Biomedical Engineering Reference
In-Depth Information
!
is the local heat flux, [W
m
2
],
K
1
],
where
k
is the material's conductivity, [W
m
1
m
1
]. “K” refers to
Kelvin, an absolute scale for
temperature. For materials with a high thermal conductivity, such as metals, there is little
if any insulating capacity. For materials with a low thermal conductivity, the material has
more insulating characteristics. Air and many gases have low thermal conductivities.
Human tissue also has a relatively low thermal conductivity and is thus relatively insulat-
ing, which aids in reducing heat transfer to the core of your body on extremely hot or cold
days. Clothing helps to further insulate the body by providing extra layers for heat conduc-
tion and by trapping air, which is itself a thermal insulator.
For many simple applications, a one-dimensional form of Fourier's law is written as
q
x
¼
k
dT
dx
and
r
T
is the temperature gradient, [K
The thermal conductivity,
, is often treated as a constant, though this is not always true.
While the thermal conductivity of a material generally varies with temperature, the varia-
tion can be small over a significant range of temperatures for some common materials. In
anisotropic materials, the thermal conductivity typically varies with orientation. For the
human body, trapped air in the lungs has a different conductivity as opposed to human tis-
sue, but both have smaller values than denser materials, such as human bone. Water (and in
many ways human blood) has a larger conductivity value, but it is also a thermal capacitor,
able to retain heat.
Since the surface area can also affect heat conduction occurring orthogonal to a plane,
Fourier's law is also written as
k
D
Q
D
t
¼
kA
D
T
D
x
where
A
is the cross-sectional surface area,
D
T
is the temperature difference between the
ends of a thickness, and
is the distance between the ends.
The thermal conductivities for various materials, including human tissue, are as follows:
D
x
Material
k (W/mK)
Human tissue (organs/muscle)
0.5
Human tissue (fat)
0.2
Human tissue (skin)
0.3
Blood
0.5
Bone
0.5-0.6
Water
0.62
Air
0.03
Glass
1.1
Aluminum
200
Copper
400
As can be seen from the preceding list, metals have high thermal conductivities, which is to
be expected. Most human tissue has relatively low thermal conductivities, suggesting that
conduction is not rapid within the human body. The skin has a lower conductivity than
