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 sele ct the spacing (S) between horizontal cylinders in an array with lamin ar natural convection, such that the total heat transfer (q) between t he array and the ambient is maximized. The volume occupied by the arra y (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 resu lts predicted theoretically are developed into accurate and well teste d correlations by means of numerical simulations and experimental meas urements. The recommended correlations are S-opt/D=2-72(H/D)Ra-1/3(D)- 1/4+0.263 and ($) over tilde(max)=0.448[(H/D)Ra-1/3(D)-1/4](-1/6) wher e ($) over tilde q(max) is the dimensionless maximum overall thermal c onductance, ($) over tilde q(max)=q(max)D(2)/[HLWk(T-w - T-infinity)]. The optimal spacing is relatively insensitive to whether the cylinder s are isothermal or with uniform heat flux.