Double diffusive Buoyancy‐driven flow in a fluid‐saturated elliptical annulus with a neural network‐based prediction of heat and mass transfer

Abstract

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.