Enter the two different temperatures into the calculator to determine the logarithmic mean temperature difference (LMTD).

LMTD Formula

The following formula is used to calculate a logarithmic mean temperature difference. 

LMTD = (T2 - T1) / (ln(T2/T1))
  • Where LMTD is the logarithmic mean temperature difference
  • T2 is the hotter of the two temperatures
  • T1 is the cooler of the two temperatures

To calculate the logarithmic mean temperature difference, divide the difference in temperature by the natural log of the hot temperature divided by the cold temperature.

Fahrenheit, Celsius, or Kelvin can all be used in the formula as long as T2 and T1 are in the same units.

LMTD Definition

What is LMTD?

LMTD, short for logarithmic mean temperature, is a metric used in thermodynamics to determine the “driving” force for heat transfer in heat flow systems such as heat exchanges.

For heat flow systems with a constant area and heat transfer coefficients, a larger LMTD means more heat is transferred, and a small LMTD means less heat is transferred.

Example Problem

How to calculate LMTD?

First, determine the hotter of the two ends of heat flow. For this example, the heat exchanger has an inlet temperature of 50C.

Next, determine the cooler of the two ends of heat flow. In this case, the outlet has a temperature of 30C.

Finally, calculate the LMTD using the formula above:

LMTD = (T2 – T1) / (ln(T2/T1))

LMTD = (50-30) / (ln(50/30))

LMTD = 39.15

FAQ

What are the practical applications of calculating LMTD in real-world scenarios?
LMTD is crucial in designing and optimizing heat exchangers, such as those used in power plants, chemical processing, HVAC systems, and refrigeration. It helps engineers and technicians determine the efficiency and effectiveness of heat transfer between two fluids, enabling them to make informed decisions about equipment size, material selection, and operational conditions.

Can LMTD be used for all types of heat exchangers?
While LMTD is a valuable tool for calculating the mean temperature difference in a heat exchanger, its application is most suitable for counterflow and parallel flow heat exchangers where the temperatures at both ends are known and relatively constant. For more complex heat exchanger designs, such as shell and tube or crossflow where temperatures can vary significantly across the unit, alternative methods like the effectiveness-NTU method may be more appropriate.

How does the choice of temperature units (Fahrenheit, Celsius, Kelvin) affect the LMTD calculation?
The choice of temperature units does not affect the outcome of the LMTD calculation as long as both temperatures (T2 and T1) are in the same unit. This is because the LMTD formula involves a temperature difference and a ratio, both of which are independent of the temperature scale used. However, it’s crucial to be consistent with the temperature units throughout the calculation to ensure accuracy.