Science & engineering · Heat exchangers
LMTD calculator.
From the four terminal temperatures to the LMTD, and the heat duty if you know U and area.
Inputs
Result
Enter the four temperatures.
How do you calculate the log mean temperature difference?
LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2), where ΔT1 and ΔT2 are the temperature differences between the two streams at each end of the exchanger. In counterflow they are hot-in minus cold-out and hot-out minus cold-in; in parallel flow they are hot-in minus cold-in and hot-out minus cold-out. When the two end differences are equal the formula is 0/0 and the LMTD simply equals that common difference. Heat duty is Q = U · A · LMTD, multiplied by a correction factor F (at most 1) for shell-and-tube and cross-flow layouts.
Worked example. Hot fluid cooled from 150 to 90°C and cold fluid warmed from 20 to 60°C in counterflow: ΔT1 = 150 − 60 = 90 K, ΔT2 = 90 − 20 = 70 K, LMTD = 20 / ln(90/70) = 79.6 K.
Counterflow gives a larger LMTD than parallel flow for the same four temperatures. If either end difference is zero or negative the streams cross and the arrangement cannot reach those outlet temperatures.
Frequently asked questions
What does LMTD stand for?
Log mean temperature difference, the effective average temperature driving force between hot and cold streams in a heat exchanger.
Why not use a simple average of the two end differences?
Temperature difference varies exponentially along the exchanger, so the logarithmic mean is the exact average for constant U and specific heats; the arithmetic mean overstates it when the ends differ a lot.
Counterflow or parallel flow: which gives a bigger LMTD?
Counterflow, for the same inlet and outlet temperatures. That is why counterflow exchangers need less area for the same duty.
What is the correction factor F?
For shell-and-tube and cross-flow exchangers, the true mean difference is F times the counterflow LMTD, with F at most 1. F comes from charts or equations for your geometry; leave it at 1 for pure counterflow or parallel flow.
Sources
Checked
LMTD definition and counterflow end-difference pairing are from the MIT notes above; the parallel-flow pairing and equal-difference limit follow directly from the same definition. Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Engineering education reference. Assumes constant specific heats and a constant overall coefficient. Not for final heat exchanger design, which requires fouling allowances, F-factors and vendor or code verification.