Calculation of the mass transfer coefficient for the combustion of a carbon particle

In this paper we address the calculation of the mass transfer coefficient around a burning carbon particle in an atmosphere of O2, N2, CO2, CO, and H2O. The complete set of Stefan–Maxwell equations is analytically solved under the assumption of no homogeneous reaction in the boundary layer. An expression linking the oxygen concentration and the oxygen flux at the particle surface (as a function of the bulk gas composition) is derived which can be used to calculate the mass transfer coefficient. A very simple approximate explicit expression is also given for the mass transfer coefficient, that is shown to be valid in the low oxygen flux limit or when the primary combustion product is CO2. The results are given in terms of a correction factor to the equimolar counter-diffusion mass transfer coefficient, which is typically available in the literature for specific geometries and/or fluid-dynamic conditions. The significance of the correction factor and the accuracy of the different available expressions is illustrated for several cases of practical interest. Results show that under typical combustion conditions the use of the equimolar counter-diffusion mass transfer coefficient can lead to errors up to 10%. Larger errors are possible in oxygen-enriched conditions, while the error is generally low in oxy-combustion.