The optimal spacing between horizontal cylinders in a fixed volume cooled by natural convection

This is a theoretical, numerical and experimental study of how to select the spacing (S) between horizontal cylinders in an array with laminar natural convection, such that the total heat transfer (q) between the array and the ambient is maximized. The volume occupied by the array (height H, width W, cylinder length L) and the cylinder diameter (D) are arbitrary but fixed, while the spacing (or number of cylinders in the array) varies. The optimal spacing and maximum heat transfer results predicted theoretically are developed into accurate and well tested correlations by means of numerical simulations and experimental measurements. The recommended correlations are Sopt/D = 2.72(H/D) 1 3 RaD − 1 4 +0.263 and q ̃ max = 0.448[( H D ) 1 3 Ra D − 1 4 ]− 1 6 where q ̃ max is the dimensionless maximum overall thermal conductance, q ̃ max = q max D2/[HLWk(T w - T∞)]. The optimal spacing is relatively insensitive to whether the cylinders are isothermal or with uniform heat flux.