The optimal spacing of cylinders in free-stream cross-flow forced convection

This is an experimental, numerical and analytical study of the optimal spacing between cylinders in cross-flow forced convection. The cylinder array occupies a fixed volume and is exposed to a free stream of given velocity and temperature. The optimal cylinder-to-cylinder spacing is determined by maximizing the overall thermal conductance between all the cylinders and the free stream. In the first part, the optimal spacing and corresponding maximum thermal conductance are determined based on experiments with forced air for H D = 6.2 and in the Re D range 50–4000, where Re D is based on the free-stream approach velocity and cylinder diameter D, and H is the array length in the flow direction. In the second part, similar results are developed based on numerical simulations for Pr = 0.72, 10 ⩽ H D ⩽ 20 and 40 ⩽ Re D ⩽ 200. In the concluding section, the experimental and numerical results for optimal spacing and maximum thermal conductance are explained and correlated analytically by intersecting the small-spacing and large-spacing asymptotes of the thermal conductance function.