Effect of the position of a circular cylinder in a square enclosure on natural convection at Rayleigh number of 107

TLDR

The study examines how the position of an inner circular cylinder influences heat transfer and fluid flow in a square enclosure. Numerical simulations of natural convection at Ra = 10⁷ were performed, varying the vertical position of the inner cylinder along the enclosure’s centerline. The convection transitions from unsteady to steady as the cylinder moves, with critical positions at δ = 0.05 and 0.18; within these bounds the flow is steady, while beyond them the flow exhibits single‑ or multi‑frequency oscillations and, for δ ≥ 0.18, a shallow Rayleigh–Benard layer produces Benard cells, altering heat‑transfer characteristics.

Abstract

Numerical calculations are carried out for the natural convection induced by temperature difference between a cold outer square cylinder and a hot inner circular cylinder for Rayleigh number of Ra=107. This study investigates the effect of the inner cylinder location on the heat transfer and fluid flow. The location of inner circular cylinder (δ) is changed vertically along the centerline of square enclosure. The natural convection bifurcates from unsteady to steady state according to δ. Two critical positions of δC,L and δC,U as a lower bound and an upper bound are δC,L=0.05 and δC,U=0.18, respectively. Within the defined bounds, the thermal and flow fields are steady state. In the unsteady region, the natural convection shows a single frequency and multiple frequency periodic patterns alternately according to δ. When the inner cylinder locates at δ≥δC,U, the space between the upper surface of inner cylinder and the top surface of the enclosure forms a relatively shallow layer where the natural convection characterized as the pure Rayleigh–Benard convection forms alternately the upwelling and downwelling plums. As a result a series of cells known as Benard cells is derived. The changes in heat transfer quantities have also been presented.