Free convection heat transfer from a horizontal cylinder affected by a downstream parallel cylinder of different diameter

Steady laminar free convection in air from an isothermal horizontal cylinder affected by a superimposed parallel cylinder of different diameter, either at same temperature of the underneath cylinder or adiabatic, 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 governing equations. Simulations are performed for ratios between the diameters of the upper and lower cylinders from 0 to 125, for inter-cylinder spacings from 0.1 up to more than 20 diameters of the bottom cylinder, and for values of the Rayleigh number in the range between 101 and 107. It is found that (a) for cylinder-spacings smaller than a first critical distance, the heat transfer performance of the bottom cylinder degrades owing to the presence of the top cylinder, whichever is the temperature condition imposed at the top cylinder surface, and (b) the thermal state of the upper cylinder surface starts being effective on the thermal behavior of the bottom cylinder once the cylinder-spacing is further reduced below a second critical distance. Dimensionless correlating-equations for the calculation of the heat transfer rate at the bottom cylinder surface, and of the first and second critical distances cited above, are also proposed.