Logarithmic Mean temperature Difference is used to measure the Heat transfer rate in double pipe heat exchanger. The rate of heat transfer is got from the formula -

Q = U.A.LMTD .

U= Heat Transfer Co-efficient

A= Heat Transfer Surface Area

LMTD= Mean Temperature Difference

LMTD is the logarithmic temperature difference between the hot and cold fluids passing through the each ends of heat exchanger pipes.

Q = U.A.LMTD .

U= Heat Transfer Co-efficient

A= Heat Transfer Surface Area

LMTD= Mean Temperature Difference

LMTD is the logarithmic temperature difference between the hot and cold fluids passing through the each ends of heat exchanger pipes.

#### Formula for LMTD calculation -

LMTD or

*Logarithmic Mean Temperature Difference is calculated by keeping some factors in mind*- The type of the heat exchanger
- temperature of the fluids at the four end positions

These are -

- 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)

For 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 :

1. For a Parallel Flow Heat Exchanger, Hot fluid entering at temperature 100 degree Celsius and exiting at 90 degree Celsius . Cold fluid Entering at 30 degree Celsius and exiting at 50 degree Celsius. Find the LMTD .

For Parallel or co - current flow ,

According to the above mentioned formulas -

LMTD = ((100 - 30)-(90-50)) / ln (100-30/90-50) = 53.6 degree Celsius .

2. For a Counter Flow Heat Exchanger for same data calculate the LMTD .

For Counter Current HE ,

LMTD = ((100-50)-(90-30))/ln(100-50/90-30) = 54.85 degree Celsius .

So Heat transfer rate for Counter Flow is higher .

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