Abstract
The heterogeneity of the porous medium properties is an important topic due to the important wide practical applications in the reservoir rocks and the petroleum reservoirs. This study aims to examine both the heterogeneity of the permeability, thermal conductivity and the nanofluid model on the dusty nanofluid within a three-dimensional cubic container. The convective transport is due to the buoyancy–driven flow resulting from two inner hot/cold cylinders separated by variable distance [Formula: see text]. The nanofluids are simulated by a non-homogeneous two phase model and the impact of a constant magnetic field in Z -direction is considered. Two systems of the governing equations are introduced for the dusty and nanofluid phase and the boundary conditions for the nanoparticle function are passively controlled. The major findings revealed that the flow structures can be well-controlled using the distance between the inner cylinders. Also, the heterogeneity in [Formula: see text] plane gives a higher rate of the heat transfer. Furthermore, the maximizing of the dusty parameter is better for enhancing the dusty temperature and velocities.