Heat Exchanger (LMTD) Calculator
Size a heat exchanger by the LMTD method — log-mean temperature difference, correction factor F, fouling, and required area for counter-current, co-current, and shell-and-tube.
When to use this calculator
Use for thermal sizing at the specification stage, when you have the four terminal temperatures and a duty and need the area to put on an enquiry. It computes the log-mean temperature difference, applies the Bowman correction factor F for shell-and-tube arrangements, derates the coefficient for fouling, and reports clean, service, and design areas separately so you can see exactly what the fouling allowance and the design margin are costing. It also flags a temperature cross, which is the condition that quietly invalidates a single-shell selection.
Required inputs
- Arrangement — counter-current, co-current, or shell-and-tube (1 shell / 2N tube passes)
- Four terminal temperatures: hot in and out, cold in and out
- Heat duty Q and overall coefficient U
- Fouling resistance R_f and design margin, plus the number of shells in series
Expected outputs
- ΔT1, ΔT2, and the LMTD
- Correction factor F, with the P and R parameters behind it
- Corrected mean temperature difference F·LMTD
- Clean, service, and design area, and the UA product
- Temperature-cross warning when the arrangement is not feasible
Formula overview
SI: temperatures in °C, duty in kW, U in W/m²·K, area in m², R_f in m²·K/W. US: °F, BTU/hr, BTU/hr·ft²·°F, ft². Because LMTD is a temperature difference, a value in °C equals the same value in K.
LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2)
counter-current ΔT1 = Th,in − Tc,out ΔT2 = Th,out − Tc,in
co-current ΔT1 = Th,in − Tc,in ΔT2 = Th,out − Tc,out
Correction factor, 1 shell / 2N tube passes (Bowman, Mueller & Nagle):
P = (Tc,out − Tc,in) / (Th,in − Tc,in)
R = (Th,in − Th,out) / (Tc,out − Tc,in)
F = f(P, R), extended to N shells in series; F = 1 for pure
counter-current and co-current flow
Fouling and area:
1/U_service = 1/U_clean + R_f
A = Q / (U_service · F · LMTD)
A_design = A · (1 + margin) UA = Q / (F · LMTD)Worked example
Counter-current water-to-water cooler:
hot 80 → 45 °C, cold 20 → 40 °C, Q = 350 kW, U_clean = 1200 W/m²·K
ΔT1 = 80 − 40 = 40 °C
ΔT2 = 45 − 20 = 25 °C
LMTD = (40 − 25) / ln(40/25) = 15 / 0.4700 = 31.9 °C
F = 1.0 (pure counter-current)
Clean area: A = 350 000 / (1200 × 31.9) = 9.1 m²
With R_f = 0.0002 m²·K/W:
U_service = 1 / (1/1200 + 0.0002) = 968 W/m²·K
A_service = 350 000 / (968 × 31.9) = 11.3 m²
A modest fouling allowance has added 24% to the area — which is why
clean and service areas are reported separately.Common mistakes
- Leaving F at 1.0 for a shell-and-tube exchanger. A 1-2 exchanger is partly co-current inside, so F is always below 1 and can fall steeply as the temperature approach tightens. Sizing on the uncorrected LMTD under-sizes the unit.
- Accepting a design where F has collapsed. Once F drops below about 0.8 the selection is very sensitive to small temperature errors — the fix is more shells in series or a genuinely counter-current arrangement, not a bigger single shell.
- Treating the clean area as the answer. The area to buy is the service area with fouling, plus whatever design margin the specification calls for; the clean figure is only useful for seeing how much the fouling allowance costs.
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