Axisymmetric stagnation-point flow of micropolar fluid in a porous annular region with reciprocating inner cylinder and radial injection

We examine axisymmetric stagnation-point flow of a micropolar fluid in a porous annulus between two concentric cylinders. The governing equations combine Eringen’s micropolar theory with a Darcy-Brinkman porous model and are reduced by similarity transformations to a nonlinear boundary-value problem solved numerically via a multidimensional shooting method. Results show that micropolar coupling produces non-monotonic microrotation profiles, while porous resistance damps shear and rotational effects. When reciprocating axial motion of the inner cylinder is combined with radial injection at the porous outer wall, the micropolar response differs qualitatively from Newtonian predictions: velocity fields reorganize, microrotation couples strongly to wall spin adherence, and heat-transfer rates depend on microstructural parameters. These findings underscore the importance of micropolar rheology for modeling flows in porous cylindrical geometries relevant to reactors, biomedical devices, and porous-media transport.