For heat exchanger design by LMTD method correction factor is needed because
1
LMTD is an approximate expression for mean temperature difference
2
actual behavior of the streams for fluid flow and heat transfer is neglected in LMTD analysis; correction factor takes care of that
3
LMTD can be derived only for limited number of cases; correction factor is needed for the other cases
4
it assures the compliance with Second law of thermodynamics