Library / Heat transfer and thermal systems / HTS-30
Heat transfer and thermal systems
Tube outlet temperature at constant wall temperature
Outlet temperature of a fluid heated or cooled in a tube whose wall is held at Tw, for constant h and cp and single-phase flow.
- Ref
- HTS-30
- Rev
- v1
- Field
- Heat transfer and thermal systems
- Result
- Tout [K]
For a fluid flowing through a tube with a constant wall temperature Tw, the temperature difference to the wall decays exponentially along the tube: Tout = Tw + (Tin − Tw) exp[−hA/(ṁcp)]. The group hA/(ṁcp) is the number of transfer units. Axial conduction and outside loss are neglected, and h is taken as constant.
Outlet temperature of a fluid heated or cooled in a tube whose wall is held at Tw, for constant h and cp and single-phase flow. A is the internal heating area; axial conduction and outside loss are neglected.
Calculator
- Number of transfer units, hA/(ṁcp)1
- Heating effectiveness, 1 − exp(−NTU)0.6321
- Heat transfer rate, ṁcp(Tout − Tin)8,850 W
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.
- The fluid leaves at 344.2 K, having covered 63.2 % of the gap between inlet and wall temperatures.
- The heat transferred is 8,850 W; doubling the area would not double it, because the driving temperature difference shrinks along the tube.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (K) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Tw Wall temperature | 250 to 1,000 K | 268.4 | 742.5 | 474.1 | +10% | +6.79 % |
| Tin Inlet temperature | 250 to 1,000 K | 325.9 | 601.8 | 275.9 | +10% | +3.21 % |
| ṁ Mass flow rate | 1e-4 to 100 kg/s | 300 | 370 | 69.97 | +10% | −0.712 % |
| A Internal heat-transfer area | 0.01 to 100 m² | 300.3 | 370 | 69.65 | +10% | +0.712 % |
| h Heat-transfer coefficient | 1 to 10,000 W/(m² K) | 300.7 | 370 | 69.3 | +10% | +0.712 % |
| cp Fluid specific heat | 500 to 5,000 J/(kg K) | 338.5 | 370 | 31.43 | +10% | −0.712 % |
Sweep of Internal heat-transfer area
| Internal heat-transfer area (m²) | Outlet temperature (K) |
|---|---|
| 0.01 | 300.3 |
| 0.03162 | 301.1 |
| 0.1 | 303.4 |
| 0.3162 | 310.2 |
| 1 | 327.5 |
| 3.162 | 355.6 |
| 10 | 369.5 |
| 31.62 | 370 |
| 100 | 370 |
Sweep one variable
Variables and how each one contributes
Outlet temperature
What the equation gives you. Everything else feeds it.
Wall temperature
The wall temperature, in K. Raises the outlet temperature towards the wall temperature. Raising it by 10 % (to 407) moves the result by +6.79 %, from 344.2 to 367.6 K.
Inlet temperature
The inlet temperature, in K. Raises the outlet temperature in proportion to the remaining difference. Raising it by 10 % (to 330) moves the result by +3.21 %, from 344.2 to 355.3 K.
Heat-transfer coefficient
The heat-transfer coefficient, in W/(m² K). A larger coefficient brings the outlet closer to the wall temperature. Raising it by 10 % (to 110) moves the result by +0.712 %, from 344.2 to 346.7 K.
Internal heat-transfer area
The internal heat-transfer area, in m². A larger area brings the outlet closer to the wall temperature. Raising it by 10 % (to 2.2) moves the result by +0.712 %, from 344.2 to 346.7 K.
Mass flow rate
The mass flow rate, in kg/s. More flow leaves less time to heat, so the outlet stays closer to the inlet. Raising it by 10 % (to 0.055) moves the result by −0.712 %, from 344.2 to 341.8 K.
Fluid specific heat
The fluid specific heat, in J/(kg K). A higher specific heat needs more heat for the same temperature change, so the outlet stays closer to the inlet. Raising it by 10 % (to 4,400) moves the result by −0.712 %, from 344.2 to 341.8 K.
Worked example with the values above
- Group: hA/(ṁcp) = 100 × 2 / (0.05 × 4,000) = 1.
- Remaining difference: exp(−1) = 0.36788.
- Tout = 370 + (300 − 370) × 0.36788 = 344.25 K.
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