CHEMICAL ENGINEERING

164 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

The following data are obtained by substituting values forT 1 in equations (i) and (ii):

T 1 

T 1 T 20.^5 ea

300 1285 0.059 0.378

400 1483 0.163 0.391

1000 2345 0.350 0.422

PROBLEM 9.32

Calculate the heat transferred by solar radiation on the flat concrete roof of a building,
8 m by 9 m, if the surface temperature of the roof is 330 K. What would be the effect of
covering the roof with a highly reflecting surface, such as polished aluminium, separated
from the concrete by an efficient layer of insulation? The emissivity of concrete at 330 K
is 0.89, whilst the total absorptivity of solar radiation (sun temperatureD5500 K) at this
temperature is 0.60.
Use the data for aluminium from Problem 9.31 which should be solved first.

Solution

The emission from a body with an emissivity,e, at a temperatureTis given by:

IDe9T^4

Thus, for the concrete:

ID 

0. 89 ð 5. 67 ð 10 ^8 ð 3304 D 598 .5W/m^2

TakingTD330 K as the equilibrium temperature, the energy emitted by the concrete
must equal the energy absorbed and, since the absorptivity of concrete,aD 0 .60, the
solar flux is then:
IsD
598. 5 / 0. 6 D 997 .4W/m^2

which approximates to the generally accepted figure of about 1 kW/m^2.
With a covering of polished aluminium, then using the data given in Problem 9.31 and
an equilibrium surface temperature ofTK, the absorptivity is:

aD 0. 475  1. 66 T^0.^5

and, with an area of
8 ð 9 D72 m^2 , the energy absorbed is:

1. 0 ð 103 ð 72

0. 475  1. 66 T^0.^5 D 3. 42 ð 104  1. 20 ð 105 T^0.^5 W(i)

The emissivity is given by:

eD 0. 475

1  263 /TD 0. 475  125 T^1

and the energy emitted is:

72 ð 5. 67 ð 10 ^8 T^4

0. 475  125 T^1 D 1. 94 ð 10 ^6 T^4  5. 10 ð 10 ^4 T^3 W (ii)