Correlating equations for the buoyancy-induced heat transfer from two differently heated cylinders set in free air side by side

Steady laminar free convection from a pair of horizontal cylinders, differently heated at temperatures th and tc, aligned side by side in free air at temperature t?, is studied numerically. A SIMPLE-C algorithm is used for the solution of the mass, momentum and energy transfer governing equations. Simulations are performed for inter-cylinder spacings from 0.1 up to 10 cylinder-diameters, for values of the Rayleigh number of the heated cylinder ranging from 10^3 to 10^7, and for values of the temperature ratio teta = (tc – tinf)/(th – tinf) in the range between –3 and +0.5. Among the main results obtained, it is found that a minimum for the heat transfer performance of both cylinders occurs at an inter-cylinder spacing which depends on Ra and teta. In addition, for teta > 0, i.e., for tinf < tc < th, such minimum is found to be followed by a shallow maximum with increasing the inter-cylinder spacing. Dimensionless correlating-equations for the calculation of the average Nusselt numbers for both cylinders, as well as of the distance at which the effects of their mutual convective interactions disappear, are proposed.