Theoretical investigation on the interaction between conducting and non-conducting walls on hydromagnetic natural convection flow of viscous incompressible and electrically conducting fluid through a vertical micro-channel taking into account the effects of induced magnetic field in presence of Hall current is presented. Governing coupled equations responsible for the flow are obtained when either the micro-channel walls are electrically conducting or are electrically non-conducting. Using the method of undetermined coefficients, exact solution are obtained and presented in dimensionless form subject to relevant boundary conditions. Expressions for fluid velocity, induced magnetic field, skin friction, volume flow rate and induced current density in both primary and secondary flow directions are also obtained. Effects of some governing parameters like Hall current parameter, rarefaction parameter and Hartmann number on the different flow situations are given using the aid of line graphs and Tables. The main conclusion of the present analysis is that, in the existence of rarefaction parameter, primary fluid velocity could be enhanced with the increase in Hall parameter when the micro-channel walls are either insulated or when the left micro-channel wall is electrically conducting. Results obtained in this work are relevant in many magnetically controlled devices and could also be used as a benchmark in checking the accuracies of result obtained in some empirical experiments.

考虑到感应磁场在霍尔电流存在的情况下的影响，介绍了通过垂直微通道的粘性不可压缩和导电流体的水磁自然对流中导电和非导电壁之间相互作用的理论研究。当微通道壁导电或不导电时，获得负责流动的控制耦合方程。使用待定系数的方法，得到精确解，并在相关边界条件下以无量纲形式呈现。还获得了流体速度、感应磁场、皮肤摩擦、体积流量和初级和次级流动方向上的感应电流密度的表达式。借助折线图和表格，给出了霍尔电流参数、稀疏参数和哈特曼数等控制参数对不同流动情况的影响。本分析的主要结论是，在稀疏参数的存在下，当微通道壁绝缘或左侧微通道壁导电时，初级流体速度可以随着霍尔参数的增加而提高。在这项工作中获得的结果与许多磁控设备相关，也可以用作检查某些经验实验中获得的结果准确性的基准。本分析的主要结论是，在稀疏参数的存在下，当微通道壁绝缘或左侧微通道壁导电时，初级流体速度可以随着霍尔参数的增加而提高。在这项工作中获得的结果与许多磁控设备相关，也可以用作检查某些经验实验中获得的结果准确性的基准。本分析的主要结论是，在稀疏参数的存在下，当微通道壁绝缘或左侧微通道壁导电时，初级流体速度可以随着霍尔参数的增加而提高。在这项工作中获得的结果与许多磁控设备相关，也可以用作检查某些经验实验中获得的结果准确性的基准。