In order to prevent frostbite in skiers, the weather forecast at most ski resorts reports the air temperature and wind chill temperature. The air temperature is measured with a thermometer that is not affected by the wind. However, the skier's rate of heat loss increases with wind speed, and the windchill temperature is the temperature that would result in the same rate of heat loss in still air as the temperature of measured air without wind. .

Assume that the internal temperature of a skin layer 3 mm thick and with a thermal conductivity of 0.25 W/mK is 35 C and the air temperature is -20 C. Under calm ambient conditions, the convection heat transfer coefficient is 20 W/m^2K. With a wind of 64 km/h, it increases to 75 W/m^2K. A frostbite can occur when the temperature of the outer surface of the skin drops to 10C.

a) For a calm environment without wind, would you recommend that skiers wear a protective mask?

b) For wind conditions of 64 km/h, would you recommend that skiers wear a protective mask?

c) estimate the temperature of ambient air without wind that could cause frostbite in skiers?