Page 438 - Modelling in Transport Phenomena A Conceptual Approach

418 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

Integrate Eq. (1) to get

meph ( Tw -Thin ) = nD(h)L
Tw - TbOut

b) Water enters the inner pipe (D = 23mm) of a double-pipe heat exchanger at
15 "C with a mass flow rate of 0.3 kg/s. Steam condenses in the annular region so
as to keep the wall temperature almost constant at 112 "C. Determine the length
of the heat exchanger if the outlet water temperature is 35 "C.

(Answer: b) 1.13m)

9.9 Consider the heating of fluid A by fluid B in a countercurrent doublepipe
heat exchanger as shown in the figure below.

a) Show from the macroscopic energy balance that the rate of heat transferred is
given by
-
S = (~&)A(TA~ - TA~) = (~~P)B(TB~ TB~) (1)
where TA and TB are the bulk temperatures of the fluids A and B, respectively.
Indicate your assumptions.
b) Over the differential volume element of thickness Az, write down the inventory
rate equation for energy for the fluids A and B separately and show that

dTA
-
(mCp)~- dz = -TITI)~UA(TB TA) (2)
.L