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Counter-currentCo-current (parallel)Optional F correction

LMTD Calculator

Calculate the log mean temperature difference for a heat exchanger from the four terminal temperatures, for counter-current or co-current (parallel) flow, with an optional correction factor for multi-pass shell-and-tube units.

Flow arrangement

Counter-current
Co-current (parallel)
ΔT1
ΔT2
LMTD
Corrected MTD (F × LMTD)

Formula

Counter-current: ΔT1 = Th,in − Tc,out ΔT2 = Th,out − Tc,in Co-current: ΔT1 = Th,in − Tc,in ΔT2 = Th,out − Tc,out LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2) Corrected MTD = F × LMTD (F = 1.0 for true counter-current; F < 1 for multi-pass shell-and-tube, read from TEMA/Bowman charts for the actual pass configuration)

If ΔT1 equals ΔT2 (a balanced, symmetric temperature approach), the ln term is undefined — in that special case LMTD simply equals ΔT1 (=ΔT2), which this calculator handles automatically.

Worked example

Counter-current exchanger: hot fluid 150 °C → 90 °C, cold fluid 25 °C → 80 °C.

StepCalculation
ΔT1 (hot in − cold out)150 − 80 = 70 °C
ΔT2 (hot out − cold in)90 − 25 = 65 °C
LMTD(70 − 65) / ln(70/65) = 5 / 0.0741 = 67.5 °C

For a 1 shell-pass, 2 tube-pass exchanger doing this same duty, F is typically in the range 0.85–0.95 depending on the dimensionless temperature ratios — read the exact value from a TEMA/Bowman F chart for the specific pass arrangement, then multiply: corrected MTD = F × 67.5 °C.

Frequently asked questions

When do I need the correction factor F?

F = 1.0 only for true counter-current or true co-current (single-pass) flow. Any multi-pass shell-and-tube, cross-flow, or multi-shell arrangement needs F < 1, read from the standard Bowman/TEMA charts for that specific pass configuration (1-2, 2-4, cross-flow, etc.) using the dimensionless ratios P and R.

Why is counter-current LMTD usually higher than co-current for the same four temperatures?

Counter-current flow maintains a more even temperature difference along the exchanger length, avoiding the "temperature cross" problem, so it delivers a higher LMTD — and therefore requires less heat transfer area — for the same duty and terminal temperatures.

What if the calculator shows a warning about temperature cross?

A temperature cross (cold outlet warmer than hot outlet, or similar) is only physically achievable in true counter-current flow, and even then it constrains F sharply in multi-pass units — sometimes making the required duty impossible in a 1-2 pass configuration. This calculator flags where the entered temperatures imply that condition.

Can I use this for condensing or evaporating service?

Only if one side has a genuinely constant temperature (isothermal condensation/evaporation) — LMTD in that special case reduces to using the constant temperature at both ends of that side. For sensible-heat-only duties (both streams changing temperature), the standard LMTD formula above applies directly.

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