� �
222
Analytical Heat Transfer
Visible
Violet
Blue
Green
Yellow
Red
X-rays
Infrared
Ultraviolet
Microwave
Thermal radiation
Gamma
rays
0.4
0.7
10 –5
10 –4
10 –3
10 –2
10 –1
1
10
10 2
10 3
10 4
μm
FIGURE 11.1
Conceptual view of hemispheric radiation.
and
dA n = dA cos θ
Therefore, differential surface radiation flux (or differential emissive power)
becomes
dq ≡ dE λ = I λ (θ, ϕ, λ, T) sin θ cos θ dθ dϕ
dA
After integration in all directions, the monochromatic hemispherical emissive power is
2π π/2
E λ =
I λ (θ, ϕ, λ, T) sin θ cos θ dθ dϕ
(11.2)
0 0
Spectral
distribution
(a)
(b)
Monochromatic
radiation emission
θ
Wavelength
FIGURE 11.2
(a) Spectral radiation varies with wavelength. (b) Directional distribution.
222
Analytical Heat Transfer
Visible
Violet
Blue
Green
Yellow
Red
X-rays
Infrared
Ultraviolet
Microwave
Thermal radiation
Gamma
rays
0.4
0.7
10 –5
10 –4
10 –3
10 –2
10 –1
1
10
10 2
10 3
10 4
μm
FIGURE 11.1
Conceptual view of hemispheric radiation.
and
dA n = dA cos θ
Therefore, differential surface radiation flux (or differential emissive power)
becomes
dq ≡ dE λ = I λ (θ, ϕ, λ, T) sin θ cos θ dθ dϕ
dA
After integration in all directions, the monochromatic hemispherical emissive power is
2π π/2
E λ =
I λ (θ, ϕ, λ, T) sin θ cos θ dθ dϕ
(11.2)
0 0
Spectral
distribution
(a)
(b)
Monochromatic
radiation emission
θ
Wavelength
FIGURE 11.2
(a) Spectral radiation varies with wavelength. (b) Directional distribution.