In a shell of a shell and tube heat exchanger with two shell passes and eight tube passes, 12.6 kg/s of water is heated in the shell from 800C to 150°C. Hot exhaust gases having roughly the same physical properties as air enter the tubes at 340°C and leave at 180°C. The total surface, based on the outer tube surface, is 930 m2 . Determine (a) the log-mean temperature difference if the heat exchanger were simple counterflow type, (b) the correction factor F for the actual arrangement, (c) the effectiveness of the heat exchanger, (d) the average overall heat transfer coefficient.

GIVEN

• A tubular heat exchanger with 2 shell passes and 8 tube passes

• Water in the shell, exhaust gases in the tubes

• Exhaust gases have roughly the same physical properties as air

• Water flow rate m w= 12.6 kg/s

• Water temperatures

? Tw,in = 80°C

? Tw,out = 150°C

• Exhaust temperatures

? Te,in = 340°C

? Te,out = 180°C

• Surface are (A) = 930 m2

FIND

(a) LMTD if the exchanger is a simple counterflow type

(b) Correction F for the actual arrangement

(c) Effectiveness (e)

(d) The overall heat transfer coefficient (U)

SKETCH



PROPERTIES AND CONSTANTS

the specific heat of water at the mean temperature of 130°C (cpw) = 4244.5 W/(kg K)


(a) for simple counterflow





(b) The LMTD must be modified



F = 0.97

(c) To find the effectiveness, the heat capacity rate of the exhaust must first be determined. An energy balance yields



The effectiveness is



(d) The rate of heat transfer is



Solving for the overall heat transfer coefficien

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