Analysis of diffusion equation with the second and third boundary conditions based on steady state approximation
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Abstract:
One dimensional diffusion equation is widely used to describe mass transfer in particles or droplets in a reactor. The length of the definition domain of the one-dimension Fick equation is limited, because it is determined by the scale of the particles or the droplets. The diffusion equation with a certain length of definition domain has no analytic solution unless series solution. So, to obtain approximate solutions of diffusion equation is of theoretical significance and practical significance. Firstly, assumption of constant concentration variance ratio is used instead of assumption of constant concentration frequently used in kinetics of process metallurgy. Secondly, a detail process to deal with diffusion equation based on steady state approximation is given, and the approximate solutions of the diffusion equation at certain conditions are obtained at the same time. By comparing the approximate solutions with the numerical solutions, it is concluded that the diffusive process of non-steady state is considerably well predicted by the approximate solutions, and approximate solutions accord with the situations being close to the final steady state a little better than accord with the situations being close to the begin of the diffusion, and it fairly satisfies the total mass balance.
