Solve the following problem:
Q: A sphere made of aluminum alloy 2024 with a diameter of 20 mm and a uniform temperature of 500°C is suddenly immersed in a saturated water bath maintained at atmospheric pressure. The surface of the sphere has an emissivity of 0.25.
(a) Calculate the total heat transfer coefficient for the initial condition. What fraction of the total coefficient is contributed by radiation?
(b) Estimate the temperature of the sphere 30 s after it is immersed in the bath.