Highly reflective aluminum coatings may be formed on the surface of a substrate by impacting the surface with molten drops of aluminum. The droplets are discharged from an injector, proceed through an inert gas (helium), and must still be in a molten state at the time of impact.

Consider conditions for which droplets with a diameter, velocity, and initial temperature of D = 500μm, V = 3 m/s, and T_i = 1100 K, respectively, traverse a stagnant layer of atmospheric helium that is at a temperature of T_∞ = 300 K. What is the maximum allowable thickness of the helium layer needed to ensure that the temperature of droplets impacting the substrate is greater than or equal to the melting point of aluminum (T_f > T mp = 933 K)? Properties of the molten aluminum may be approximated as p = 2500 kg/m³ ∙ c = 1200 J/kg ∙ K. and k = 200 W/m ∙ K.

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- Droplet injector T--r - Helium, T. -Molten aluminum, V, D -Aluminum coating -Cold substrate