Consider the plasma jet of Problem 7.96. When new ceramic coating materials are developed, spray trials are performed using small, circular substrates called coupons that can be coated easily and subsequently tested for the new coating material's wear or corrosion resistance. Consider a 50-mm-diameter, 3-mm-thick 304 stainless steel coupon to be used in a spray trial with the goal of building up a 100-μm-thick ceramic coating.

(a) For a coupon that is insulated on its backside, determine how long the plasma torch can be in place before the coupon melts. How thick would the sprayed ceramic layer be when the coupon melts? The plasma heat transfer coefficient is 609 W/m² ∙ K, and the heat transfer rate due to the impinging droplets is 140 W. The initial temperature of the coupon is 300 K.

(b) It is proposed to cool the backside of the coupon with an air jet at an exit temperature and velocity of T_e.a = 300 K and V_e.a = 30 m/s, respectively. The air jet nozzle diameter is D_a = 10 mm. The nozzle and the coupon's backside surface are separated by La = 50 mm. Will this scheme significantly) increase the thickness of the sprayed ceramic layer that can be deposited?