Flow pattern in heat exchangers
Two flow principles are used in heat exchangers: with-current or countercurrent, the latter only in plate exchangers of particular construction (Fig. 7.10). In the with-current system, the liquids on both sides of the exchange material flow in the same direction, or approximately in the same direc-tion as in the shell and tube exchanger. In this case the temperature gradient between the media is high at the start but gradually decreases. The highest possible temperature that can be achieved in the cold liquid being heated is the mean temperature between the two flowing liquids. This requires equal flow of both liquids; otherwise the temperature depends on the flow ratio of the two liquids. In a countercurrent exchanger the cold media flows in
the opposite direction to the hot media. The tem-perature of the cold media thus gradually increases and the hot water is correspondingly chilled. With a countercurrent exchanger, the temperature of the cold media can be raised to almost the temperature of the hot media, depending of the size of the exchanger.
Find the LMTD for a countercurrent heat exchanger having the following temperatures: hot water into the exchanger, t1= 11°C; hot water out of the exchanger, t2= 5°C; cold water into the exchanger, t3= 3°C; cold water out of the exchanger, t4= 7°C.
DT1 =t1 − t4
= 11 − 7 = 4
DT2 =t2 − t3
= 5 − 3 = 2
LMTD = 4-2 / ln( 4/2)= 2.89
With parallel/linear temperature equalizing the answer would be slightly higher at 3.0. The way to achieve the conditions shown in the example is to have different media flow rates on the two sides of the transfer plates. If there are no energy losses to the surroundings and the water flow in both circuits is equal T1 will equal T2 and this value can then be used for further calculations.
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