In a manufacturing process, a transparent film is being bonded to a substrate as shown in the sketch. To cure the bond at a temperature To, a radiant source is used to provide a heat flux qo (W/m²), all of which is absorbed at the bonded surface. The back of the substrate is maintained at T₁ while the free surface of the film is exposed to air at T_∞ and a convection heat transfer coefficient h.

(a) Show the thermal circuit representing the steady-state heat transfer situation. Be sure to label all elements, nodes, and heat rates. Leave in symbolic form.

(b) Assume the following conditions: T_∞ = 20°C, h = 50 W/m² ∙ K, and T₁ = 30°C. Calculate the heat flux qo that is required to maintain the bonded surface at T_o = 60°C.

(c) Compute and plot the required heat flux as a function of the film thickness for 0 ≤ L_f ≤ 1 mm.

(d) If the film is not transparent and all of the radiant heat flux is absorbed at its upper surface, determine the heat flux required to achieve bonding. Plot your results as a function of L_f for 0 ≤ L_f ≤ mm.

Air L= 0.25 mm k= 0.025 Wim-K L= 1.0 mm k, = 0.05 W/m-K Film Bond, To Substrate T1