Heat Transfer Area Calculation: LMTD Method Explained with Example
Basic formula for heat transfer area A:
Q = K x A x dTm
That is: A = Q / (K x dTm)
Where: Q is heat load (W), K is overall heat transfer coefficient (W/m2.C), dTm is log-mean temperature difference (C).
1. Empirical Values of Overall Heat Transfer Coefficient K
| Exchanger Type and Media | K Range (W/m2.C) |
|---|---|
| Plate (water-water) | 3000 - 6000 |
| Shell-and-tube (water-water) | 800 - 1500 |
| Shell-and-tube (steam-water) | 2000 - 4000 |
| Air-air (finned tube) | 30 - 80 |
| Flue gas-water (with fouling) | 40 - 80 |
2. Calculation of Log-Mean Temperature Difference dTm
For counter-flow arrangement:
dTm = (dT1 - dT2) / ln(dT1/dT2)
Where: dT1 = hot fluid inlet temp - cold fluid outlet temp; dT2 = hot fluid outlet temp - cold fluid inlet temp.
3. Calculation Example
Given: Heat 5 kg/s water from 20C to 60C, heat source is 0.3 MPa saturated steam (133C), using a plate heat exchanger.
Solution:
1 Heat load: Q = 5 x 4.18 x (60-20) = 836 kW
2 Log-mean temperature difference (counter-flow): dT1 = 133-60 = 73C; dT2 = 133-20 = 113C; dTm = (113-73)/ln(113/73) = 40/ln(1.548) = 40/0.437 ~ 91.5C
3 Select K = 3000 W/m2.C (steam-water plate exchanger)
4 Heat transfer area: A = 836000 / (3000 x 91.5) ~ 3.05 m2
5 Design margin 15%: A_design = 3.05 x 1.15 ~ 3.5 m2
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