Question 3: The wind chill, which is experienced on a cold and windy day, is related to increased heat transfer from exposed human skin to the surrounding atmosphere. Consider a layer of fatty tissue (k = 0.2 W/(m K)) that is 3 mm thick, with its interior surface maintained at a temperature of 36°C. On a calm day, the convection heat transfer coefficient on the outer surface is 25 W/(m² K), but with 30 km/h winds, it reaches 65 W/(m² K). In both cases, the ambient air temperature is -15°C.
What is the ratio of the heat loss per unit area from the skin on the calm day to the windy day? What will be the skin's outer surface temperature for the calm day and the windy day? What temperature would the air have to be on the calm day to produce the same heat loss occurring with the air temperature at -15°C on the windy day?