*Article* **Numerical Study of Natural Convection Heat Transfer in a Porous Annulus Filled with a Cu-Nanofluid**

**Lingyun Zhang 1,2, Yupeng Hu 2,\* and Minghai Li 2,\***


**Abstract:** Natural convection heat transfer in a porous annulus filled with a Cu nanofluid has been investigated numerically. The Darcy–Brinkman and the energy transport equations are employed to describe the nanofluid motion and the heat transfer in the porous medium. Numerical results including the isotherms, streamlines, and heat transfer rate are obtained under the following parameters: Brownian motion, Rayleigh number (103–10<sup>5</sup> ), Darcy number (10−4–10−<sup>2</sup> ), nanoparticle volume fraction (0.01–0.09), nanoparticle diameter (10–90 nm), porosity (0.1–0.9), and radius ratio (1.1–10). Results show that Brownian motion should be considered. The nanoparticle volume fraction has a positive effect on the heat transfer rate, especially with high Rayleigh number and Darcy number, while the nanoparticle diameter has an inverse influence. The heat transfer rate is enhanced with the increase of porosity. The radius ratio has a significant influence on the isotherms, streamlines, and heat transfer rate, and the rate is greatly enhanced with the increase of radius ratio.

**Keywords:** natural convection; heat transfer; water-based nanofluid; Brownian motion; porous medium; Darcy–Brinkman equation; numerical simulation
