.01 |
| 31.62 | 0.03162 |
| 100 | 0.1 |
| 316.2 | 0.3162 |
| 1,000 | 1 |
| 3,162 | 3.162 |
| 10,000 | 10 |
| 31,620 | 31.62 |
| 100,000 | 100 |
Sweep one variable
Variables and how each one contributes
Number of transfer units
What the equation gives you. Everything else feeds it.
Overall conductance
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.
Smaller heat-capacity rate
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
- Ratio of the two quantities: UA / Cmin = 1,000 / 1,000.
- The units W/K cancel, leaving a pure number.
- 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