Wearing layers of clothing in cold weather is often recommended because dead-air spaces between the layers keep the body warm. The explanation for this is that the heat loss from the body is less. Compare the rate of heat loss for single 2 cm thick layer of wool [k = 0.04 W/(m K)] with three 0.67 cm layers separated by 1.5 mm air gaps. The thermal conductivity of air is 0.024 W/(m K).
GIVEN
• Wool insulation
• Thermal conductivities
? Wool (kw) = 0.04 W/(m K
? air (ka) = 0.024 W/(m K)
FIND
• Compare the rate of heat loss for a single 2 cm thick layer of wool to that of three 0.67 cm layers separated by 1.5 mm layers of air gaps.
ASSUMPTIONS
• Heat transfer can be approximated as one dimensional, steady state conduction
SKETCH
The thermal resistance for the single thick layer, is.
Therefore the rate of conductive heat transfer is
The thermal resistance for the three thin layers is the sum of the resistance of the wool and the air
between the layers
Therefore, the rate of conductive heat transfer for the three layer situation is
Comparing the rate of heat loss for the two situations
Therefore, for the same temperature difference, the heat loss through the three layers of wool is only
80% of the heat loss through the single layer.
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