Heat Exchanger LMTD Calculator

The log-mean temperature difference of a heat exchanger and the area needed for a given duty.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Heat flows from the hot fluid to the cold fluid across the exchanger wall, but the temperature difference changes along the length. The log-mean temperature difference is the right average for a counter-flow or parallel-flow exchanger: ΔTlm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2).

The area then follows from Q = U A ΔTlm. For shell-and-tube and cross-flow exchangers a correction factor below 1 applies, so the real area is larger. The overall coefficient U should include fouling.

Formulas used

  • \Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)}
  • Q = U A\,\Delta T_{lm}

Worked example

With the default numbers in the calculator above:

  1. Temperature difference at each end: 90 K and 70 K
  2. Log-mean temperature difference: 79.58 K
  3. Area needed for the duty: 7.854 m²

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Which is better, counter-flow or parallel flow?

Counter-flow. It gives a larger log-mean difference for the same end temperatures, so a smaller exchanger.

What is a typical U?

Clean water to water in a shell-and-tube exchanger is roughly 800 to 1500 W/m²·K. Use the supplier figure when you have it.

What if the temperatures cross?

This simple method needs both end differences above zero. A temperature cross needs more than one pass.

Related calculators

Further reading: Incropera and DeWitt, Fundamentals of Heat and Mass Transfer; Cengel, Heat and Mass Transfer.

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