In this paper, we summarize a numerical study of two-dimensional natural convection in an annular elliptical space fluid-saturated porous, by solving numerically the mass balance equations, momentum and energy, using Darcy's law, Boussinesq approximation, vorticity-stream function formulation and the finite volumes method for the discretization of partial derivative equations. Both walls delimiting the annular space are maintained at two uniform different temperatures. The external parameters considered are the eccentricity of the inner elliptic wall (0.55, 0.688, 0.86, 0.9 and 0.999) and Rayleigh-Darcy number (Ram = 500). The results indicate that there are two main modes of natural convection: natural convection with only two cells and with more cells, their description is given in detail. The average equivalent conductivity is presented in terms of external parameters and allows us to see that it increases when the internal wall eccentricity increases.

This paper presents a numerical study of buoyancy‐driven double‐diffusive convection within an elliptical annulus enclosure filled with a saturated porous medium. An in‐house built FORTRAN code has been developed, and computations are carried out in a range of values of Darcy–Rayleigh number Ram (10 ≤ Ram ≤ 500), Lewis number Le (0.1 ≤ Le ≤ 10), and the ratio of buoyancy forces N (−5 ≤ N ≤ 5). In addition, three methods are used, namely the multi‐variable polynomial regression, the group method of data handling (GMDH), and the artificial neural network (ANN) for the predictions of heat and mass transfer rates. First, results are successfully validated with existing numerical and experimental data. Then, the results indicated that temperature and concentration distributions are sensitive to the Lewis number and thermal and mass plumes are developing in proportion to the Lewis number. Two particular values of Lewis number Le = 2.735 and Le = 2.75 captured the flow's transition toward an asymmetric structure with a bifurcation of convective cells. The average Nusselt number tends to have an almost asymptotic value for Le » 5. For the case of aiding buoyancies N > 1, the average Nusselt Number trueNu¯ $\bar{{Nu}}$ decreased by 33% when the Lewis number increased to its maximum value. Then, it increased by 10% when the Lewis number increased to Le = 1 for the case of opposing buoyancies N < 1 and then decreased by 33% when the Lewis number increased to its maximum value., contrary to the behavior of the average Sherwood number trueSh¯ $\bar{{Sh}}$ that increased by 700% for both cases N > 1 and N < 1. New correlations of trueNu¯ $\bar{{Nu}}$, and trueSh¯ $\bar{{Sh}}$ as a function of Ram, Le, and N are derived and compared with GMDH and ANN methods, and the ANN method showed higher performance for the prediction of trueNu¯ $\bar{{Nu}}$ and trueSh¯ $\bar{{Sh}}$ with R2 exceeding 0.99.

The presented work concerned a computation of two-dimensional heat transfer by laminar natural convection in a heat pipe cross section. The cylindrical annular space was categorized into two cases, in the first case the space was filled with a Newtonian fluid and the second case filled with a fluid-saturated porous medium. The mathematical model was described by continuity, momentum and energy equations in the cylindrical coordinates system using Boussinesq’s approximation and Brinkman’s equation. The numerical simulation was carried out using Comsol Multiphysics software. The effects of Rayleigh number, aspect ratio and permeability on the temperature and the velocity fields were examined and results obtained were validated and found to be qualitatively in a good agreement with those in the literature.

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