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?