Buoyant convection in a vertical cylinder with azimuthally-varying sidewall temperature (Q1579230)

This parer studies steady three-dimensional free convection flow of Boussinesq fluid in a vertically mounted cylindrical container. The boundary conditions maintain the wall temperature inhomogeneous in the horizontal azimuthal direction, but increasing in the vertical direction. Interest is confined to flows with globally stable stratification and substantial azimuthal variations in thermal boundary conditions. The transformed non-dimensional full governing equations are solved numerically using the finite difference technique. Flow details near the cylinder axis are not of primary interest, so that the refinement of grid points in a neighborhood of the axis is omitted (in fact, the authors are interested in gaining an understanding of physical aspects of flow, rather than in developing numerical codes). It is shown that when the wall temperature is vertically uniform, the azimuthal variation of wall temperature is absorbed in boundary layer. The interior core is stably stratified with horizontal isotherms. In the horizontal planes the fluid moves from hot to cold regions, forming two circulation cells near the endwall zones. However, near the mid-height due to symmetry, the horizontal motions produce a four-cell structure. In the axial planes linking \(\varphi =0^\circ\) and \(\varphi= 180^\circ\), a single cell is visible, but in the neutral axial plane linking \(\varphi= 90^\circ\) and \(\varphi= 270^\circ\) four cells are manifested. The authors also present some results for other thermal boundary conditions.