A sphere-shaped material, made of aluminium, is taken out of an oven at a uniform temperature of 350oC. The material, which has a diameter of 20 cm, is then exposed to air in a room at standard ambient conditions. 1. Calculate the convection heat transfer coefficient for that cooling mechanism! 2. In order to speed up the cooling process, a fan is placed in the room. The fan operation makes the air moving with the velocity of 3 m/s. Calculate the convection heat transfer coefficient for this cooling mechanism! 3. Proof quantitatively that the cooling mechanism using a fan is faster than that without utilizing a fan!