Poached eggs are cooked in bath of boiling water at 100°C. Over time they reach thermal equilibrium with the bath. They are then quickly removed from the boiling water and placed in ice water at 0°C to stop the cooking process. Assume the eggs are perfect spheres with a diameter of 4 cm, a thermal conductivity of 2 W/mK, and a thermal diffusivity of 1e^-6 m^2/s. It is very important that the temperature within the eggs remains spatially uniform during the cooling process.
a) Find the maximum heat transfer coefficient of the ice bath that is allowable. b) Assuming the heat transfer coefficient found in (a) is used. Find the eggs should remain in the ice bath to cool them to 75°C.