LMTD Calculator - Log Mean Temperature Difference for Heat Exchangers
Calculate LMTD, ΔT1, ΔT2 and effectiveness for counterflow and parallel flow heat exchangers.
The log mean temperature difference (LMTD) is the driving force for heat transfer in a heat exchanger. Because the temperature gap between hot and cold streams changes along the length of the exchanger, you cannot just average the two end deltas - the LMTD weights them correctly. LMTD plugs straight into the heat exchanger design equation Q = UA × LMTD, where U is the overall heat transfer coefficient and A is the heat transfer surface area. The LMTD formula is (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2), with ΔT1 and ΔT2 being the temperature differences at each end of the exchanger.
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Frequently asked questions
Use LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2). For counterflow, ΔT1 = T_hot_in - T_cold_out and ΔT2 = T_hot_out - T_cold_in. For parallel flow, ΔT1 = T_hot_in - T_cold_in and ΔT2 = T_hot_out - T_cold_out. When ΔT1 = ΔT2, the natural log term is undefined, so LMTD simply equals that common value.
ΔT1 = 90 - 50 = 40°C, ΔT2 = 60 - 20 = 40°C. Since ΔT1 = ΔT2, LMTD = 40°C. This is a balanced counterflow case where both ends have the same temperature gap.
The temperature difference between hot and cold streams varies exponentially along the exchanger, not linearly, so an arithmetic mean overestimates the driving force when ΔT1 and ΔT2 differ. LMTD always gives a value less than or equal to the arithmetic mean and is the correct value to use with the Q = UA × LMTD design equation.
Solve A = Q / (U × LMTD) for the required surface area. Example: to transfer 100 kW with LMTD = 40°C and a typical shell-and-tube U of 500 W/m²·K, you need A = 100,000 / (500 × 40) = 5 m² of heat transfer area. Then pick a correction factor F (typically 0.8-1.0) for non-counterflow geometries.
Counterflow (streams flow in opposite directions) gives a higher LMTD and therefore needs less surface area for the same heat duty. Parallel flow (same direction) has a lower LMTD because the two streams approach each other and the temperature gap collapses at the outlet. Counterflow can also achieve closer approach temperatures - the cold outlet can exceed the hot outlet, which is impossible in parallel flow.