Log Mean Temperature Difference (LMTD) Calculator
Enter hot and cold stream temperatures and choose flow arrangement to calculate LMTD. Use consistent temperature units (°C or °F).
What is LMTD?
LMTD stands for Log Mean Temperature Difference. It is the effective average temperature driving force between hot and cold fluids in a heat exchanger. Because the temperature difference changes from one end of the exchanger to the other, a simple arithmetic average is not accurate. LMTD gives a physically meaningful average that works directly in exchanger sizing equations.
Engineers use LMTD in the classic design relationship: Q = U × A × F × LMTD, where Q is heat duty, U is overall heat transfer coefficient, A is heat transfer area, and F is the correction factor (for complex flow arrangements).
LMTD Formula
The formula is:
LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2)
If ΔT1 equals ΔT2, then LMTD is simply that same temperature difference.
Counter-current flow
- ΔT1 = Th,in − Tc,out
- ΔT2 = Th,out − Tc,in
Parallel (co-current) flow
- ΔT1 = Th,in − Tc,in
- ΔT2 = Th,out − Tc,out
How to use this LMTD calculator
- Choose the correct flow arrangement first.
- Enter inlet and outlet temperatures for both streams.
- Click Calculate LMTD.
- Optionally add Q, U, and F to estimate exchanger area.
Temperature units can be Celsius or Fahrenheit, but keep them consistent. Since LMTD is a temperature difference, the numerical difference in K and °C is the same.
Worked example
Suppose a counter-current exchanger has: Th,in = 180°C, Th,out = 120°C, Tc,in = 60°C, Tc,out = 95°C.
- ΔT1 = 180 − 95 = 85°C
- ΔT2 = 120 − 60 = 60°C
- LMTD = (85 − 60) / ln(85/60) ≈ 71.5°C
If Q = 250,000 W, U = 600 W/m²·K, and F = 0.95, then: A = 250000 / (600 × 0.95 × 71.5) ≈ 6.13 m².
Why LMTD matters in design
A small change in LMTD can significantly change required heat transfer area. Lower LMTD means you need more area (and often more capital cost). Higher LMTD allows a more compact exchanger. That is why correct temperature data, correct flow assumption, and realistic U-values are critical during preliminary sizing.
Common mistakes and troubleshooting
- Negative ΔT values: Usually indicates inconsistent temperatures or wrong flow arrangement selected.
- Mixing units: Do not enter one stream in °C and the other in °F.
- Invalid process direction: Check if hot stream is truly hotter than cold stream at both ends for your selected model.
- Forgetting correction factor F: Shell-and-tube multipass exchangers often need F less than 1.
LMTD vs. NTU method
LMTD is preferred when inlet and outlet temperatures are known or specified by process requirements. The NTU-effectiveness method is convenient when outlet temperatures are unknown and you know exchanger size and UA. In practice, engineers often use both methods at different stages of design and rating.
Quick FAQ
Can I use this for condensers and boilers?
Yes, but phase-change sections can have nearly constant temperature on one side. LMTD still applies, though segment-by-segment analysis is often better for accuracy.
Is this calculator suitable for detailed mechanical design?
No. It is a fast thermal estimate tool. Final design should include pressure drop limits, fouling factors, property variation, correction factors, and code compliance.
What if ΔT1 and ΔT2 are nearly equal?
Then LMTD approaches that same value. The calculator handles this edge case automatically to avoid numerical instability.