Sizing a heat exchanger from the log mean temperature difference

Why the arithmetic temperature difference gives the wrong area, and how the log mean fixes it.

The engineering question

The exchanger computed from the average temperature difference is too small. What is the correct driving temperature difference?

Worked example

The figures below were produced by running the LMTD Calculator with the same inputs — during the build, from its authoritative engine.

Results
LMTD	32.4358 °C
Required heat transfer area	25.6918 m²
Hot-side temperature drop	30 °C
Cold-side temperature rise	25 °C
Correction factor (F)	1
Assessment	LMTD 32.4 °C (counter-flow, F = 1.0) → heat-transfer area ≈ 25.7 m² for the 500 kW duty.

Terminal differences are hot inlet less cold outlet, and hot outlet less cold inlet.
The log mean of those two differences is the true driving force.
Area is duty divided by U, the correction factor and the log mean difference.

Sanity check

LMTD always lies between the two terminal differences. A value outside that range means the temperatures have been mixed up.

Tools for this problem

These are the EngiMetric calculators that compute the numbers in this topic. Each one shows its formula, its units and its limits rather than returning a bare result.

LMTD Calculator Log mean temperature difference for a counter-flow heat exchanger and the heat transfer area it implies.

Engineering review required

This topic supports professional engineering work; it does not replace a sealed design. The result depends on site data, the governing standard and engineering judgement, and should be confirmed by a competent engineer before it is built.

References & standards

TEMA — heat exchanger standards and correction factors
Incropera & DeWitt — heat transfer