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 absorbed 90% of any incident solar radiation, while having an emissivity of 0.20. The density ? and specific heat C of aluminum are known to be 2,700 kg/m3 and 900 J/kg. oK, respectively. Consider conditions for which the plate is at a temperature of 25oC and its top surface is suddenly exposed to ambient air at T? = 20oC and to solar radiation that provides an incident flux of 1,000 W/m2. The convection heat transfer coefficient between the surface and the air is h = 25 W/m2.oK. Stefan-Boltzmann constant: ? = 5.67?10-8 W/m2.oK4.

1) The initial rate of change of the plate temperature is

2) Neglect heat loss by radiation, the steady state temperature of the plate is

3) Include heat loss by radiation, the steady state temperature of the plate is

4) Neglect heat loss by radiation,
the time it takes for the plate to reach 40oC is