Laminar natural convection from a vertical array of horizontal heated cylinders inside a water-filled rectangular enclosure cooled at sides

Purpose: The purpose of this study is to investigate numerically the laminar natural convection from a pair of horizontal heated cylinders, set one above the other, inside a water-filled rectangular enclosure cooled at sides, with perfectly insulated top and bottom walls, through a control-volume formulation of the finite-difference method, with the main aim to evaluate the effects of the center-to-center cylinder spacing, the size of the cavity and the temperature difference imposed between the cylinders and the cavity sides. Design/methodology/approach: The system of the conservation equations of the mass, momentum and energy, expressed in dimensionless form, is solved by a specifically developed computer code based on the SIMPLE-C algorithm for the pressure-velocity coupling. Numerical simulations are executed for different values of the Rayleigh number based on the cylinder diameter, as well as the center-to-center cylinder spacing and the width of the cavity normalized by the cylinder diameter. Findings: The main results obtained may be summarized as follows: the existence of an optimum cylinder spacing for maximum heat transfer rate is found at any investigated Rayleigh number; as a consequence of the downstream confinement, a periodic flow arises at sufficiently high Rayleigh numbers; the amplitude of oscillation of the periodic heat transfer performance of the cylinder array decreases as the cylinder spacing is increased and the cavity width is decreased, whereas the frequency of oscillations remains almost the same; at very small cavity widths, a transition from the typical two-cell to a four-cell flow pattern occurs. Originality/value: The computational code used in the present study incorporates an original composite polar/Cartesian discretization grid scheme.