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
Formula
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.
| Step | Calculation |
|---|---|
| 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.