Correlating equations for free convection heat transfer from horizontal isothermal cylinders set in a vertical array

Steady laminar free convection from flat vertical arrays of equally-spaced, horizontal isothermal cylinders set in free air, is studied numerically. A specifically developed computer-code based on the SIMPLE-C algorithm is used for the solution of the mass, momentum and energy transfer governing equations. Simulations are performed for arrays of 2–6 circular cylinders, for center-to-center separation distances from 2 up to more than 50 cylinder-diameters, and for values of the Rayleigh number based on the cylinder-diameter in the range between 5 × 102 and 5 × 105. It is found that the heat transfer rate at the bottom cylinder remains the same as a single cylinder. In contrast, the downstream cylinders may exhibit either enhanced or reduced Nusselt numbers depending on their location in the array and on the geometry of the array. Heat transfer dimensionless correlating equations are proposed both for any individual cylinder in the array and for the whole tube-array. New correlation-equations for the calculation of the heat transfer rate from a single cylinder to the surrounding air are also proposed and compared to those available in the open literature.