CHEMICAL ENGINEERING

HEAT TRANSFER 173

T 1 D 

388  377 D11 deg K,T 2 D 

333  293 D40 deg K

and from equation 9.9:

TmD 

40  11 /ln 

40 / 11 D 22 .5degK.

Mass flowD
162 / 2085 D 0 .0777 kg/s

Heat load:QD 0. 0777 ð 2. 1
377  293 D 13 .71 kW

In equation 9.1:UD
250 / 1000 D 0 .250 kW/m^2 K,

The area required:AD 13. 71 /
0. 250 ð 22. 5 D 2 .44 m^2.

PROBLEM 9.41

The radiation received by the earth’s surface on a clear day with the sun overhead is
1kW/m^2 and an additional 0.3kW/m^2 is absorbed by the earth’s atmosphere. Calculate
approximately the temperature of the sun, assuming its radius to be 700,000 km and the
distance between the sun and the earth to be 150,000,000 km. The sun may be assumed
to behave as a black body.

Solution

The total radiation receivedD 1 .3kW/m^2 of the earth’s surface. The equivalent surface
area of the sun is obtained by comparing the area of a sphere at the radius of the sun,
7 ð 105 km and the area of a sphere of radius (radius of sunCdistance between sun and
earth) or:

A 1 /A 2 D 4 $

 7 ð 1052 / 4 $

 150 ð 106 C 7 ð 1052 D 2. 16 ð 10 ^5.

Therefore radiation at the sun’s surfaceD 

1. 3 ð 103 / 2. 16 ð 10 ^5 D 6. 03 ð 107 W/m^2.

For a black body, the intensity of radiation is given by equation 9.112:

6. 03 ð 107 D 5. 67 ð 10 ^8 T^4 and TD5710 K

PROBLEM 9.42

A thermometer is immersed in a liquid which is heated at the rate of 0.05 K/s. If the
thermometer and the liquid are both initially at 290 K, what rate of passage of liquid over
the bulb of the thermometer is required if the error in the thermometer reading after 600 s
is to be no more than 1 deg K? Take the water equivalent of the thermometer as 30 g,
the heat transfer coefficient to the bulb to be given byUD 735 u^0.^8 W/m^2 K. The area
of the bulb is 0.01 m^2 whereuis the velocity in m/s.