In a production facility, 3-cm-thick large brass plates (k = 110 W/m·K, ρ = 8530 kg/m³, c_p= 380 J/kg·K, and α = 33.9 × 10^-6m²/s) that are initially at a uniform temperature of 25°C are heated by passing them through an oven maintained at 700°C. The plates remain in the oven for a period of 10 min. Taking the convection heat transfer coefficient to be h = 80 W/m²·K, determine the surface temperature of the plates when they come out of the oven. Solve this problem using analytical one-term approximation method (not the Heisler charts). Can this problem be solved using lumped system analysis? Justify your answer.

Furnace, 700C 3 cm Brass plate 25C