Animals in cold climates often depend on two layers of insulation: a layer of body fat [of thermal conductivity 0.200 W/mK] surrounded by a layer of air trapped inside fur or down. We can model a black bear (Ursus americanus) as a sphere 1.50 m in diameter having a layer of fat 3.90 cm thick. (Actually, the thickness varies with the season, but we are interested in hibernation, when the fat layer is thickest.) In studies of bear hibernation, it was found that the outer surface layer of the fur is at 2.60 degrees Celsius during hibernation, while the inner surface of the fat layer is at 31.0 degrees Celsius. What should the temperature at the fat-inner fur boundary be so that the bear loses heat at a rate of 51.5 W? How thick should the air layer (contained within the fur) be so that the bear loses heat at a rate of 51.5 W?

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  1. Calculate the surface area of the fat-fur boundry, then the surface area of the outer fur boundry.

    Outer layer

    solve for Tinner.
    Then, on the fur layer...
    I don't see the thermal conductivity for the fur layer...

  2. I wasn't given the thermal conductivity of the fur layer, all the info the problem gives is included above...

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  3. I believe you have to use 0.200 W/mK = R = (L fat) / k; solve for k and now you should have a new value for R which is (L fat + L fur) / k and assume that the fur you add simply increases the length of the fat insulating layer.

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  4. I'll be honest though, this process is not working for me.

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  5. It may be that you must also change the Area variable to contain both the Radius to the fat layer and the thickness of the hair

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  6. You use the thermal conductivity for air, which is 0.024 W/(m*K), for part B.

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