If an aluminum plate 4 mm thick is mounted in a horizontal position, and its bottom surface is well insulated. A special, thin coating is applied to the top surface such that it absorbs 80% of any incident solar radiation, while having an emissivity of 0.25. The density p and specific heat c of aluminum are known to be 2700 kg/m3 and 900 J/kg K, respectively. (a) Consider conditions for which the plate is at a temperature of 25 C and its top surface is suddenly exposed to ambient air at T=20 C and to solar radiation that provides an incident flux of 900 W/m2 . The convection heat transfer coefficient between the surface and the air is h = 20 W/m^2 K. What is the initial rate of change of the plate temperature?