Determine the heat transfer area requirements of Problem 10.40 if (a) 1-2 shell and tube, (b) an unmixed crossflow, and (c) a parallel flow heat exchanger are used, respectively.

Question

GIVEN

• An air-to-gas heat exchanger

• Entering temperatures

? Ta,in = 350°C

? Tg,in = 700°C

• Mass flow rates: ma = mg = 5 kg/s

• Specific heats: cpa = cpg = 1.05 kJ/(kg K) = 1050 J/(kg K)

• Overall heat transfer coefficient (U) = 75 W/(m2 K)

FIND

The heat transfer area (A) as a function of the effectiveness (e) for (a) A 1-2 shell and tube heat exchanger (b) An unmixed crossflow heat exchanger (c) A parallel flow heat exchanger

ASSUMPTIONS

• For case (a) the air is in the tubes

SKETCH

Answer 1

for counterflow



This must be corrected for case (a) and (b) where





Therefore P = e

Since



The solution for parts (a) and (b) are the same expect that the mean temperature (?T) must be multiplied by the factor F with the following results



where F for part (a) and for part (b) where P = e and Z = 1.0.

(c) For parallel flow



Where:





Tabulating these results