Natural convection in a square enclosure with a circular cylinder and adiabatic side walls according to the bottom wall temperature variation

Abstract

Two-dimensional numerical simulations are conducted for natural convection in an enclosure with a hot inner cylinder located at the center in the Rayleigh number range from 105 to 106. The Prandtl number is set to be 0.7 corresponding to the air. We investigate the effect of various temperature conditions on the bottom wall on thermal and flow structures of the natural convection in the enclosure. It is identified that the streamlines and isotherms in the enclosure depend on the Rayleigh number and the temperature condition imposed on the bottom wall of the enclosure. When Ra=105, small inner vortices are formed in the lower part of the cylinder and they show significant changes in their size due to the increase in the temperature on the bottom wall. When Ra=106, secondary vortices are formed in the lower part of the cylinder because of the separation of the main convection flow from the side walls. And the magnitude of the convection velocity at Ra=106 becomes much larger than that at Ra=105, which leads to the occurrence of a stronger upwelling plume above the top surface of the cylinder. The numerical solutions at Ra=105 reach the steady state after fully converged regardless of the variation in the temperature condition on the bottom wall. On the other hand, the numerical solutions for all cases at Ra=106 except the case with the temperature condition of zero show the time dependent characteristics.