Log Mean Temperature Difference

\[LMTD=\frac{\Delta T_1-\Delta T_2}{\ln\left(\frac{\Delta T_1}{\Delta T_2}\right)}\]

Variables

LMTDlog mean temperature difference (K)

dT1[ΔT1]temperature difference at one end of the heat exchanger (K)

dT2[ΔT2]temperature difference at the other end of the heat exchanger (K)

Description

What is this formula?

The log mean temperature difference calculates the effective average temperature difference that drives heat transfer in a heat exchanger when the temperature difference changes along its length.

When to use it

Use this formula for steady-state heat exchanger calculations, especially when estimating heat duty, heat transfer area, or overall heat transfer coefficient in parallel-flow or counterflow exchangers.

Example

A counterflow heat exchanger has a temperature difference of 80 K at one end and 30 K at the other end.

Formula:

LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)

Substitution:

LMTD = (80 - 30) / ln(80 / 30)

LMTD = 50 / 0.9808

Result:

LMTD = 50.97 K

The effective driving temperature difference is approximately 51.0 K.

Applications

- Heat exchanger design

- Shell-and-tube exchanger calculations

- Process heating and cooling

- Condenser and evaporator analysis

- Chemical plant energy balances

Note

This formula assumes steady-state operation and a heat exchanger arrangement where the two terminal temperature differences are known. For multipass shell-and-tube exchangers or crossflow exchangers, a correction factor is often applied to the LMTD.