LMTD Calculator — Logarithmic Mean Temperature Difference
Calculate the Logarithmic Mean Temperature Difference (LMTD) and Arithmetic Mean Temperature Difference (AMTD) for counter-flow and parallel-flow heat exchangers.
📐 LMTD Calculator for Heat Exchangers
The Logarithmic Mean Temperature Difference (LMTD) is the correct average temperature difference to use when analyzing heat exchangers. It accounts for the fact that the temperature difference between the hot and cold fluids varies along the length of the exchanger.
Parallel-flow: ΔT₁ = Th,in − Tc,in , ΔT₂ = Th,out − Tc,out
Counter-flow: ΔT₁ = Th,in − Tc,out , ΔT₂ = Th,out − Tc,in
Enter Flow Temperatures
📊 Results
Logarithmic Mean Temperature Difference (LMTD):
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°C (or °F)
Understanding LMTD
The LMTD method is the classical approach to sizing and rating heat exchangers. It is used in the fundamental heat transfer equation:
Where Q is the heat duty, U is the overall heat transfer coefficient, A is the heat transfer area, and F is the LMTD correction factor for multi-pass or cross-flow configurations.
Counter-Flow vs Parallel-Flow
- Counter-flow always produces a higher LMTD than parallel-flow for the same inlet/outlet temperatures.
- Counter-flow can heat the cold fluid to a temperature above the hot fluid outlet (temperature cross).
- Parallel-flow has a minimum approach temperature at the outlet — the cold fluid can never exceed the hot outlet temperature.
When to Use LMTD vs. AMTD
| Method | Formula | When to Use |
|---|---|---|
| LMTD | (ΔT₁−ΔT₂)/ln(ΔT₁/ΔT₂) | Standard heat exchanger design — accurate for all cases |
| AMTD | (ΔT₁+ΔT₂)/2 | Only when ΔT₁ ≈ ΔT₂ (within ~10%); otherwise overestimates |
Rule of thumb: If ΔT₁/ΔT₂ < 1.5, AMTD is within 1% of LMTD and may be used as a quick approximation.
Frequently Asked Questions
Because the temperature difference between the two fluids changes exponentially along the length of the exchanger. A simple arithmetic average overestimates the driving force. The logarithmic mean correctly integrates this variation.
The formula becomes 0/0 (indeterminate). In this special case, LMTD = ΔT₁ = ΔT₂. The calculator handles this automatically.
For shell-and-tube exchangers with multiple passes or cross-flow arrangements, the true mean temperature difference is F × LMTD (where LMTD is for pure counter-flow). F ≤ 1 and is obtained from charts based on P and R parameters.
No. If you get a negative value, the temperature assignments are reversed — swap the hot and cold streams or check your inlet/outlet values.