CHEMICAL ENGINEERING

HEAT TRANSFER 215

On integration:

0. 0002307 tD

∫ 323

293

dT/

 422. 3  1. 1 TD 

1 / 1. 1 [ln 

1 /

 422. 3  1. 1 T]^333293

Thus, on heating from 293 to 323 K:

0. 0002307 tD 0 .909 lnf[422. 3 


1. 1 ð 293 ]/[422. 3 


2. 1 ð 323 ]gD 0 .909 ln
   100 / 67

and: tD1578 s
0 .44h

PROBLEM 9.83

A thermometer is situated in a duct in an air stream which is at a constant temperature.
The reading varies with the gas flowrate as follows:

air velocity (m/s) thermometer reading (K)

6.1 553

7.6 543

12.2 533

The wall of the duct and the gas stream are at somewhat different temperatures. If the
heat transfer coefficient for radiant heat transfer from the wall to the thermometer remains
constant, and the heat transfer coefficient between the gas stream and thermometer is
proportional to the 0.8 power of the velocity, what is the true temperature of the air
stream? Neglect any other forms of heat transfer.

Solution

As with Problem 9.78, a heat balance on the thermometer gives: hw
TwT
Dhg
TTg wherehwandhgare the coefficients for radiant heat transfer from the
wall and for convection to the gas respectively andTw,TandTgare the temperatures of
the wall, thermometer and gas, respectively,above a datum of 533 K.

WhenuD 12 .2m/s,hw

Tw 0 Dhg 

0 CTg (i)

WhenuD 7 .6 m/s, sincehg/u^0.^8 ,hw

Tw 10 Dhg 

7. 6 / 12. 20.^8  10 CTg (ii)

WhenuD 6 .1m/s,hw

Tw 20 Dhg 

6. 1 / 12. 20.^8  20 CTg (iii)

Dividing equation (i) by equation (ii):Tw/

Tw 10 D 

12. 2 / 7. 60.^8 Tg/

Tg 10

D 1. 46 Tg/

Tg 10 (iv)

and dividing equation (i) by equation (iii):Tw/

Tw 20 D 

12. 2 / 6. 10.^8 Tg/

Tg 20

D 1. 741 Tg/

Tg 20 (v)