*3.1. Grid Generation and Independence Test*

In the finite element method, grid generation is the technique to discretize the computational domain into subdomains. In this study, we have adopted unstructured triangular elements in the interior and structured quadrilateral elements on the boundary. Figure 2 is the grid generation of the structure with a legend of quality measure. A quality of 1 represents the best possible grid quality, and a quality of 0 represents the worst possible grid quality. For purpose of ensuring the grid independence of the numerical solution, different grid levels in the Comsol Multiphysics are examined. As shown in Table 3, the average Nusselt number of on the inner cylinder at different grids is presented for Cu nanofluid when the nanoparticle volume fraction (*φ*) is 0.5, nanoparticle diameter (*d*sp) is 50 nm, Rayleigh number (*Ra*) is 10<sup>5</sup> , porosity (*ε*) is 0.5, and Darcy number (*Da*) is 10−<sup>2</sup> . The difference between normal and extremely fine is within 1.35%. By comprehensive considering the calculation accuracy and cost, the extra fine level is chosen in this study.

criteria, 10−6 has been chosen for all dependent variables.

*3.1. Grid Generation and Independence Test* 

**Figure 2.** Grid generation of the structure with a legend of quality measure. **Figure 2.** Grid generation of the structure with a legend of quality measure.

**Table 3.** Comparison of the average Nusselt number for Cu nanofluid at different levels when *ϕ* = **Table 3.** Comparison of the average Nusselt number for Cu nanofluid at different levels when *φ* = 0.5, *d*sp = 50 nm, *Ra* = 10<sup>5</sup> , *ε* = 0.5, and *Da* = 10−<sup>2</sup> .

of residuals to all basis functions in a basis. In Galerkin formulation, weighting functions are chosen to become identical to basis functions [36]. In this paper, we have employed a segregated and parallel direct (Pardiso) solver to solve those equations. As convergence

In the finite element method, grid generation is the technique to discretize the computational domain into subdomains. In this study, we have adopted unstructured triangular elements in the interior and structured quadrilateral elements on the boundary. Figure 2 is the grid generation of the structure with a legend of quality measure. A quality of 1 represents the best possible grid quality, and a quality of 0 represents the worst possible grid quality. For purpose of ensuring the grid independence of the numerical solution, different grid levels in the Comsol Multiphysics are examined. As shown in Table 3, the average Nusselt number of on the inner cylinder at different grids is presented for Cu nanofluid when the nanoparticle volume fraction (*ϕ*) is 0.5, nanoparticle diameter (*d*sp) is 50 nm, Rayleigh number (*Ra*) is 105, porosity (*ε*) is 0.5, and Darcy number (*Da*) is 10−2. The difference between normal and extremely fine is within 1.35%. By comprehensive considering the calculation accuracy and cost, the extra fine level is chosen in this study.

