A horizontal structure consists of an L_A = 10-mm-thick layer of copper and an L_B = 10-mm-thick layer of aluminum. The bottom surface of the composite structure receives a heat flux of q" = 100 kW/m², while the top surface is exposed to convective conditions character characterized by h 40 W/m² · K, T∞ = 25°C. The initial temperature of both materials is T_i,A  = T_i,B  = 25°C, and a contact resistance of R"t,c = 400 X 10^–6 m² · K/W exists at the interface between the two materials.

(a) Determine the times at which the copper and aluminum each reach a temperature of T_f  = 90°C. The copper layer is on the bottom.
(b) Repeat part (a) with the copper layer on the top.