Chapter 4, Problem 32P

Plasma spraying is a process used for coating a material surface with a protective layer to prevent the material from degradation. In a plasma spraying process, the protective layer in powder form is injected into a plasma jet. The powder is then heated to molten droplets and propelled onto the material surface. Once deposited on the material surface, the molten droplets solidi1y and form a layer of protective coating. Consider a plasma spraying process using alumina $(k=30\text{ W/m}\text{.K, }p=3970{\text{ kg/m}}^{\text{3}},andcp=800\text{ J/kg}\text{.K)}$ and powder that is injected into a plasma jet at ${\text{T}}_{\infty }{\text{ = 15,000}}^{\text{o}}{\text{C and h =10,000 W/m}}^{\text{2}}\text{.K}\text{.}$. The alumina powder is made of spherical particles with an average diameter of 60 $\mu m$ and a melting point at 2300°C. Determine the amount of time it would take for the particles, with an initial temperature of 20°C, to reach their melting point from the moment they are injected into the plasma jet.