This preview shows page 1. Sign up to view the full content.
Chapter 11
Fundamentals of Thermal Radiation
1135
A small surface is subjected to uniform incident radiation. The rates of radiation emission through
two specified bands are to be determined.
A
= 1 cm
2
45
°
Assumptions
The intensity of incident radiation is constant.
Analysis
(
a
) The rate at which radiation is incident on a surface per
unit surface area in the direction (
θ
,
φ
) is given as
φθθ
θφ
d
d
I
dA
Q
d
dG
i
i
sin
cos
)
,
(
=
=
&
The total rate of radiation emission through the band
between 0
°
and 45
°
can be expressed as
2
sin
cos
)
,
(
2
0
45
0
1
π
φθ
θθ
i
i
I
d
d
I
G
=
=
∫∫
==
since the incident radiation
is constant (
I
i
= constant), and
2
/
)
0
sin
45
(sin
sin
cos
2
sin
cos
2
2
45
0
2
0
45
0
πθ
πφ
=
−
=
=
∫
=
d
d
d
Approximating a small area as a differential area, the rate of radiation energy emitted from an area of 1 cm
2
in the specified band becomes
W
3.46
=
×
⋅
×
=
=
=
−
)
m
10
1
)(
sr
W/m
10
2
.
2
(
5
.
0
5
.
0
2
4
2
4
1
1
,
dA
I
dA
G
Q
i
i
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Radiation

Click to edit the document details