Heat Exchanger LMTD Calculator
Find LMTD for counter-flow and parallel-flow heat exchangers.
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Formulas
LMTD = (ΔT1 - ΔT2) / ln(ΔT1/ΔT2)Counter-flow is always more efficient (higher LMTD) than parallel-flow.
LMTD Method
Used to size heat exchangers. Q = U × A × LMTD. Counter-flow: hot inlet opposite cold inlet (most efficient). Parallel: both enter same end. Counter-flow always gives higher LMTD for same temperatures.
What LMTD Means
The log mean temperature difference (LMTD) is the effective average temperature difference driving heat transfer between two fluids in a heat exchanger. Because the difference varies along the exchanger, a logarithmic average is used:
LMTD = (ΔT1 - ΔT2) / ln(ΔT1/ΔT2)ΔT1 and ΔT2 are the temperature differences between the hot and cold fluids at each end of the exchanger.
The heat transferred is then Q = U × A × LMTD, where U is the overall heat transfer coefficient and A is the surface area.
Worked Example
Hot side: 80 → 50 °C; cold side: 20 → 40 °C. End differences: ΔT1 = 80−40 = 40 K, ΔT2 = 50−20 = 30 K:
LMTD = (40 - 30) / ln(40/30) = 10 / 0.288 = 34.8 K
Counterflow vs Parallel Flow
| Arrangement | Characteristic |
|---|---|
| Counterflow | Higher LMTD, more efficient |
| Parallel flow | Lower LMTD, simpler |
Counterflow keeps a larger, more uniform temperature difference along the exchanger, so it transfers more heat for the same area.
Frequently Asked Questions
Why use a logarithmic mean rather than a simple average?
The temperature difference changes exponentially along the exchanger, not linearly. The log mean correctly weights this curve, giving the true driving difference.
What if ΔT1 equals ΔT2?
The formula becomes indeterminate (ln(1) = 0). In that case the LMTD simply equals that common temperature difference.
What is the correction factor F?
For shell-and-tube or cross-flow exchangers, LMTD is multiplied by a correction factor F (< 1) to account for the more complex flow geometry.