Biomedical Transport Processes - Introduction to Biomedical Engineering - page 979

human tissue, suggesting that conduction into the body (as on a hot day) is also limited. It is
interesting to note that air, like most gases, has a very low thermal conductivity. Thus,
trapped air within clothing provides excellent resistance to thermal conduction in either
direction—into or out of the body. On an extremely cold day, a parka with trapped air
within a nylon covering provides excellent thermal resistance. A three-layer model can be
utilized to examine heat transfer via thermal conduction, as shown in Figure 14.43.
By applying Fourier's law to each layer and assuming that there is no accumulation of
heat within any layer, the equations become

Q1 ¼ K1 ð T1-T2 Þ=D X1 Q2 ¼ K2 ð T2-T3 Þ=D X2 Q3 ¼ K3 ð T3-T4 Þ=D X3

Since there is no accumulation of heat, then Q1 ¼ Q2 ¼ Q3 ¼ Q. Rearranging the preceding

equations gives

T1-T2 ¼ Q D X1 = K1 T2-T3 ¼ Q D X2 = K2 T3-T4 ¼ Q D X3 = K3

Summing these equations results in

T1-T4 ¼ Q =ðD X1 = K1 þ D X2 = K2 þ D X3 = K3 Þ or

Q ¼ð T1-T4 ÞðD X1 = K1 þ D X2 = K2 þ D X3 = K3 Þ

Since the thermal conductivities are in the denominator, any one term can affect the over-
all heat transfer rate. Thus, if air is one of the layers, its thermal conductivity is so low that
with 1/K as a factor, it would dominate the other layers. As a result, it is usually the layer
with the lowest thermal conductivity that affects the overall heat transfer rate via conduc-
tion. This is why trapped air is such a good thermal insulator. Note that T1-T4 will eventu-
ally equal out if there is no continual heat source, but the rate of transfer will be slower with
air as one of the layers.
If the body maintains a certain level of heat production, then a coat with trapped air will
help to maintain skin and body temperature without a danger of hypothermia. Figure 14.44
shows the temperature distribution inside and at the body surface.

FIGURE 14.43 A three-layer model for steady-state heat conduction.