Plasma Spray-coating processes are often used to provide surface protection of materials exposed to hostile environments, which induce degradation through factors such as wear, corrosion, or outright thermal failure. Ceramic coatings are commonly used for this purpose. By injecting Ceramic powder through the nozzle (anode) of a plasma torch, the particles are entrained by the plasma jet, within which they are then accelerated and heated. During their time in flight, the ceramic particles must be heated to their melting point and experience complete conversion to the liquid state. the coating is formed as the molten droplets impinge (splat) on the substrate material and experience solidification. Consider conditions for which Spherical Alumina (Al2O3) particles of diameter Dp= 50µm, density p=3970 Kg/m3, thermal conductivity kp=10.5 W/m·K, and specific heat cp=1560 J/kg·K are injected into an arc plasma, which is at T8=10000K and provides a coefficient of h=30000 W/m2·K for convective heating of the particles. The melting point and latent heat of fusion of alumina are Tmp=2318 K and hsf = 3577 kJ/kg respectively (a) Neglecting radiation, obtain an expression for the time-in-flight, ti-f required to heat a particle from its initial temperature Ti to its melting point Tmp and, and once at the melting point, for the particle to experience complete melting. Evaluate ti-f for Ti =300K and the prescribed heating conditions
(b) Assuming alumina to have an emissivity of ep = 0.4 and the particles exchange radiation with large surroundings at Tsurr =300K asses the validity of neglecting radiation.