一、二类边界条件下扩散方程的一个稳态近似结果  

Analysis of diffusion equation with the first and second boundary conditions based on steady state approximation

作　　者：王成善[1,2] 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：《中南大学学报（自然科学版）》2013年第7期2712-2719,共8页Journal of Central South University:Science and Technology

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(CSTC 2009BB4197)

摘　　要：将动力学处理非稳态问题的浓度随时间不变的稳态假设发展为浓度变化率随时间不变的稳态假设,对有限长度区间内扩散方程进行稳态近似法处理,获得一、二类边界条件下扩散方程的一个稳态近似解。并将其与精确数值解对比。研究结果表明:稳态近似法获得的结果和精确解随时间变化是同步的,利用近似解可以准确地预测达到最终稳态的时间;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较差;稳态近似法获得的结果基本上满足总体质量守恒。An assumption of constant concentration variance ratio was made and substituted for the assumption of constant concentration frequently used in kinetics of process metallurgy.A detailed process to deal with diffusion equation based on steady state approximation was given,and the approximate solutions of the diffusive equation with the first and the second boundary conditions were obtained in the meantime.The approximate solutions were compared with the numerical solutions.The results show that the steady state approximation’s results and solutions synchromze with time.The diffusive process is considerably well predicted by the approximate solutions,and the approximate solutions accord with the situations closing to the final steady state a little better than those far from the final steady state.The results obtained by steady station approximation fairly satisfies the total mass balance.

关 键 词：冶金动力学 扩散方程 非稳态 稳态法 近似分析解 

分 类 号：TF512[冶金工程—钢铁冶金]