Example: (Plasma Spray)
Assume spherical alumina particles are used in the plasma jet. (diameter D=50 mm, density r=3970 kg/m3, thermal conductivity k=10.5 W/m.K and specific heat cp=1560 J/kg, and an initial temperature of 300 K) The plasma is maintained at a temperature of 10,000 K and has a convection coefficient of h=30,000 W/m2.K. The melting temperature of the particle is 2318 K and the latent heat of fusion is 3577 kJ/kg. (a) Determine the time required to heat a particle to its melting point, (b) determine the time for the particle to melt completely after it reaches the melting temperature. (Special notes: why the particles follow the plasma jet? Does the particles travel at the same velocity as the local jet velocity? Does the jet has a uniform velocity?
Energy balance: energy in = energy storage in solid