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 solidify and form a layer of protective coating. Consider a plasma spraying process using alumina (k = 30 W/m⋅K, ρ = 3970 kg/ m³ , and c_p = 800 J/kg⋅K) powder that is injected into a plasma jet at T_∞ = 15,000°C and h = 10,000 W/m²⋅K. The alumina powder is made of spherical particles with an average diameter of 60 μm 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.