A small dog has thick fur, with a thermal conductivity of 0.040 W/(m · K). The dog's metabolism produces heat?
at a rate of 39 W and its internal (body) temperature is 34°C. If all of this heat flows out through the dog's fur, what is the outside temperature? Assume the dog has a surface area of 0.45 m2, and that the length of the dog's hair is 1.7 cm. ?
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Use Fourier's law of heat conduction:
H = ∆Q/∆dt = k∙A∙∆T/dx
(H heat flow, k thermal conductivity, A area of the layer, ∆T temperature difference, ∆x thickness of the layer.
So the heat difference between dog's body and surrounding is:
∆T = H∙∆x / (k∙A)
= 34W ∙ 0.017m / (0.04W/Km ∙ 0.45m²)
= 32.11°C
The outside temperature is
T = 34°C - 32.11°C =1.889°C