Effects of magnetic field on porosity and solid deformation for radial fluid flow through deformable porous shells

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.