CHEMICAL ENGINEERING

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 andT 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 andT 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 ATm 1 DU 2 ATm 2

or: U 1 /U 2 D 

28. 85 / 34. 1 D 0. 846 (i)

The water velocity,u/ 1 /T,whereTis the rise in temperature of the water,

or: uDK/TwhereKis a constant.

∴ u 1 /u 2 DT 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