Biomedical Engineering Reference
In-Depth Information
Conditions of validity: free convection averaged over the lower
surface of a heated plate or upper surface of a cooled plate having
a dimension
L
; 10
5
≤
Ra
L
≤ 10
10
.
function of their temperature and radiative constitutive proper-
ties. All surfaces also are continuously receiving thermal energy
from their environment. The balance between radiation lost and
gained defines the net radiation heat transfer for a body. The
wavelengths of thermal radiation extend across a spectrum from
about 0.1 μm to 100 μm, embracing the entire visible spectrum.
It is for this reason that some thermal radiation can be observed
by the human eye, depending on the temperature and properties
of the emitting surface.
The foregoing observations indicate that there are three pro-
perties of a body (i.e., a system) and its environment that govern
the rate of radiation heat transfer: (1) the
surface temperature
,
(2) the
surface radiation properties
, and (3) the
geometric sizes,
shapes, and configurations
of the body surface in relation to
the aggregate surfaces in the environment. Each of these three
effects can be quantified and expressed in equations used to cal-
culate the magnitude of radiation heat transfer. The objective of
this presentation is to introduce and discuss how each of these
three factors influences radiation processes and to show how
they can be grouped into a single approach to analysis.
1/4
(1.6 6)
Nu
=
0.27 Pa
L
L
Conditions of validity: free convection averaged over the entire
circumferential surface of a horizontal cylinder having an
isothermal surface and a diameter
D
;
Ra
D
≤ 10
12
.
2
1/6
0.387 Pr
(1.67)
D
Nu
=+
+
0.6
D
[1
(0.559/) ]
pr
9/16
8/27
Conditions of validity: alternatively, free convection averaged
over the entire circumferential surface of a horizontal cylinder
having an isothermal surface and a diameter
D.
n
(1.68)
Nu
=
CRa
D
D
1.2.4.1 temperature Effects
The first property to consider is temperature. The relationship
between the temperature of a perfect radiating (black) surface
and the rate at which thermal radiation is emitted is known as
the
Stefan-Boltzmann law
:
where the values of
C
and
n
are functions of
Ra
D
as given in the
table below:
Ra
D
C
n
10
-10
-10
-2
0.675
0.058
10
-2
-10
2
1.02
0.148
10
2
-10
4
0.85
1.88
b
=σ
4
ET
(1.70)
10
4
-10
7
0.48
0.25
10
7
-10
12
0.125
0.333
where
E
b
is the blackbody emissive power [W/m
2
], and σ is the
Stefan-Boltzmann constant, which has the numerical value
Conditions of validity: free convection averaged over the entire
circumferential surface of a sphere having an isothermal surface
and a diameter
D
;
Ra
D
≤ 10
11
; Pr ≥ 0 .7.
−
8
W
σ=
5.678
×
10
.
m
24
⋅
Note that the temperature must be expressed in absolute units
(K).
E
b
is the rate at which energy is emitted diffusely (without
directional bias) from a surface at temperature
T
T(K) having per-
fect radiation properties. It is the summation of radiation emit-
ted at all wavelengths from a surface. A perfect radiating surface
is termed black and is characterized by emitting the maximum
possible radiation at any given temperature. The blackbody
monochromatic (at a single wavelength, λ) emissive power is
calculated from the Planck distribution as
1/4
9/16
0.589
Ra
D
Nu
=+
+
2
(1.69)
D
4/9
[1
(0.469 /Pr)
]
1.2.4 radiation Heat transfer
Thermal radiation is primarily a surface phenomenon as it
interacts with a conducting medium (except in transparent or
translucent fluids, which will be considered at the end of this
discussion), and it is to be distinguished from laser irradiation,
which comes from a different type of source. Thermal radiation
is important in many types of heating, cooling, and drying pro-
cesses. In the outdoor environment, solar thermal radiation can
have a significant influence on the overall heat load on the skin.
Thermal radiation occurs via the propagation of electromag-
netic waves. It does not require the presence of a transmitting
material as do conduction and convection. Therefore, thermal
radiation can proceed in the absence of matter, such as in the
radiation of heat from the sun to earth. All materials are con-
tinuously emitting thermal radiation from their surfaces as a
2
λ=
π
λ
2
hc
hc
kT
o
o
2
E
(, )
T
W/mm
⋅µ
λ
,
b
−
(1.71)
2
exp
1
λ
where
h
= 6.636 × 10
-34
[J·s] is the Planck constant,
k
= 1.381 ×
10
-23
(J/K) is the Boltzmann constant, and
c
o
= 2.998 × 10
8
(m/s)
is the speed of light in vacuum. The Planck distribution can
be plotted showing
E
λ,
b
as a function of Λ for specific constant
values of absolute temperature,
T
. The result is the nest of spec-
tral emissive power curves in Figure 1.7. Note that for each
