Library / Heat transfer and thermal systems / HTS-29
Heat transfer and thermal systems
Dittus–Boelter Nusselt number for heating or cooling
Turbulent Nusselt number in a smooth tube, with the exponent n = 0.4 when the fluid is heated and 0.3 when it is cooled.
- Ref
- HTS-29
- Rev
- v1
- Field
- Heat transfer and thermal systems
- Result
- NuD
The Dittus–Boelter correlation Nu = 0.023 Re^0.8 Prⁿ describes turbulent flow in a smooth tube, with n = 0.4 when the fluid is heated and 0.3 when it is cooled. This version takes n as an input, generalising the fixed heating form on the existing page. It holds for Re ≥ 10⁴, 0.7 ≤ Pr ≤ 160 and L/D ≥ 10, with bulk properties.
Turbulent Nusselt number in a smooth tube, with the exponent n = 0.4 when the fluid is heated and 0.3 when it is cooled. It generalises the fixed heating form on the existing Dittus–Boelter page. Use for Re ≥ 10⁴, 0.7 ≤ Pr ≤ 160 and L/D ≥ 10.
Calculator
- Nusselt number for heating (n = 0.4)230
- Nusselt number for cooling (n = 0.3)230
- Coefficient for water with k = 0.6 W/(m K) in a 20 mm tube6,900 W/(m² K)
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.
- With n = 0.4 the Nusselt number is 230; the heating form would give 230 and the cooling form 230.
- At Pr = 1 the exponent has no effect, since 1 to any power is 1; the heating and cooling forms differ only when Pr moves away from 1.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| Pr Prandtl number | 0.7 to 160 | 199.4 | 1,751 | 1,552 | +10% | +3.89 % |
| ReD Reynolds number based on diameter | 10,000 to 1,000,000 | 36.45 | 1,451 | 1,415 | +10% | +7.92 % |
| n Exponent (0.4 heating, 0.3 cooling) | 0.3 to 0.4 | 230 | 230 | 0 | +10% | 0 % |
Sweep of Reynolds number based on diameter
| Reynolds number based on diameter | Nusselt number |
|---|---|
| 10,000 | 36.45 |
| 133,800 | 290.2 |
| 257,500 | 490.2 |
| 381,300 | 671 |
| 505,000 | 840.2 |
| 628,800 | 1,001 |
| 752,500 | 1,156 |
| 876,300 | 1,306 |
| 1,000,000 | 1,451 |
Sweep one variable
Variables and how each one contributes
Nusselt number
What the equation gives you. Everything else feeds it.
Reynolds number based on diameter
The Reynolds number based on the tube diameter. Raises the Nusselt number as Re^0.8. Raising it by 10 % (to 110,000) moves the result by +7.92 %, from 230 to 248.2.
Prandtl number
The Prandtl number. Raises the Nusselt number as Prⁿ. Raising it by 10 % (to 1.1) moves the result by +3.89 %, from 230 to 238.9.
Exponent (0.4 heating, 0.3 cooling)
The Prandtl exponent: 0.4 for heating, 0.3 for cooling. A larger exponent gives a larger Nusselt number when Pr is above 1. Raising it by 10 % (to 0.44) moves the result by +0 %, from 230 to 230.
Worked example with the values above
- Reynolds term: Re^0.8 = 100,000^0.8 = 10,000.
- Prandtl term: Pr^n = 1^0.4 = 1.
- Nu = 0.023 × 10,000 × 1 = 230.
Assumptions and limits
- Fluid properties are evaluated at the film or bulk temperature as stated, and are otherwise constant.
- The geometry and flow regime match the correlation range, such as smooth tubes, single cylinders or isothermal plates.
Common mistakes
- Using a correlation outside its Reynolds, Prandtl or Rayleigh range.
- Using the wrong characteristic length, for example plate length instead of tube diameter.
- Taking the properties at the wall or free-stream temperature when the film temperature is intended.
Statistics and uncertainty
Published correlations typically scatter by 10 % to 25 % against experiment, and the property evaluation temperature adds to the error. Use the result as an estimate to be confirmed by test for critical designs.
Where it is used
- Estimating coefficients for heat sinks, ducts, tubes and walls.
- Screening calculations before a detailed model or test.
Maths you need
- Reynolds number: Re = ρUL/μ
- Prandtl number: Pr = μcp/k
- Nusselt number: Nu = hL/k