Numerical Solution of 2D Natural Convection in a Concentric Annulus with Solid-Liquid Phase Change

摘要

Heat transfer processes involving phase change either, solidification or melting, appear frequently in nature and in industrial applications. In this paper the convective patterns that arise from a 2D shear driven annular flow (without and with melting), are presented. The convective annular flow with radial gravity can be considered as a simplified model of the atmospheric flow in the terrestrial equatorial plane (bounded by the warm surface of the Earth and the cold tropopause). The governing equations have been numerically solved by the Spectral Element Method. The numerical results reported in this paper, for the cases without melting (at two different radius ratio η=r_i/r_0) are in qualitative agreement with analytical results and experimental data obtained elsewhere for 2D annular electroconvection systems. For the cases with melting, the material between the two concentric circles (with radius ratio η =0.35) is initially solid. The melting process takes place from the internal circle with temperature T_h, where T_h is greater than the melting temperature T_m. The heat transfer rate at the internal circle and the convective flow patterns have been obtained for the cases without shear and with shear. The Couette shear is induced by a constant rotation of the internal circle. As the phase change process takes place, three parameters of the system depend on the fluid layer depth: the Rayleigh number, the Reynolds number and the radius ratio of the annular fluid layer. We found that as the fluid layer depth increases, different flow patterns appear. We discuss the critical azimuthal mode number and its relationship with the Nusselt number.