Condenser, where the hot fluid temperature varies

In some type of heat exchanger, the temperature of both the fluids is varying and there fore logarithmic mean temperature will have to be calculated. The temperature changes of water and hot fluid may be represented graphically by the following figure. During the process the hot fluid will reject heat in the following manner:

(a) To cool down to saturation temperature, (process DC)
(b) To liquefy (process CB)
(c) To subcool the liquid (process BA)

At the same time the water will receive heat and will get heated from tc1 to tc2.

This type of condenser may be assumed to consist of three sections i.e. (i) desuperheater (ii) liquefier (iii) subcooler.

Here if th1, 2, 3 & 4 is known then LMTD of each section can be calculated and average mean temperature difference is approximately given by:

ΔT m =                                  total heat rejection (HR) (kJ/min)                        (eq. 1.35)

(HRD-C/ ΔT m (D-C)) + (HRC-B/ ΔT m (C-B)) + (HRB-A/ ΔT m (B-A))

And then with this LMTD values for Q and/or U can be calculated.