Consider the plasma spray coating process of Problem 5.25. In addition to the prescribed conditions, the argon plasma jet is known to have a mean velocity of V = 400 m/s, while the initial velocity of the injected alumina particles may be approximated as zero. The nozzle exit and the substrate are separated by a distance of L = 100 mm. and pertinent properties of the argon plasma may be approximated as k = 0.671 W/m ∙ K, c p = 1480 J/kg ∙ K. μ = 2.70 X 10^-4 kg/s ∙ m, and v = 5.6 X 10^-3 m²/s.

(a) Assuming the motion of particles entrained by the plasma jet to be governed by Stokes' law, derive expressions for the particle velocity, V_p(t), and its distance of travel from the nozzle exit, x_p(t), as a function of time, t, where t = 0 corresponds to particle injection. Evaluate the time-in-f1ight required for a particle to traverse the separation distance, x_p = L, and the velocity V p at this time.

(b) Assuming an average relative velocity of (V – V_p) = 315 m/s during the time-of-f1ight, estimate the convection coefficient associated with heat transfer from the plasma to the particle. Using this coefficient and assuming an initial particle temperature of T_i = 300 K, estimate the time-in-f1ight required to heat a particle to its melting point, T mp' and, once at T mp' for the particle to experience complete melting. Is the prescribed value of L sufficient to ensure complete particle melting before surface impact?