CHEMICAL ENGINEERING

HEAT TRANSFER 135

The radius of the magnesia,r 3 D
75 CxD
0. 075 C 0. 001 xmwherexmm is the
thickness of the magnesia.
Hence the area at the surface of the magnesia,A 3 D 2 $
0. 075 C 0. 001 xm^2 /m

andQD10[2$
0. 075 C 0. 001 x]
370 C 280 D
424. 1 C 5. 66 xW/m (i)

For conduction through the insulation

QDk

 2 $rml

T 1 T 2 /

r 2 r 1 (equation 9.22)

wherermD
r 2 r 1 /lnr 2 /r 1.

∴ QD 0 .17[2$ð 1. 0
r 2 r 1 ]
1100 T 2 /[
r 2 r 1 ln
0. 075 / 0. 025 ]

D 0. 972

1100 T 2 W/m (ii)

For conduction through the magnesia

In equation 9.22:

QD 0 .09[2$ð 1. 0 

r 3 r 2 ]

T 2  370 /[

r 3 r 2 ln 

0. 075 C 0. 001 x/ 0 .075]

D 0. 566 

T 2  370 /ln 

1 C 0. 013 x (iii)

For a value ofx,Qis found from (i) and henceT 2 from (ii). These values are substituted
in (iii) to give a second value ofQ, with the following results:

xQD 

424. 1 C 5. 66 x T 2 D 

1100  1. 028 Q QD 0. 566 

T 2  370 /

(mm) (W/m) (K) ln
1 C 0. 013 x(W/m)

5.0 452.4 635 2380

7.5 466.6 620 1523

10.0 480.7 606 1092

12.5 494.9 591 832

15.0 509.0 577 657

17.5 523.2 562 531

20.0 537.3 548 435

From a plot of the two values ofQ, a balance is attained whenxD 17 .5 mm. With
this thickness,T 2 D560 Kwhich is below the maximum permitted and hence the use of

the magnesia would be feasible.

PROBLEM 9.9

In order to heat 0.5 kg/s of a heavy oil from 311 K to 327 K, it is passed through tubes of
inside diameter 19 mm and length 1.5 m forming a bank, on the outside of which steam
is condensing at 373 K. How many tubes will be needed?