Natural convection in air, in vertical convergent channels, is analyzed to carry out thermal design and optimization criteria. A scale analysis is developed to estimate the optimal geometrical configuration in terms of total volume and average wall temperature. The best geometrical configuration obtained by this analysis is the parallel-plates channel. New correlations for mass flow rate, radiative heat flux, and dimensionless maximum wall temperature are proposed in the emissivity range from 0.10 to 0.90, convergence angle ranging from 0 degrees. to 10 degrees., ratio between minimum and maximum channel spacing in the range from 0.048 to 1.0, aspect ratio, the ratio between wall length and minimum channel spacing, in the range from 10 to 58, and average channel Rayleigh number in the range from 5.0 to 2.3 x 10(5). For the same convergence angle and ratio between minimum and maximum channel spacing ranges, new average Nusselt number correlations are also given. These correlations are evaluated for emissivity value equal to 0.90, for aspect ratio, referred to the minimum channel spacing, ranging from 10 to 80 and average channel Rayleigh number ranging from 2.5 x 10(-2) to 2.3 x 10(5).