Natural convection in a square enclosure with different positions and inclination angles of an elliptical cylinder Part I: A vertical array of one elliptical cylinder and one circular cylinder

Abstract

This paper numerically investigates the two-dimensional natural convection in a square enclosure with a vertical array of a hot elliptical cylinder and a hot circular cylinder with Rayleigh numbers in the range of 104⩽Ra⩽106. An immersed boundary method was used to capture the wall boundary of the cylinders. The effects of the position and inclination angle ϕ of the elliptical cylinder were investigated. When the Rayleigh number increases to Ra = 106, the numerical solutions reach an unsteady state for all cases of the lower elliptical cylinder and the cases of the upper elliptical cylinder except at ϕ=90°. The transition of the flow regime from unsteady state to steady state depends on the flow direction and the space between the upper cylinder and top wall of the enclosure due to the changes in the inclination angle of the elliptical cylinder. At Ra = 106 in the case of upper elliptical cylinder at ϕ=0°, the time- and surface-averaged Nusselt numbers for the walls of the enclosure increase by about 1.99% compared to the case of two circular cylinders. The thermal performance and flow stability were influenced by the position and inclination angle of the elliptical cylinder.