Animals in cold climates often depend on two layers of insulation: a layer of body fat (of thermal conductivity 0.200W/(m?K) ) surrounded by a layer of air trapped inside fur or down. We can model a black bear as a sphere 1.50m in diameter having a layer of fat 4.00×10?2m thick, as shown in the figure.(Figure 1) In studies of bear hibernation, it was found that the outer surface layer of the fur is at TC = 2.70?C during hibernation, while the inner surface of the fat layer is at TH = 31.0?C. How thick should the air layer (contained within the fur) be so that the bear loses heat at a rate of 50.0W ? Thermal conductivity of air is kair = 2.40×10?2W/(m?K) .
What is the thickness of the air layer (contained within the fur), Lair?