Wind chill, the phenomenon experienced on a cold, windy day, is related to the increased heat transfer from exposed human skin to the surrounding atmosphere. Consider a layer of skin, \(3 \mathrm{~mm}\) thick \((k=0.37)\) whose interior surface is maintained at a temperature of \(36^{\circ} \mathrm{C}\).

On a calm day the heat transfer coefficient at the outer surface is \(10 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\) but with a \(30 \mathrm{~km} / \mathrm{hr}\) wind, it reaches \(25 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\). In both cases the air temperature is \(-15^{\circ} \mathrm{C}\).

a. What is the ratio of the heat loss per unit area from the skin for the calm day to that for the windy day?

b. What temperature would the air have to assume on the calm day to produce the same heat loss occurring with the air temperature at \(-15^{\circ} \mathrm{C}\) on the windy day?

c. What thickness of fat \(\left(k_{f a t}=0.2 \mathrm{~W} / \mathrm{mK}\right)\) underneath the skin layer would be necessary to counteract the increased heat transfer on the windy day? Consider the same overall temperature difference.