扩散方程的稳态近似分析:Ⅱ.稳态近似解  

Analysis of diffusion equation based on steady state assumption:Ⅱ.approximate analytic solutions

作　　者：王成善[1,2] 李丹丹[1] 时艳文 严诚[1] 穆小静[3] 

机构地区：[1]重庆大学材料科学与工程学院,重庆400044 [2]重庆大学重庆市冶金工程重点实验室,重庆400044 [3]重庆大学化学化工学院,重庆400044

出　　处：《重庆大学学报（自然科学版）》2014年第7期81-89,共9页Journal of Chongqing University

基　　金：国家自然科学基金资助项目(50704040);重庆市自然科学基金资助项目(CSTC2009BB4197)

摘　　要：通过与有足够精度的数值解对比和理论分析得出:稳态近似法获得的结果基本上满足总体质量守恒;从扩散开始,一直到最终稳态的过程中,稳态近似解和精确解随时间变化是同步的;稳态近似解与接近最终稳态的情形吻合程度好,与远离最终稳态的情形吻合程度差些。近似解全面反映了传质参数或准数对传质过程的定性影响。对扩散方程的稳态近似法处理过程和由此获得的近似解工程上可以应用。Based on the analytic solutions obtained by steady state approximation, the approximate analytic solutions on a closed interval is completed. It is concluded by some theoretical analysis and some comparisons with numerical solutions that the diffusive process 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 with the situations being close to the start of the diffusion,and it fairly satisfies the total mass balance. Approximate solutions totally reflect the qualitative effects of the main coefficients or dimensionless numbers on a mass transfer. The approximate solutions may be applied in many fields in engineering.

关 键 词：动力学 提取冶金 菲克扩散方程 有限长度扩散区间 稳态近似解 数值解 

分 类 号：TF512[冶金工程—钢铁冶金]