Library / Heat transfer and thermal systems / HTS-45
Heat transfer and thermal systems
Overall conductance of a fouled cylindrical tube
Overall conductance UA of a tube with convection and fouling on both sides and conduction through the wall.
- Ref
- HTS-45
- Rev
- v1
- Field
- Heat transfer and thermal systems
- Result
- UA [W/K]
The overall conductance of a tube with convection and fouling on both sides and conduction through the wall adds the resistances in series: 1/UA = (1/hi + Rfi)/Ai + ln(ro/ri)/(2πkL) + (1/ho + Rfo)/Ao, with Ai = 2πriL and Ao = 2πroL. Rfi and Rfo are area-specific fouling resistances on their own sides. UA does not depend on the reference area.
Overall conductance UA of a tube with convection and fouling on both sides and conduction through the wall. Rfi and Rfo are area-specific fouling resistances on their own sides; the answer does not depend on the reference area.
Calculator
- Total resistance, 1/UA0.04862 K/W
- Wall conduction resistance, ln(ro/ri)/(2πkL)0.001934 K/W
- Share of the total resistance due to fouling0.08729
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 tube conducts 20.57 W for every kelvin between the two fluids, with 8.73 % of the resistance from fouling.
- The wall itself accounts for 3.98 %, so the film coefficients and fouling decide the performance, not the metal.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (W/K) | Local step | Change in result |
|---|---|---|---|---|---|---|
| L Tube length | 0.1 to 20 m | 2.057 | 411.4 | 409.3 | +10% | +10 % |
| ho Outside coefficient | 10 to 50,000 W/(m² K) | 0.7416 | 44.72 | 43.98 | +10% | +5.22 % |
| hi Inside coefficient | 10 to 50,000 W/(m² K) | 0.6157 | 30.28 | 29.67 | +10% | +3.07 % |
| k Wall conductivity | 0.1 to 500 W/(m K) | 2.969 | 21.39 | 18.42 | +10% | +0.363 % |
| Rfi Inside fouling resistance | 0 to 0.005 m² K/W | 7.899 | 21.26 | 13.37 | +10% | −0.326 % |
| Rfo Outside fouling resistance | 0 to 0.005 m² K/W | 8.906 | 21.75 | 12.85 | +10% | −0.543 % |
| ri Inner radius | 0.005 to 0.0119 m | 13.61 | 22.74 | 9.129 | +10% | +5.66 % |
| ro Outer radius | 0.012 to 0.05 m | 20.57 | 24.52 | 3.95 | +10% | +3.49 % |
Sweep of Outside fouling resistance
| Outside fouling resistance (m² K/W) | Overall conductance (W/K) |
|---|---|
| 0 | 21.75 |
| 6.25e-4 | 18.43 |
| 0.00125 | 15.99 |
| 0.001875 | 14.12 |
| 0.0025 | 12.64 |
| 0.003125 | 11.44 |
| 0.00375 | 10.45 |
| 0.004375 | 9.616 |
| 0.005 | 8.906 |
Sweep one variable
Variables and how each one contributes
Overall conductance
What the equation gives you. Everything else feeds it.
Inner radius
The inner radius, in m. A larger inner radius adds inside area, so the conductance rises. Raising it by 10 % (to 0.011) moves the result by +5.66 %, from 20.57 to 21.73 W/K.
Outer radius
The outer radius, in m. A larger outer radius thickens the wall but adds outside area; here the net effect depends on the resistances. Raising it by 10 % (to 0.0132) moves the result by +3.49 %, from 20.57 to 21.29 W/K.
Tube length
The tube length, in m. Raises UA in direct proportion. Raising it by 10 % (to 1.1) moves the result by +10 %, from 20.57 to 22.62 W/K.
Inside coefficient
The inside convection coefficient, in W/(m² K). A larger coefficient raises UA, with falling returns once other resistances dominate. Raising it by 10 % (to 1,100) moves the result by +3.07 %, from 20.57 to 21.2 W/K.
Outside coefficient
The outside convection coefficient, in W/(m² K). A larger coefficient raises UA, with falling returns once other resistances dominate. Raising it by 10 % (to 550) moves the result by +5.22 %, from 20.57 to 21.64 W/K.
Wall conductivity
The wall conductivity, in W/(m K). A higher conductivity lowers the small wall resistance. Raising it by 10 % (to 16.5) moves the result by +0.363 %, from 20.57 to 20.64 W/K.
Inside fouling resistance
The inside fouling resistance, in m² K/W. More fouling lowers UA. Raising it by 10 % (to 1.1×10−4) moves the result by −0.326 %, from 20.57 to 20.5 W/K.
Outside fouling resistance
The outside fouling resistance, in m² K/W. More fouling lowers UA. Raising it by 10 % (to 2.2×10−4) moves the result by −0.543 %, from 20.57 to 20.46 W/K.
Worked example with the values above
- Inside resistance (film + fouling): 0.017507 K/W; wall: 0.0019345 K/W; outside: 0.029178 K/W.
- Total: 0.04862 K/W.
- UA = 1 / 0.04862 = 20.568 W/K.
Assumptions and limits
- Steady operation with constant properties and overall coefficient, and an insulated exterior.
- The flow arrangement matches the formula exactly, including which fluid is mixed.
Common mistakes
- Using the wrong stream as Cmin when forming the capacity ratio.
- Mixing up NTU with UA.
- Using a counterflow formula for a parallel or crossflow unit.
Statistics and uncertainty
Effectiveness formulas are exact for their ideal arrangements, but real exchangers have bypass, leakage and non-uniform flow, which lower performance by a few per cent to 10 %. Fouling allowances are largely judgement.
Where it is used
- Rating exchangers from known UA and flow rates.
- Estimating the effect of fouling on duty.
Maths you need
- Capacity rate: C = ṁcp, in W/K
- NTU: UA divided by Cmin
- Effectiveness: actual heat transfer over the thermodynamic maximum