Rotating cylinder and magnetic field on solid particles diffusion inside a porous cavity filled with a nanofluid

This study deals with the roles of a magnetic field and circular rotation of a circular cylinder on the dissemination of solid phase within a nanofluid-filled square cavity. Two wavy layers of the non-Darcy porous media are situated on the vertical sides of a cavity. An incompressible smoothed particle hydrodynamics (ISPH) method was endorsed to carry out the blending process concerning solid phase into nanofluid and porous media layers. Initially, the solid phase is stationed in a circular cylinder containing two open gates. Implications of a buoyancy ratio (N = −2: 2), Hartmann number (Ha = 0: 100), rotational frequency (Formula presented.), Darcy parameter (Formula presented.), Rayleigh number (Formula presented.), nanoparticles parameter (Formula presented.), and amplitude of wavy porous layers (Formula presented.) on the lineaments of heat/mass transport have been carried out. The results revealed that the diffusion of the solid phase is permanently moving toward upward except at opposing flow mode (Formula presented.) toward downward. The lower Rayleigh number reduces the solid-phase diffusions. A reduction in a Darcy parameter lessens the nanofluid speed and solid-phase diffusions in the porous layers. A reduction in (Formula presented.) from (Formula presented.) to (Formula presented.) diminishes the maximum of streamlines (Formula presented.) by 13.19% at (Formula presented.), by 46.75% at (Formula presented.), and by 74.75% at (Formula presented.).