Biomedical Engineering Reference
In-Depth Information
where a represents spectral absorption factor, r represents the spectral reflection factor, and
t represents the spectral transmission factor.
The radiative heat transfer rate is given by the Stefan-Boltzmann law
AT
4
Q
r
¼ s
where
is the Boltzmann constant and A is the surface area of the radiating source.
The temperature is in an absolute scale (
Kelvin, corresponding to
s
C, or
Rankin,
corresponding to
F).
To predict the exact amount of radiative heat transfer between two surfaces, the preced-
ing equation is expanded as
T
1
4
T
2
4
Q
r
¼
sF
1
A
1
ð
Þ
where F is the facing factor that represents the amount of the emitting surface (1) facing the
receiving surface (2) with the surface area A representing surface 1. Correspondingly, this
equation can use F
2
and A
2
to represent the facing factor for the receiving surface toward
the emitting surface with the surface area of 2. Boltzmann's constant and the temperature
gradient are unchanged for either form of the equation. The facing factor can be approxi-
mated as a disk of radius R if the distance between the two surfaces is large, such as the
earth to the sun. For shorter distances, the facing factor is a complex interaction between
the angles of the two surfaces that face each other.
As can be seen, thermal radiation is affected by the frequency of the emitted energy. This
is why sunscreen ointments have ultraviolet protection, since this type of energy can be
damaging to skin. In addition, it is common to feel warmer on the sunny side of the street
as opposed to the shady side, given the radiative heat transfer. Radiation can be a signifi-
cant source of heat as compared to the other forms (conduction and convection) because
radiation is composed primarily of sunlight and the respective heating of the earth.
14.3.6 The Greenhouse Effect
Emitted radiation from the sun consists of a spectrum of electromagnetic radiation of
varying frequencies and wavelengths. The sun's surface temperature is approximately
10,000
C. When this energy hits the earth's surface, it can be absorbed, reflected, or trans-
mitted through. The amount of each of these factors depends on the surface temperature
of the earth and the exact material (water, soil, man-made materials). However, the reflec-
tivity, absorptivity, or transmissivity is frequency dependent. In addition, the frequency
spectrum of the incoming thermal energy is shifted due to the different surface temperature
of the earth as compared to the sun.
As the energy reached the earth through its atmosphere, the transmissivity was high
(allowing it to pass through the atmosphere) and the reflectivity and absorptivity were
low. However, as the energy hit the earth's surface, the new temperature shifted the spec-
trum such that the new reflectivity was high and the transmissivity was low. Thus, when
some of the thermal energy was reflected back from the earth's surface toward the atmo-
sphere, it did not transmit through toward outer space but instead was reflected back
toward the earth's surface. At each reflection back, more energy was absorbed into the
earth's surface, heating the earth. Normal conduction and convection would heat the
