%0 Journal Article
%A Nuñez , Jose
%A Beltran, Alberto
%D 2018
%I Begell House
%K onset of natural convection, numerical stability analysis, partial cooling
%N 8
%P 773-786
%R 10.1615/HeatTransRes.2018019154
%T ON THE ONSET OF NATURAL CONVECTION IN A PARTIALLY COOLED CYLINDER
%U https://www.dl.begellhouse.com/journals/46784ef93dddff27,384b49846be20a1e,63664f535ecae5ba.html
%V 49
%X Recent experimental configurations like the liquid metal electrode for the development of a liquid metal battery and the inverted Bridgman configuration for growing crystals involve natural convection of fluids confined in vertical cylinders heated from below and partially cooled from above. A cylindrical cavity subjected to such conditions is studied from a numerical point of view, assuming the Rayleigh number, the noncooled size, and the aspect ratio (height/diameter) parameters over ranges 103 ≤ Ra ≤ 105, 0 ≤ γ ≤ 0.875, and 0.5 ≤ α ≤ 1.25, respectively, for all cases with Pr = 6.67 being assumed. The governing equations for natural convection are discretized employing a mixed Fourier–Finite volume method using the SIMPLEC algorithm as velocity decoupling strategy. Steady flow transitions from axisymmetric to nonaxisymmetric were obtained; interestingly, the average Nusselt number shows a monotonic de-creasing behavior as a function of while an increasing behavior as function of Ra is observed. In particular, symmetry breaking instability as a function of critical parameters of the convective flow is determined by a numerical stability analysis. Finally, a stability map for Ra vs. γ is constructed for α = 1.0.
%8 2018-05-04