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

Abstract

Two-dimensional numerical simulations were used to analyze the temperature-driven natural convection phenomena in a square enclosure with an inner cylinder in the Rayleigh number range of Ra =105 ~ 106. The immersed boundary method based on the finite volume method (FVM) was applied to generate and treat inner cylinders, which remained at constant high temperature with no-slip boundary condition. The cylinder remained at a constant high temperature with no-slip boundary conditions. The detailed phenomena of natural convection were investigated according to the bottom wall temperature with a cold and isothermal top walls and adiabatic side walls. The numerical solutions at a Rayleigh number of 105 reached steady state once the solutions fully converged. When the Rayleigh number increased to 106, the solution showed unsteady characteristic depending on the bottom wall temperature. In addition, the distribution of the isotherms in the lower part of the enclosure depended on the temperature variation of the bottom wall and the Rayleigh number. These effects had a significant influence on the convection structure in the lower part of the enclosure and on the corresponding heat transfer on the walls. The convection structures in the enclosure changed significantly in several cases at 106 with a high bottom wall temperature.