Kostenloser LMTD Rechner
Berechnen Sie LMTD for counter-flow und parallel-flow heat exchangers. Essential for heat exchanger design und sizing.
LMTD (Counter-Flow)
69.52 °C
LMTD (Counter-Flow) vs Hot Fluid Inlet Temp
Formel
## Log-Mean Temperature Difference The LMTD is the effective average temperature difference between the hot and cold streams across a heat exchanger. It accounts for the fact that the temperature difference varies along the length. ### Formula **LMTD = (delta_T1 - delta_T2) / ln(delta_T1 / delta_T2)** For counter-flow: delta_T1 = T_hot_in - T_cold_out, delta_T2 = T_hot_out - T_cold_in. For parallel-flow: delta_T1 = T_hot_in - T_cold_in, delta_T2 = T_hot_out - T_cold_out. Counter-flow always gives a higher LMTD (and thus smaller exchanger area) than parallel-flow.
Lösungsbeispiel
Hot fluid: 150→90°C, Cold fluid: 30→70°C.
- 01Counter-flow: delta_T1 = 150 - 70 = 80°C, delta_T2 = 90 - 30 = 60°C
- 02LMTD = (80 - 60) / ln(80/60) = 20 / ln(1.333) = 20 / 0.2877 = 69.52°C
- 03Parallel-flow: delta_T1 = 150 - 30 = 120°C, delta_T2 = 90 - 70 = 20°C
- 04LMTD = (120 - 20) / ln(120/20) = 100 / ln(6) = 100 / 1.7918 = 55.80°C
Häufig Gestellte Fragen
What if delta_T1 equals delta_T2?
When the two temperature differences are equal, the LMTD formula yields 0/0 (indeterminate). In this special case, LMTD simply equals delta_T1 = delta_T2, since the temperature difference is uniform along the exchanger.
Why is counter-flow LMTD higher?
Counter-flow maintains a more uniform temperature difference along the exchanger length. Parallel-flow has a large difference at the inlet and small at the outlet, resulting in a lower effective average.
What about shell-and-tube exchangers with multiple passes?
Multi-pass exchangers are neither pure counter-flow nor parallel-flow. A correction factor F (0 to 1) is applied: effective LMTD = F × LMTD_counter. F depends on the temperature ratios P and R.
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