LMTD

LMTD, short for log mean temperature difference, is a common metric used in heat exchanger analysis to describe the driving temperature difference between hot and cold streams along the length of the exchanger. Because the temperature difference typically changes from one end to the other, LMTD provides a single representative value for estimating heat transfer in steady-state, single-pass configurations.

The LMTD is defined as (ΔT1 − ΔT2) / ln(ΔT1/ΔT2), where ΔT1 and ΔT2 are the temperature differences at the two ends of the heat exchanger. In a counterflow arrangement, ΔT1 is the difference between the hot inlet temperature and the cold outlet temperature, and ΔT2 is the difference between the hot outlet temperature and the cold inlet temperature. In parallel-flow arrangements, ΔT1 and ΔT2 correspond to the inlet and outlet temperature differences across the length. If ΔT1 equals ΔT2, the LMTD equals that common value.

LMTD is used in the basic heat transfer equation Q = U A LMTD, where Q is the heat transfer rate, U is the overall heat transfer coefficient, and A is the heat transfer area. This relation helps size heat exchangers and compare configurations such as parallel-flow and counterflow.

Limitations include the assumption of steady state, constant U, and negligible heat losses, as well as uniform properties along the length. For cases with significant property changes or phase changes, more detailed methods (such as segmenting the exchanger or using the NTU method) may be required. See also concepts like counterflow and parallel-flow heat exchangers and the NTU method for alternative design approaches.