ConverterHub

LMTD Heat Exchanger Calculator

Enter the four stream temperatures and the flow arrangement to find the LMTD.

How it is calculated

You enter the hot stream inlet and outlet temperatures, the cold stream inlet and outlet temperatures, and the flow arrangement. For counter-current flow the tool takes 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. Then LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁ ÷ ΔT₂), and if the two differences are equal, LMTD equals that value. Temperatures are in °C. If either end difference is zero or negative (a temperature cross, or a typed-in error) there is no result. Values are shown to three decimals.

Worked example

A hot oil stream cools from 120 °C to 70 °C while water heats from 25 °C to 60 °C in a counter-current exchanger. Step 1: ΔT₁ = 120 − 60 = 60 °C. Step 2: ΔT₂ = 70 − 25 = 45 °C. Step 3: LMTD = (60 − 45) ÷ ln(60 ÷ 45) = 15 ÷ 0.28768 = 52.141. The tool shows 52.141 °C. With the same temperatures in parallel flow, the end differences become 95 °C and 10 °C and the LMTD drops to 37.756 °C.

Try this example →

Common mistakes

  • Pairing the wrong ends for counter-current flow: hot inlet goes with cold outlet, not cold inlet. Using the parallel pairing gives 37.756 °C instead of 52.141 °C for the example.
  • Using the arithmetic mean of the two end differences. For these values it is 52.5 °C, which is close here but overstates the driving force more and more as the two differences move apart.
  • Entering temperatures in °F: the result is labelled °C and the logarithmic mean of Fahrenheit differences is not a valid °C value.
  • Swapping hot and cold stream columns, which can give a negative end difference and no result.
  • Applying LMTD directly to multi-pass or cross-flow exchangers; those need a correction factor that this tool does not include.

About this calculator

The log mean temperature difference (LMTD) is the correct average driving temperature difference to use when sizing a heat exchanger, because the temperature gap between hot and cold streams changes continuously along the exchanger's length. It's calculated as LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁ ÷ ΔT₂), where ΔT₁ and ΔT₂ are the temperature differences between the hot and cold streams at each end of the exchanger — arranged differently depending on whether the flow is counter-current or parallel (co-current).

Mechanical and chemical engineers use LMTD, together with the overall heat transfer coefficient (U) and heat transfer area (A), in the design equation Q = U × A × LMTD to size shell-and-tube exchangers, condensers, and radiators. A simple arithmetic average of the two end temperature differences would overstate the driving force in most real exchangers, which is why the logarithmic mean is the industry-standard method.

Was this helpful?

You can pick up to 3 reactions.

Comments

  • Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators