206 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
What is the coefficient for the water when the exchanger is operating with cocurrent
flow if its value is proportional to the 0.8 power of the water velocity?
Calculate the film coefficient from the organic liquid, on the assumptions that it remains
unchanged, and that heat transfer resistances other than those attributable to the two liquids
may be neglected.
Solution
i) For countercurrent flow:
T 1 D
353 333 D20 deg K andT 2 D
328 288 D40 deg K.
∴From equation 9.9:TmD
40 20 /ln
40 / 20 D 28 .85 deg K.
ii)For co-current flow:
T 1 D
353 288 D65 deg K andT 2 D
328 313 D15 deg K.
∴ TmD
65 15 /ln
65 / 15 D 34 .1degK.
Taking countercurrent flow as state 1 and co-current flow as state 2, then, in
equation 9.1:
QDU 1 ATm 1 DU 2 ATm 2
or: U 1 /U 2 D
28. 85 / 34. 1 D 0. 846 (i)
The water velocity,u/ 1 /T,whereTis the rise in temperature of the water,
or: uDK/TwhereKis a constant.
∴ u 1 /u 2 DT 2 /T 1 D
313 288 /
333 288 D 0. 556.
But:hi/u^0.^8 or:hiDk^0 u^0.^8
Thus: hi 1 /hi 2 D
u 1 /u 20.^8 D
0. 5560.^8 D 0. 625
∴ 600 /hi 2 D 0 .625 andhi 2 D960 W/m^2 K.
From equation 9.201, ignoring scale and wall resistances:
1 /UD 1 /hoC 1 /hi
∴ 1 /U 1 D 1 /hoC 1 /600 andU 1 D 600 ho/
600 Cho
and 1 /U 2 D 1 /hoC 1 /960 andU 2 D 960 ho/
960 Cho
∴ U 1 /U 2 D
600 / 960
960 Cho/
600 Cho D 0 .846 (from (i))
∴ 0. 625
960 Cho D 0. 846
600 Cho andhoD417 W/m^2 K.
PROBLEM 9.75
A reaction vessel is heated by steam at 393 K supplied to a coil immersed in the liquid
in the tank. It takes 1800 s to heat the contents from 293 K to 373 K when the outside