Natural convection in a square enclosure with a circular cylinder at different horizontal and diagonal locations

Numerical calculations are carried out for natural convection induced by a temperature difference between a cold outer square cylinder and a hot inner circular cylinder. The immersed-boundary method (IBM) to model the inner circular cylinder based on the finite volume method is used to study a two-dimensional natural convection for different Rayleigh umbers varying in the range of 103–106. The location of the inner circular cylinder is changed horizontally along the centerline of square enclosure or diagonally along a diagonal line of the square enclosure. We investigate both effects of the inner cylinder location in an enclosure and the buoyancy-induced convection on heat transfer and fluid flow. The existence of local peaks of the Nusselt number along the surfaces of the cylinder and the enclosure is determined by the gap and the thermal plume governed by the conduction and the convection, respectively. Detailed analysis results for the distribution of streamlines, isotherms and Nusselt number are presented in this paper.