Chapter 5, Problem 5.26P

The plasma spray-coating process of Problem 5.25 can be used to produce nanostructured ceramic coatings. Such coatings are characterized by low thermal conductivity, which is desirable in applications where the coating serves to protect the substrate from hot gases such in a gas turbine engine. One method to produce a nanostructured coating involves spraying spherical particles, each of which is composed of agglomerated ${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$ nanoscale granules. To form the coating, particles of diameter $D_p=50\mu \text{m}$ must be partially molten when they strike the surface, with the liquid ${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$ providing a means to adhere the ceramic material to the surface, and the un-melted ${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$ providing the many grain boundaries that give the coating its low thermal conductivity. The boundaries between individual granules scatter phonons and reduce the thermal conductivity of the ceramic panicle to $k_p=5\text{W/m}\cdot \text{K}\text{.}$ The density of the porous particle is reduced to $\rho =3800{\text{kg/m}}^{\text{3}}.$ All other properties and conditions are specified in Problem 5.25.

1. Determine the time-in-flight corresponding to $30\%$ of the particle mass being melted.
2. Determine the time-in-flight corresponding to the particle being $70\%$ melted.
3. If the particle is traveling at a velocity $V=35\text{m/s,}$ determine the standoff distances between the nozzle and the substrate associated with your answers in parts (a) and (b).