Chapter 3, Problem 3.10P

The wind chill, which is experienced on a cold, windy day, is related to increased heat transfer from exposed human skin to the surrounding atmosphere. Consider a layer of fatty tissue that is 3 mm thick and whose interior surface is maintained at a temperature of 36°C. On a calm day the convection heat transfer coefficient at the outer surface is $25{\text{W/m}}^{\text{2}}\cdot \text{K,}$ but with 30 km/h winds it reaches $65{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ In both cases the ambient air temperature is $-15°\text{C}\text{.}$

1. What is the ratio of the heat loss per unit area from the skin for the calm day to that for the windy day?
2. What will be the skin outer surface temperature for the calm day? For the windy day?
What temperature would the air have to assume on the calm day to produce the same heat loss occurring with the air temperature at $-15°\text{C}$ on the windy day?