In the present study, we explore mechanical response of a radially constrained elastic porous shell during the passage of charged fluid (electrically conducting fluid). A constant magnetic field is exposed on the binary mixture of fluid and solid. The governing dynamics involved in the motion of fluid as well as solid deformation was based on the rate of applied compression at the inner radius of the shell. A nonlinear diffusion equation applicable to planar, cylindrical, and spherical geometry was developed for the porosity along with informal integral boundary conditions on both the extremities. An equation for solid deformation is derived in the form of an integral equation for planar, cylindrical, and spherical geometry. The governing system of equations is solved numerically using the method of lines for the transient case whereas an exact solution is provided for the steady-state problem. In the case of linear permeability, an excellent agreement is noticed between both the solutions. The comparison of the fluid flow through the planar, cylindrical, and spherical shell is used to explore the process of fluid flow affected by the geometrical constraint. Graphical results highlight the influence of different physical parameters on the porosity and solid displacement. Moreover, a detailed analysis of the fluid flow through a thick and thin-walled porous shell is also presented.

在本研究中，我们探讨了带电流体（导电流体）通过过程中径向约束的弹性多孔壳的机械响应。恒定磁场暴露在流体和固体的二元混合物上。流体运动以及固体变形所涉及的控制动力学是基于壳体内半径处的压缩率。针对孔隙度以及两个末端的非正式积分边界条件，开发了适用于平面，圆柱和球形几何形状的非线性扩散方程。以平面，圆柱和球形几何形状的积分方程形式导出了固体变形方程。对于瞬态情况，使用线法对方程的控制系统进行数值求解，而为稳态问题提供精确的解。在线性渗透率的情况下，两个解决方案之间都发现了极好的一致性。通过平面，圆柱形和球形壳的流体流动的比较用于探索受几何约束影响的流体流动的过程。图形结果突出了不同物理参数对孔隙率和固体位移的影响。此外，还提供了对流过厚而薄壁的多孔壳的流体的详细分析。通过平面，圆柱形和球形壳的流体流动的比较用于探索受几何约束影响的流体流动的过程。图形结果突出了不同物理参数对孔隙率和固体位移的影响。此外，还提供了对流过厚而薄壁的多孔壳的流体的详细分析。通过平面，圆柱形和球形壳的流体流动的比较用于探索受几何约束影响的流体流动的过程。图形结果突出了不同物理参数对孔隙率和固体位移的影响。此外，还提供了对流过厚而薄壁的多孔壳的流体的详细分析。