The first fluid (superheated steam) will cool down from its initial temperature (120 oC) to the saturation point (100 oC) and then start to condense at this same temperature (100 oC).

For design purposes, the LMTD is best calculated by assuming that the first fluid is at a constant temperature of 100 oC. This is allowed because the latent heat liberated during condensation is much larger then the sensible heat liberated by cooling down from 120 oC to 100 oC.

Use of the LMTD concept requires that the heat capacity (m.c_p) can be regarded as constant, as well as the overall heat transfer coefficient (U). For phase-change in parts of the heat exchanger both of these are violated, hence LMTD has no meaning.

For simple calculations, one might (as Leander suggests), ignore the superheating/subooling regions if the major part of the heat duty is in the phase-change region. However, this might sometimes lead to serious errors, especially when you are cooling a superheated vapor (small amount of heat, but also a low heat transfer coefficient) . A different approach would be to split the heat exchanger into separate regions, each having approximatel constant (m.c_p) and U, and then calculate area requirement for each zone. The sum of areas is then an estimate of the total heat exchanger surface requirement.

Thank you so much Leander & Erling