Animals in cold climates often depend on two layers of insulation: a layer of bo
ID: 1305629 • Letter: A
Question
Animals in cold climates often depend on two layers of insulation: a layer of body fat [of thermal conductivity0.2W/(m?K) ] surrounded by a layer of air trapped inside fur or down. We can model a black bear (Ursus americanus) as a sphere 1.51m in diameter having a layer of fat 4.15cm thick. Assume the outer surface layer of the fur is at 2.7?C during hibernation, while the inner surface of the fat layer is at 31.07?C.
How thick should the air layer (contained within the fur) be so that the bear loses heat at a rate of 51.32W?
Explanation / Answer
rate of heat transfer H = dQ/dt = KA(T2-T1)/L
where K = coeffficient of thermal conductivity
A = area
T2-T1 = change of temperartue
so here L = KADT/H
L = 0.2* 4pi*1.51*1.51*(31.07-2.7)/51.32
L = 3.18 m
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