A. Bejan et al., THE OPTIMAL SPACING BETWEEN HORIZONTAL CYLINDERS IN A FIXED VOLUME COOLED BY NATURAL-CONVECTION, International journal of heat and mass transfer, 38(11), 1995, pp. 2047-2055
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.