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Logarithmic Mean Temperature Difference (LMTD) Calculator

Formula

The formula to calculate the Logarithmic Mean Temperature Difference (LMTD) is:

$LMTD = \frac{T2 - T1}{\ln{\left(\frac{T2}{T1}\right)}}$

Where:

$LMTD$ is the logarithmic mean temperature difference
$T2$ is the hotter of the two temperatures
$T1$ is the cooler of the two temperatures

What is LMTD?

LMTD, short for Logarithmic Mean Temperature Difference, is a metric used in thermodynamics to determine the “driving” force for heat transfer in heat flow systems such as heat exchangers. For heat flow systems with a constant area and heat transfer coefficients, a larger LMTD means more heat is transferred, and a smaller LMTD means less heat is transferred.

Example Calculation

Let's assume the following values:

Hotter Temperature (T2) = 150 °C
Cooler Temperature (T1) = 100 °C

Using the formula to calculate the Logarithmic Mean Temperature Difference:

$LMTD = \frac{150 - 100}{\ln{\left(\frac{150}{100}\right)}} = \frac{50}{\ln{(1.5)}} \approx 42.84 \text{ °C}$

The Logarithmic Mean Temperature Difference (LMTD) is approximately 42.84 °C.