 # Shell - Tube Heat Exchanger : LMTD calculation

## What is the LMTD ? How to calculate it ? How to correct it ?

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1. Shell-Tube heat exchangers
2. Shell-Tube heat exchanger calculation procedure

## 1. LMTD : Logarithmic Mean Temperature Difference With

ΔT1 = temperature difference on one side of the heat exchanger (end 1)
ΔT2 = temperature difference on the other side of the heat exchanger (end 2)

The LMTD allows to represent the driving force of heat exchange along the exchanger and accounts for the fact that the difference in between the cold side and the hot side is changing all along the equipment. The use of the LMTD is valid for co-axial heat exchangers.

Typical examples of temperature profiles along co-axial heat exchangers, for co-current and counter current are given below : The LMTD in the case of counter-current is noted LMTDcc.

Example :

Counter current HX with

• Hot fluid temperature in = 100c
• Hot fluid temperature out = 75c
• Cold Fluid temperature in = 20c
• Cold fluid temperature out = 60c
• DT1 = 75-20 = 55c
• DT2 = 100-60 = 40c
• LMTD = (40-55)/(ln(40/55)) = 47.1 c

## 2. Correction factor of the LMTD

### How to correct the LMTD to account for other configuration than counter current ?

Very few heat exchangers are purely co current or counter current, which allows to apply the LMTD. Most of the them will be partially co current and partially counter current. It is quite easy to visualize it for a 2 pass tube / 1 pass shell heat exchanger for example.

In this case, the LMTD must be corrected by a coefficient F which accounts for those non idealities. F can be calculated from abacus.