**4. Results and Discussion**

In this section, numerical simulations are carried out to investigate the flow and heat transfer characteristics of the nanofluid filled in the porous annulus. The results present the effects of several parameters, such as Brownian motion, nanoparticle diameter *d*sp (10–90 nm), nanoparticle volume fraction *φ* (0.01–0.09), Rayleigh number *Ra* (103–10<sup>5</sup> ), Darcy number *Da* (10−4–10−<sup>2</sup> ), porosity *ε* (0.1–0.9), and radius ratio *RR* (1.1–10) on the isotherms and streamlines, the local Nusselt number (*Nu*loc), and the average Nusselt number (*Nu*avg).
