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.
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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 .