An Emperor penguin in Antarctica may be modeled as a cylinder 1m high with a diameter of 0.2m. The male Emperor penguin warms his egg for sixty-four days during the Antarctic winter (no solar input), in deep sub-zero temperatures. During this time the male Emperor loses approximately 20kg of body mass.
a) If the fat has an energy value of 39kJ/g, what is the average rate of heat loss from a penguin that loses 20kg of fat over sixty-four days?
b) Assuming that the penguin’s feet are adiabatic and heat is lost to convection (Tinf = 20C, h = 10 W m2K) and radiation (Tsky = ?30?C, Tground = ?20?C, with the ground assumed to be a flat plane), what must the temperature of the outermost feathers be?
c) Assuming the feathers make a conduction barrier that obeys radial thermal resistance behavior with a corrected penguin height of 1.05m (so you can neglect the top in this part), and the thermal conductivity is about 2 W mK , what must the thickness of the penguin feather layer be? The penguin’s body temperature is 39?C, and the feather layer is assumed uniform.