The present paper explores an analytical solution to study the two-dimensional concentration distribution of a solute in a conducting fluid flowing between two parallel plates in the presence of a transverse magnetic field. Mei’s homogenization technique is used to acquire the mean concentration distributions up to the second-order approximation and the transverse concentration distributions up to third order. An uneven form of the concentration cloud and the transverse variation of the concentration distribution in a hydromagnetic flow are illustrated for the initial stage. The rate of progress towards uniformity of a solute cloud seems much slower than that of normality. It is observed that the peak of the transverse mean concentration and transverse variation of the concentration distribution of the solute significantly decrease with the increase in the magnetic field for small dispersion times. This is because, with an increase in the magnetic field, the velocity profiles flatten at the central core region between the parallel plates. The research proposes a time scale of 10δ²/D (where δ is half the distance between two parallel plates and D is the molecular diffusivity) to characterize the dispersion process to approach the transverse uniformity.

本文探索了一种分析解决方案，以研究在存在横向磁场的情况下，在两个平行板之间流动的导电流体中溶质的二维浓度分布。Mei的均质化技术用于获取直至二阶近似值的平均浓度分布和直至三阶近似值的横向浓度分布。在初始阶段，示出了浓度云的不均匀形式和在水磁流中浓度分布的横向变化。达到溶质云均匀性的速度似乎比正常速度慢得多。观察到，在较小的分散时间下，横向平均浓度的峰值和溶质的浓度分布的横向变化随着磁场的增加而显着减小。这是因为随着磁场的增加，速度分布在平行板之间的中心铁心区域变平。该研究提出的时间尺度为10δ ² / d（其中，δ是一半的两个平行板之间的距离和d是分子扩散率）来表征分散过程接近横向均匀性。