##### LMTD

• Classify the types of heat exchangers with suitable examples.
• Analyze heat exchanger performance by using the method of log mean temperature difference (LMTD) as well as NTU method and heat exchanger effectiveness for parallel and counter flow heat exchangers.
• Apply fundamentals of heat transfer to understand the design of heat exchangers and to be able to specify the type and size of heat exchanger to satisfy the needs of a particular engineering process application.

The logarithmic mean temperature difference (also known as log mean temperature difference or simply by its initials LMTD) is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger. The larger the LMTD, the more heat is transferred. The use of the LMTD arises straightforwardly from the analysis of a heat exchanger with constant flow rate and fluid thermal properties.
For counterflow in tubular heat exchangers, $\Delta T_{lm} = \dfrac{(T_{Ho}- T_{Ci}) - (T_{Hi}- T_{Co})}{ln\left ( \dfrac{T_{Ho}- T_{Ci}}{T_{Hi}- T_{Co}} \right )}$

For parallel flow heat exchanger, $\Delta T_{lm} = \dfrac{(T_{Ho}- T_{Co}) - (T_{Hi}- T_{Ci})}{ln\left ( \dfrac{T_{Ho}- T_{Co}}{T_{Hi}- T_{Ci}} \right )}$

###### Solved Example: 84-1-01

LMTD in case of counter flow heat exchanger as compared-to parallel flow heat exchanger is: