Derive an equation for the time necessary to completely burn a 100 m carbon particle as a

Derive an equation for the time necessary to completely burn a 100 μm carbon particle as a function of D₀. Also calculate the burning rate constant. Use the KS values of the parameter values, for example, C_A∞, given in Example 14-3.
a. diffusion controlled with D_AB = 10^–4 m²/s
b. reaction controlled with kr = 0.01 m/s
c. combined reaction and diffusion controlled
Additional Information:
ρc = 188 mol/m³

Example 14-3

There is a 100 micron carbon dust particle in air at 1 atm. Calculate K_S and the time for the particle to burn completely (d_p = 0). The average value of the diffusivity near the burning particle is 10^–4 m²/s and the density of the carbon particle is 2.26 × 10⁶ g/m³.