## What is Log Mean Temperature Difference (LMTD) ?

Logarithmic Mean Temperature Difference measures heat transfer in a double pipe heat exchanger. It is calculated using the following formula:

Q = U.A.LMTD

Where,

U= Co-efficient of Heat Transfer

A= Surface Area of Heat Transfer

LMTD= Mean Temperature Difference

LMTD represents the ** logarithmic mean temperature difference **between hot and cold fluids flowing through the ends of heat exchanger pipes.

## Formula To Calculate Log Mean Temperature Difference LMTD

LMTD, or Logarithmic Mean Temperature Difference, is determined by considering factors such as the heat exchanger type and the temperatures at the four end positions, namely:

- Inlet temperature of the hot fluid
- Inlet temperature of the cold fluid
- Outlet temperature of the cold fluid
- Outlet temperature of the hot fluid

LMTD = dT1 – dT2 /ln (dT1/dT2)

In the case of parallel flow:

dT1 = Temperature of the hot fluid entering – Temperature of the cold fluid entering

dT2 = Temperature of the hot fluid exit – Temperature of the cold fluid exit

For counter flow:

dT1 = Temperature of the hot fluid entering – Temperature of the cold fluid exiting

dT2 = Temperature of the hot fluid exit – Temperature of the cold fluid entering

## Mathematical Example on Log Mean Temperature Difference (LMTD)

**Q.** In a Parallel Flow Heat Exchanger, the hot fluid enters at 100 degrees Celsius and exits at 90 degrees Celsius. The cold fluid enters at 30 degrees Celsius and exits at 50 degrees Celsius. Calculate the LMTD.

**Solution:**

In the case of parallel or co-current flow:

* LMTD*=((100−30)−(90−50))/ln((100−30)/(90−50))=53.6°C

For a Counter Flow Heat Exchanger with the same data:

* LMTD*=((100−50)−(90−30))/ln((100−50)/(90−30))=54.85°C

Hence, the heat transfer rate is higher for counter flow.

## Conclusion

That was all about ** Log Mean Temperature Difference (LMTD)**. If you still have any questions let us know in the comments.