Solved: An aluminum plate 4 mm thick is mounted in a
Chapter , Problem 1.45(choose chapter or problem)
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 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/m2 K. What is the initial rate of change of the plate temperature? (b) What will be the equilibrium temperature of the plate when steady-state conditions are reached? (c) The surface radiative properties depend on the specific nature of the applied coating. Compute and plot the steady-state temperature as a function of the emissivity for 0.05 1, with all other conditions remaining as prescribed. Repeat your calculations for values of S 0.5 and 1.0, and plot the results with those obtained for S 0.8. If the intent is to maximize the plate temperature, what is the most desirable combination of the plate emissivity and its absorptivity to solar radiation? 1
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