Log Mean Temperature Difference (LMTD)

Log Mean Temperature Difference (LMTD) is a logarithmic average of the temperature difference between the hot and cold fluid streams at each end of the heat exchanger. The bigger the value of LMTD, the higher heat is transferred.

The rate of heat transfer (q) = UAΔT_m

In the above formula, ΔT_m is the log mean temperature difference.

ΔT_m can be expresses as:

For Parallel Flow Heat Exchanger:

∆T₁ = T_hot,in – T_cold,in
∆T₂ = T_hot,out – T_cold,out

For Counter Flow Heat Exchanger:

Derivation of Log Mean Temperature Difference (LMTD)

The below image describes the derivation of Log Mean Temperature Difference (LMTD).

Log Mean Temperature Difference (LMTD) Assumptions:

1. The total heat transfer coefficient (U) is steady throughout the heat energy
2. The specific heats (C_p) and mass flow rates of the two liquids are consistent.
3. The flow conditions are steady.
4. There is no change of phase in both of the liquids during the heat transfer.
5. There is no deficiency of heat to the surroundings, because of the heat exchanger being perfectly insulated.
6. Axial conduction along the containers of the heat exchanger is negligible.
7. The changes in kinetic energy and potential energy are negligible.