Influence of upstream conduction on the thermally optimum spacing of isothermal, natural convection-cooled vertical plate arrays

The influence of upstream conduction on the thermal optimization of the spacing used in arrays of equally spaced, natural convection-cooled vertical plates is investigated. The optimization is carried out analytically by maximizing the total heat transfer rate per unit horizontal area with respect to plate spacing. Correlations for the average Nusselt number are taken from the literature, derived analytically or obtained from results of an elliptic numerical model. Ranges of the Rayleigh number (based on the channel length) for which upstream conduction effects modify the optimum spacing obtained using the Elenbaas asymptote, are determined for two different Prandtl numbers.