Every heat exchanger you'll ever size — a car radiator, an HVAC chiller, a power-plant condenser, a process cooler — comes down to one equation: Q = U·A·LMTD. And the trickiest term in it is the LMTD, the log-mean temperature difference — the true average temperature gap driving heat from the hot fluid to the cold one. Use a simple average instead and you'll undersize your exchanger. This free LMTD calculator (validated against standard references) computes the log-mean temperature difference for counterflow and parallel flow, then gives you the heat duty, required area, or UA in one step.
Table of Contents
The LMTD & Duty Calculator
Enter the four stream temperatures and choose the flow arrangement. The tool returns the LMTD and the terminal differences, and — if you add U, A or Q — the heat duty, required area, or UA. Works in °C, K or °F (keep all four temperatures in the same unit).
🔥 Heat Exchanger LMTD Calculator
What Is LMTD?
Inside a heat exchanger, the temperature gap between the hot and cold fluids is not constant — it's large at one end and small at the other. Since heat transfer is driven by that gap, we need a single effective average to represent the whole exchanger. That average is the log-mean temperature difference (LMTD).
The LMTD Formula
where ΔT₁ and ΔT₂ are the temperature differences between the hot and cold streams at the two ends of the exchanger. The only subtlety is how you define those two end differences — and that depends on the flow arrangement.
Counterflow vs Parallel Flow
| Arrangement | ΔT₁ (one end) | ΔT₂ (other end) |
|---|---|---|
| Counterflow (streams opposite) | Th,in − Tc,out | Th,out − Tc,in |
| Parallel flow (streams together) | Th,in − Tc,in | Th,out − Tc,out |
Counterflow almost always wins. For the same four temperatures it produces a higher LMTD, so it needs less area for the same duty. It can also cool the hot stream below the cold outlet temperature — something parallel flow physically cannot do. That's why the vast majority of real exchangers are designed as counterflow (or as close to it as geometry allows). The flow regime inside the tubes also matters for the heat-transfer coefficient — check it with our Reynolds number calculator.
Heat Duty: Q = U·A·LMTD
Once you have the LMTD, the exchanger's heat duty (the rate of heat transfer) follows from the master sizing equation:
Rearrange it to solve for whatever you need:
where Q is the duty (W), U the overall heat-transfer coefficient (W/m²·K), A the surface area (m²), and F the correction factor. You should always get the same duty from an energy balance on either stream: Q = ṁ·cp·ΔT. This is a heat-transfer cousin of the sensible-heat load in our HVAC AC load calculator, and the same U·A·ΔT thinking used when sizing a chiller's cooling load.
The Correction Factor F
The plain LMTD formula is exact only for pure counterflow or parallel flow. Real shell-and-tube and cross-flow exchangers have more complex internal paths that aren't perfectly counterflow, so we apply a correction factor F (between 0 and 1):
- F = 1.0 — ideal single-pass counterflow or parallel flow.
- F < 1.0 — multipass shell-and-tube or cross-flow; read F from standard charts using the dimensionless ratios
RandP. - Keep F above ~0.75–0.8. A very low F means the arrangement is a poor thermal match — add shell passes or rethink the design.
Worked Examples
Example 1 — Counterflow cooler
Hot fluid 100 → 60 °C, cold fluid 20 → 50 °C, counterflow:
- ΔT₁ = 100 − 50 = 50 °C; ΔT₂ = 60 − 20 = 40 °C
- LMTD = (50 − 40) / ln(50/40) = 44.8 °C
- With U = 500 W/m²·K and A = 10 m²: Q = 500 × 10 × 44.8 = 224 kW
Example 2 — Same duty, parallel flow
Same temperatures but parallel flow:
- ΔT₁ = 100 − 20 = 80 °C; ΔT₂ = 60 − 50 = 10 °C
- LMTD = (80 − 10) / ln(80/10) = 33.7 °C — much lower
- For the same 224 kW you'd now need A = 224000 / (500 × 33.7) ≈ 13.3 m² — about 33% more area!
Example 3 — Sizing for a target duty
Need 250 kW with U = 500 and the counterflow LMTD of 44.8 °C:
- A = 250000 / (500 × 44.8) ≈ 11.2 m²
Common Mistakes
- Using the arithmetic mean instead of LMTD. It's always too optimistic and undersizes the exchanger.
- Swapping the terminal differences. Counterflow and parallel flow define ΔT₁/ΔT₂ differently — use the right pairing.
- Forgetting the F factor. Shell-and-tube and cross-flow need F < 1; using raw counterflow LMTD overstates performance.
- Temperature cross. If a terminal ΔT goes zero or negative, the temperatures are physically impossible for that arrangement — the calculator flags this.
- Applying LMTD across a phase change with big property swings. For boiling/condensing with large changes, split into zones or use effectiveness-NTU.
- Assuming constant U. Fouling and property changes shift U over time; add a fouling margin.
- Mixing temperature units. Keep all four temperatures in the same scale (°C, K or °F).
Frequently Asked Questions
What is LMTD?
The log-mean temperature difference — the correct average temperature driving force between hot and cold fluids along a heat exchanger. Because the gap changes end to end, a simple average overstates it; the log-mean is the value used in Q = U·A·LMTD.
What is the LMTD formula?
LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂). For counterflow, ΔT₁ = Th,in − Tc,out and ΔT₂ = Th,out − Tc,in; for parallel flow, ΔT₁ = Th,in − Tc,in and ΔT₂ = Th,out − Tc,out.
Why is counterflow better than parallel flow?
It keeps a more uniform temperature gap, giving a higher LMTD for the same temperatures, so it needs less area. It can also cool the hot stream below the cold outlet — impossible in parallel flow.
What is heat duty in a heat exchanger?
Q, the rate of heat transfer (W or kW). Found from Q = U·A·F·LMTD, or from an energy balance Q = ṁ·cp·ΔT on either stream.
What is the LMTD correction factor F?
A factor (0–1) that corrects counterflow LMTD for real shell-and-tube or cross-flow geometry. F = 1 for ideal single-pass; read F < 1 from charts using R and P, and keep it above ~0.75–0.8.
Can I use LMTD when a fluid changes phase?
Yes if the phase-change fluid stays at nearly constant temperature (condensers/evaporators) — use that constant temperature at both ends. For large property changes, split into zones or use effectiveness-NTU.
Conclusion
The LMTD is the heart of heat-exchanger sizing: it captures the real temperature driving force, and it feeds straight into Q = U·A·F·LMTD to give you duty, area, or UA. Get the flow arrangement right, apply a correction factor for shell-and-tube or cross-flow, and never fall back on a simple average. Do that and your exchanger will be sized correctly the first time.
Use the calculator above whenever you rate or size an exchanger — four temperatures in, LMTD and duty out, with counterflow-vs-parallel and correction factors handled for you.
For more heat transfer, fluid mechanics and CFD tutorials plus free engineering calculators, explore Free CFD Tutorial. If this tool helped you, please share it with your colleagues and students.