Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

whereqrepresents the rate of thermal energy, per unit time, emitted by the surface; eis the emis-

sivity of the surface, 0 e 1, and sis the Stefan –Boltzmann constant (s5.67 10

 8

W/m

2

K

4

);Arepresents the area of the surface in m

2

, andTsis the surface temperature of the

object expressed in Kelvin. Emissivity, e, is a property of the surface of the object, and its value

indicates how well the object emits thermal radiation compared to a black body (an ideal per-

fect emitter). It is important to note here that unlike the conduction and convection modes,

heat transfer by radiation can occur in a vacuum. A daily example of this is the radiation of the

sun reaching the earth’s atmosphere as it travels through a vacuum in space. Because all objects

emit thermal radiation, it is the net energy exchange among the bodies that is of

interest to us. Because of this fact, thermal radiation calculations are generally complicated in

nature and require an in-depth understanding of the underlying concepts and geometry of

the problem.

Example 11.12 On a hot summer day, the flat roof of a tall building reaches 50C in temperature. The area of

the roof is 400 m

2

. Estimate the heat radiated from this roof to the sky in the evening when the
temperature of the surrounding air or sky is at 20C. The temperature of the roof decreases as
it cools down. Estimate the rate of energy radiated from the roof, assuming roof temperatures
of 50, 40, 30, and 25C. Assume e0.9 for the roof.
We can determine the amount of thermal energy radiated by the surface from Equa-
tion (11.23). For roof temperature of 50C, we get

The rest of the solution is shown in Table 11.7.

qesAT

4

s^1 0.92a5.67^10

 8

a

W

m

(^2) #
K
4
bb1400 m
2
21 323 K 2
4
222,000 W
328 Chapter 11 Temperature and Temperature-Related Parameters
TABLE 11.7 The Results of Example 11.12
Surface Surface
Temperature Temperature (K) Energy Emitted by the Surface (W)
(C) T(K) T(C)  273 qeessATs^4
50 323 (0.9)(5.67 10 ^8 )(400)(323)^4 222,000 W
40 313 (0.9)(5.67 10 ^8 )(400)(313)^4 196,000 W
30 303 (0.9)(5.67 10 ^8 )(400)(303)^4 172,000 W
25 298 (0.9)(5.67 10 ^8 )(400)(298)^4 161,000 W
Most of you will take a heat transfer or a transport phenomenon class during your third
year where you will learn in more detail about various modes of heat transfer. You will also
learn how to estimate heat transfer rates for various situations, including the cooling of electronic
devices and the design of fins for transformers or motorcycle and lawn mower engine heads
and other heat exchangers, like the radiator in your car or the heat exchangers in furnaces and
boilers. The intent of this section was to briefly introduce you to the concept of heat transfer
and its various modes.
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