Mathematical models for mass transport through arcs and flames

Summary

The transport of particles, caused by axial and radial diffusion and axial flow of convection, will be considered in a D.C. arc and in a laminar flame. The following mathematical model will be discussed. Assuming a steady state in both cases the mass transport may be described in cylindrical coordinates (r, z) by the following partial differential equation $\frac{1}{v}\frac{\partial }{{\partial v}}\left( {Dv\frac{{\partial C}}{{\partial v}}} \right) + \frac{\partial }{{\partial z}}\left( {Dv\frac{{\partial C}}{{\partial z}}} \right) - {\text{W}}\frac{{\partial C}}{{\partial z}} = 0.$ where C means the particle concentration, D the coefficient of diffusion, and W the axial velocity. D and W are taken to be constant; various boundary conditions, corresponding to different approximations of the physical situation, are considered. Solutions of (0.1) are obtained in an explicit form.