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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.

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.

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.

The computational code used in the present study incorporates an original composite polar/Cartesian discretization grid scheme.

This paper aims to investigate numerically buoyancy-induced convection from a pair of differentially heated horizontal circular cylinders set side by side in a nanofluid-filled adiabatic square enclosure, inclined with respect to gravity so that the heated cylinder is located below the cooled one, using a two-phase model based on the double-diffusive approach assuming that the Brownian diffusion and thermophoresis are the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase.

The system of the governing equations of continuity, momentum and energy for the nanofluid, and continuity for the nanoparticles, is solved by a computational code based on the SIMPLE-C algorithm. Numerical simulations are performed for Al₂O₃ + H₂O nanofluids using the average volume fraction of the suspended solid phase, the tilting angle of the enclosure, the nanoparticle size, the average nanofluid temperature and the inter-cylinder spacing, as independent variables.

The main results obtained may be summarized as follows: at high temperatures, the nanofluid heat transfer performance relative to that of the pure base liquid increases with increasing the average volume fraction of the suspended solid phase, whereas at low temperatures it has a peak at an optimal particle loading; the relative heat transfer performance of the nanofluid has a peak at an optimal tilting angle of the enclosure; the relative heat transfer performance of the nanofluid increases notably as the average temperature is increased, and just moderately as inter-cylinder spacing is increased and the nanoparticle size is decreased.

The two-phase computational code used in the present study incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity and the coefficient of thermophoretic diffusion, all based on a high number of literature experimental data.