Air at 5°C, with a convection heat transfer coefficient of 30 W/m² · K, is used for cooling metal plates coming out of a heat treatment oven at an initial temperature of 300°C. The plates (k = 180 W/m · K, ρ = 2800 kg/m³, and c_p = 880 J/kg · K) have a thickness of 10 mm. Using EES (or other) software, determine the effect of cooling time on the temperature gradient in the metal plates at the surface. By varying the cooling time from 0 to 3000 s, plot the temperature gradient in the plates at the surface as a function of cooling time. Hint: Use the lumped system analysis to calculate the plate surface temperature. Make sure to verify the application of this method to this problem.