Chapter 1, Problem 1.23P

Using the information in Problem 1.22, estimate the ambient air temperature that could cause frostbite on a calm day on the ski slopes.

1.22 In order to prevent frostbite to skiers on chair lifts, the weather report at most ski areas gives both an air temperature and the wind-chill temperature. The air temperature is measured with a thermometer that is not affected by the wind. However, the rate of heat loss from the skier increases with wind velocity, and the wind-chill temperature is the temperature that would result in the same rate of heat loss in still air as occurs at the measured air temperature with the existing wind.

Suppose that the inner temperature of a 3-mm-thick layer of skin with a thermal conductivity of $\text{0}\text{.35 W/m K is 35°C}$ and the air temperature is $\text{—20°C}$. Under calm ambient conditions the heat transfer coefficient at the outer skin surface is about ${\text{20 W/m}}^{\text{2}}\text{K}$ (see Table 1.4), but in a 40-mph wind it increases to ${\text{75 W/m}}^{\text{2}}\text{K}$.

1. If frostbite occurs when the skin temperature drops to about $\text{10°C}$, do you advise the skier to wear a face mask?

2. What is the skin temperature drop due to the wind?