To calculate the char consumption

At the investigated temperatures, the superficial gas velocity in the reactor is between 0.14 and 0.17 m/s. The Reynolds number for the flow in the reactor is around 40 and the Reynolds number for the flow around the initial particle is around 10.
Note that the temperature and each Indirubin have different apparent boundary layer thicknesses: species with a higher diffusivity have a thicker apparent boundary layer. The boundary conditions for Eqs. (7) and (8) are at r = 0:equation(13)dcidr=0equation(14)dTdr=0at r = R + δm,jequation(15)cj=cj,∞cj=cj,∞and at r = R + δhequation(16)T=T∞T=T∞
In Eq. (15), the concentration of the species in the bulk gas at the reactor inlet is used. This can be justified by the fact that the production rates of gases during the char conversion were always low compared to the total gas flow. In the case the influence of the released gases on the bulk gas composition would be significant, another modeling approach would be required, resolving the concentration and velocity field in the reactor.