Finite difference approach and successive over relaxation (SOR) method for MHD micropolar fluid with Maxwell–Cattaneo law and porous medium

Abstract

This analysis considered the flow of micropolar fluid to describe the micro-rotational influence of fluid particles. The oscillatory motion of stretchable disk is responsible for the fluid flow. The impacts of magnetic field and porous medium are incorporated in a momentum equation. The Maxwell–Cattaneo law of material-invariant version having damped-hyperbolic equation is proposed in order to overcome the limitations of Fourier’s law. The model of three-dimensional flow problem is then normalized by adopting suitable similarity variables. The resulting normalized system of partial differential equations is solved in a numerical way using first and second order central and backward finite difference approximations by converting the semi-infinite domain into the finite one. The resulting expressions are solved iteratively using the successive over relaxation parameter method. The impacts of various dimensionless parameters are elaborated through graphs and tables. Higher values of porosity and magnetic parameters reduced the radial velocity curves. Micropolar parameters, namely vortex and spin gradient viscosity parameters, enhanced the microrotational tangential velocity profiles. Radial shear stresses and frictional torque are decreased due to larger values of the vortex viscosity parameter. Couple stresses along radial and tangential directions are enhanced for increasing values of porosity parameter. The three-dimensional and two-dimensional flow phenomenon is also sketched. The numerical results for the limiting scenario are compared for various physical parameters to validate the numerical scheme.