Answer Happy

Question 1. (25 points) Consider a material manufacturing process, where a thin film is deposited on top of a substrate, as shown in the figure below. The temperature of the bottom surface of the substrate is kept at To = 30 °C. The top surface is exposed to a radiative heat flux of q" = 3000 [W/m²], which is fully absorbed at the top surface. In addition, there is convective heat transfer with a fluid at temperature To = 20 °C and the convective coefficient h=40 W/(m²K) . Determine the temperature at the interface between the film and the substrate, Ti . The thickness of the film is a = 0.2 mm and the thickness of the substrate is b = 1.0 mm. Thermal conductivity of the film k;=0.02 W/(m.K), and the thermal conductivity of the substrate ks =0.06 W/(m.K). h To 1 q" Film T. Substrate T."