Spectral quasilinear numerical simulation of micropolar convective wall plumes in high permeability porous media

Laminar natural convection plume of a microstructural non-Newtonian fluid along a vertical surface about a line heat source in a saturated high permeability porous medium is studied. The transformed non-linear boundary value problem is solved numerically using a rigorously tested SQLM algorithm, which combines a spectral collocationmethod with the quasilinearization method (QLM). The effects of Grashof number, Prandtl number, Darcy number and Eringen micropolar rheological material parameters are examined. Excellent stability and convergence of the spectral method is demonstrated. Validation of solutions with the Keller box finite difference is included. Applications of the study arise in geological (petroleum) fluid dynamics.