Configurations for single-scale cylinder pairs in natural convection

• Buoyancy-induced flow around single scale cylinder pairs is examined.
• Optimum designs are demonstrated using theory, experiment and numerical analyses.
• Multiple constructal configurations exist for vertically aligned pairs.
• Confirmation of the predictions provides insight into cylinder interactions.

A thermal-fluid system consisting of an isothermal heated cylinder pair cooled naturally in air is examined. The single-scale cylinder pairs are horizontally orientated and investigated in both horizontal and vertical alignment to determine if optimal configurations exist which maximize heat dissipation at the local cylinder and global array levels. Numerical and experimental approaches are used to assess cylinder interactions in the laminar flow regime 104 ≤ RaD ≤ 105. Experimental measurements and numerical predictions confirm the scaling relationships determined using scale analyses and intersection of asymptotes methods. The optimal horizontally aligned configuration was found when the separation distance resulted in merging of the thermal boundary layers of adjacent cylinders, hence confirming the constructal approach for this geometry and flow regime. Similar separation distance result from combined objectives of maximizing local cylinder and overall array heat transfer performance. In contrast, vertically aligned pairs have multiple constructal configurations and depend on the significance of internal local convective resistances. Upper cylinder Nusselt number is enhanced over a single cylinder when the combined effects of lower cylinder plume velocity and temperature impose a beneficial buoyancy-assisted flow. Through defining the plume characteristics and applying a mixed convection analogy, a prediction of the local and global thermal performances is presented.