Many specialized applications (ranging from advanced gas-turbine blades to medical devices and implants) require metal components that are coated with a protective material layer. In a manufacturing plant for such coatings, an infrared lamp is used for curing the coating on metal plates. The lamp provides a uniform irradiation of which a flux of 1600 W/m² is absorbed by the metal plate surface, which has an emissivity of 0.5 for the radiation at the temperature of the coating. Air is used to cool the plate, which is kept in an enclosed containment, and it enters the enclosure at 20°C and leaves from the coating process at 30°C. 

(a) If the convection heat transfer coefficient between the coated plate surface and the cooling air is 15 W/m² K, estimate the temperature of the coating on the plate surface. 

(b) If the engineer who invented the coating believes that a cure temperature (or surface temperature) of 50°C provides a coating with better durability, estimate the infrared lamp irradiation necessary to attain the required average cure temperature for the process.