write the assumptions pleaseeeeee and solving

Question 2 (Problem \# 5.21 Textbook modified) (30 points) Plasma spray-coating processes are often used to provide surface protection for materials exposed to harsh environments, which induce degradation through factors such as wear, corrosion, or outright thermal failure. Ceramic coatings are commonly used for this purpose. In this process, ceramic powder is injected through a nozzle (anode) of a plasma torch where the particles are carried by the plasma jet. During this process, the ceramic particles are accelerated and heated at the same time by the plasma. During their time-in-flight, the ceramic particles must be heated to their melting point and experience complete conversion to the liquid state (phase change). The coating is formed as the molten droplets impinge (splat) on the surface and experience rapid solidification. A pictorial representation of plasma coating of substrate surfaces is provided below: Consider spherical alumina particles (Al2O3) being sprayed using plasma under the following conditions: For Al2O3 particles: Dp=50m;=3970kg/m3;kp=10.5W/mK;Cp=1560J/kgK Initial temperature =Ti=300k Meiting temperature =Tmp=TF=2318K latent heat of melting ==hsf=3577kJ/kg For Plasma: T=10,000Kh=30,000W/m2k The particles are so small and highly conductive, that Lumped Capacitive Resistance Model is easily applicable. In addition, calculated Biot number is less than 0.1 which satisfies the requirement of applicability of this model