Double-diffusive convection within a partially porous medium constitutes a complex coupling phenomenon, where boundary conditions at the interface between porous and free zones play a key role. As a part of this research, we have numerically modeled the double-diffusive convection of a nanofluid (Cu- \(H_{2}O\) ) circulating in a partially porous annular space between two coaxial cylinders, reproducing realistic configurations, in which we looked into the contribution of putting discret hot cells in the inner cylinder in order to control all the cavity and minimize the size of the hot source. In addition, we tried to use recent and experimental models of Corcione to better understand the heat and mass transfer processes. The inner cylinder is associated with a higher nanoparticles concentration. In contrast, the external cylinder is maintained at a uniform cold temperature, corresponding to a region with a lower nanoparticles concentration. However, the base walls are designed to be impermeable and adiabatic. Then, to solve the system of nonlinear and coupled conservation equations, we used a method based on the vorticity-stream function, combined with a finite-difference scheme. The numerical results represented by the streamlines, isotherms, isoconcentrations, and Nusselt and Sherwood numbers highlight the critical influence on some control parameters like the Rayleigh number, Darcy number, buoyancy ratio forces, the aspect ratio number, and nanoparticle concentration. For instance, the average Nusselt number increases by about 242 \(\%\) and 177 \(\%\) when the Rayleigh number rises from \(10^{4}\) to \(10^{6}\) for aspect ratios of 0.5 and 3, respectively, while the Sherwood number improves by nearly 50 \(\%\) as the aspect ratio decreases from 3 to 0.5. In addition, the thermal and mass transfer rates increase by approximately 102 \(\%\) and 196 \(\%\) when the Darcy number rises from \(10^{-5}\) to \(10^{-1}\) simultaneously with a reduction in the aspect ratio from 3 to 0.5, which underlines the pronounced effect of permeability and geometry on the transport process.
