Chapter 3, Problem 3.6P

In a manufacturing process, a transparent film is beingbonded to a substrate as shown in the sketch. To cure thebond at a temperature $T_0,$ a radiant source is used to providea heat flux $q_0^{"}\left({\text{W/m}}^2\right),$ all of which is absorbedat the bonded surface. The back of the substrate is maintainedat $T_1$ while the free surface of the film is exposed toair at $T_{\infty }$ and a convection heat transfer coefficient h.

1. Show the thermal circuit representing the steady-stateheat transfer situation. Be sure to label all elements,nodes, and heat rates. Leave in symbolic form.
2. Assume the following conditions: $T_{\infty }=20°\text{C,}h=50{\text{W/m}}^2\cdot \text{K,}$ and $T_1=30°\text{C}\text{.}$ Calculate the heat flux $q_0^{"}$ that is required to maintain the bonded surface at $T_0=60°\text{C}\text{.}$ Compute and plot the required heat flux as a functionof the film thickness for $0\le L_f\le 1\text{mm}\text{.}$ If the film is not transparent and all of the radiantheat flux is absorbed at its upper surface, determinethe heat flux required to achieve bonding. Plot yourresults as a function of $L_f$ for $0\le L_f\le 1\text{mm}\text{.}$