Problem 3 High-performance gas turbine engines commonly used for aircraft propulsion and power generation are subject to high operating temperatures, often in excess of 1500 C. Operation at high temperatures is a big challenge for material science. Even the most advanced superalloys, like Inconel 718, have melting points that are significantly lower, typically 1370-1450 C. To protect metal parts like blades, vanes, and combustors from heat, thermal-barrier coatings (TBC) are used. TBCs are made of porous multi-layered ceramics and exhibit low thermal conductivity and emissivity while maintaining high thermal and structural integrity. TBC coupon at 1500 C The Center for Advanced Coatings at Florida Tech manufactures and performs high-heat-flux experiments on various thermal-barrier coatings. A typical TBC test coupon is a flat cylinder with a diameter of 25.4 mm and a thickness of 3 mm. Test coupons are continuously heated with a high- power laser beam so that the coupon's average temperature reaches 1500 C. The coupon radiates heat in all directions at the rate of 96 W. Find the emissivity of the coupon. The Stefan-Boltzman constant is = 5.67.10-8 W/mK4.