""
""
1.1.3.1 Stefan–Boltzmann Law
For real surface,
q = εσT
4
(1.4)
s
For ideal (black) surface, ε = 1
q = σT
4
s
and
q
""
≡
"" A s
q
or q = q
A s
where ε is the emissivity of the real surface, ε = 0 − 1 (ε metal < nonmetal ε),
T s the absolute temperature of the surface, K (K = ◦ C + 273.15), σ the Stefan–
Boltzman constant, σ = 5.67 × 10 −8 W/m 2 K 4 , and A s the surface area for
radiation (m 2 ).
4
Analytical Heat Transfer
q rad
′′
Any surface at T s , ε, A s
FIGURE 1.3
Radiation from a solid surface.
at a temperature greater than absolute zero. According to Stefan–Boltzmann,
radiation heat rate is proportional to the surface’s absolute temperature’s
fourth power, the Stefan–Boltzmann constant, and the surface emissivity. The
surface emissivity primarily depends on material, wavelength, and temperature. It is between 0 and 1. In general, the emissivity of metal is much less
than nonmetal. Note that radiation from a surface can go through air as well
as vacuum environment.
1.1.4 Combined Modes of Heat Transfer
In real application, often radiation occurs when conduction or convection
takes place. This is called combined modes of heat transfer. For example,
Figure 1.4 shows heat transfer between two surfaces involving radiation and
convection simultaneously.