Consider the acceleration-grid foil (k = 40 W/m ∙ K, a = 3 X 10-5 m2/s, F = 0.45) of Problem 4.72. Develop an implicit, finite-difference model of the foil, which can be used for the following purposes.

(a) Assuming the foil to be at a uniform temperature of 300 K when the ion beam source is activated, obtain a plot of the mid span temperature-time history. Al what elapsed time does this point on the foil reach a temperature within 1 K of the steady-state value?

(b) The foil is operating under steady-state condition when, suddenly, the ion beam is deactivated. Obtain a plot of the subsequent mid span temperature time history. How long does it take for the hottest point on the foil to cool to 315 K, a safe-to-touch condition?