Using the information estimate the ambient air temperature that could cause frostbite on a calm day on the ski slopes.
GIVEN
• Skier’s skin of thickness (L) = 3 mm = 0.003 m exposed to cold air
• Inner surface temperature of skin (Tsi) = 35°C
• Thermal conductivity of skin (k) = 0.35 W/(m K)
• Convective heat transfer coefficient in still air ( ch ) = 20 W/(m2 K)
• Frostbite occurs at an outer skin surface temperature (Tso) = 10°C FIND
• The ambient air temperature (T?) that could cause frostbite ASSUMPTIONS
• Steady state conditions prevail
• One dimensional conduction occurs through the skin
• Radiative loss (or gain from sunshine) is negligible
SKETCH
The rate of conductive heat transfer through the skin at frostbite conditions is
The rate of convective heat transfer from the surface of the skin,
These heat transfer rates must be equal
Solving for the ambient air temperature
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