For safety reasons, a heat exchanger performs as shown in (a) of accompanying figure. An engineer suggests that it would be wise to double the heat transfer area so as to double the heat transfer rate. The suggestion is made to add a second, identical exchanger as shown in (b). Evaluate this suggestion, that is, show whether or not the heat transfer rate would double.

Question

GIVEN

Case 1

Heat exchanger as shown above.

• Overall heat transfer coefficient times the transfer area (UA) = 40,000 kJ/(hr K)

• Heat capacity rates

? Ch = 80,000 kJ/(h K)

? Cc = 40,000 kJ/(h K)

• Entering temperatures

? Tb,in = 400 K

? Tc,in = 300 K Case 2 Two of the same heat exchanges as shown above in Figure B. FIND

• Does the heat transfer rate double?

ASSUMPTIONS

• Heat exchangers are simple counterflow geometry

Answer 1

The number of transfer units is: NTU = (UA)/Cmin = (40,000)/(40,000) = 1.0

e1 = 0.54

Case 2

For this case, the transfer area is doubled, therefore

UAtotal = 2(UA) = 80,000 kJ/(h K) NTU = (80,000)/(40,000) = 2.0

e2 = 0.78

Applying



The rate of heat transfer does not double. It is increased by only 44%.