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

Abstract

This paper presents the results of immersed boundary method-based two-dimension numerical simulations of natural convection in a square enclosure with an inner circular cylinder at a Prandtl number of 0.7. This simulation spans three decades of Rayleigh number from 103 to 106. This study focuses on the effect of the bottom wall temperature variation of the enclosure on thermal and flow structures of natural convection in the enclosure. The distribution of streamlines and isotherms in the enclosure depend strongly on the Rayleigh number and the bottom wall temperature. When the Rayleigh number becomes larger, the variation in the distribution of streamlines and isotherms in the enclosure according to the bottom wall temperature becomes larger, resulting in the large variation in the number, size, and formation of the convection cells in the enclosure. The distribution of local and averaged Nusselt numbers on the cylinder surface and the top and bottom walls of the enclosure depending on the Rayleigh number and the bottom wall temperature is presented in this paper.