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Heat Exchanger LMTD Calculator

Work out heat exchanger lmtd instantly with clear inputs, formula shown and shareable results.

About Heat Exchanger LMTD Calculator

Because the temperature difference varies along a heat exchanger, the correct average is logarithmic: (dT1 - dT2)/ln(dT1/dT2). With 60 K at one end and 20 K at the other the LMTD is 36.4 K, not the 40 K an arithmetic mean would suggest - so using the simple mean would oversize the duty by 10%.

Formulas

Log mean temperature difference

LMTD = (dT1 - dT2) / ln(dT1 / dT2)

Heat duty

Q = U A x LMTD

Worked example

With the default values below, Heat Exchanger LMTD Calculator returns Log Mean Temperature Difference of 36.410. Change any input above and every figure here is recalculated in your browser.

Inputs used

Temperature difference at one endminimum 0 K
60 K
Temperature difference at the other endminimum 0 K
20 K
Overall UA valueminimum 0 W/K
500 W/K

Results

Log Mean Temperature Difference
36.410 K
Arithmetic Mean For Comparison
40.000 K
Heat Duty At That UA
18,204.8 W
LMTD As A Fraction Of The Arithmetic Mean
0.9102

Step by step

  1. 1Values used
  2. 2Log mean temperature difference
  3. 3Heat duty
  4. 4Log Mean Temperature Difference= 36.410 K
  5. 5Arithmetic Mean For Comparison= 40.000 K
  6. 6Heat Duty At That UA= 18,204.8 W
  7. 7LMTD As A Fraction Of The Arithmetic Mean= 0.9102

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

When is the arithmetic mean acceptable?

When the two terminal differences are within about 40% of each other, the error is under 2%. Wide ratios need the log form.

What if the two differences are equal?

The logarithm becomes indeterminate but the limit is simply that common difference, which the calculator returns directly.

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