= A metallic solid (density p= 4000 kg/m, specific heat C, = 150 J/kg/K, thermal conductivity k =10 W/m/K) spherical particle of diameter 500 um moves through a gas in a chamber at a speed of 5 m/s. The particle is initially at a temperature of 300 K and it is suddenly introduced into the chamber. The walls of the chamber and the gas in the chamber are at 1000 K. The properties of the gas are g (dynamic viscosity) = 4 x 105 kg/m/s, pg (density) = 0.4 kg/m, Pr (Prandtl number) = 0.7, and kg (thermal conductivity) = 0.067 W/m/K. The absorptivity of the particle is =0.6. (a) Develop the general governing equation that describes the variation of the temperature of the particle for this problem, and give the associated constraints (i.e. boundary and/or initial conditions). Do not solve. (b) Make the appropriate assumptions to simplify the problem as much as possible, while retaining the most important effects. (c) Solve the governing equation for the simplified problem to determine the length of the chamber required to heat the particle to a temperature of 700 K.