We have previously described a method for the precise study of steady two-dimensional convection problems in the asymptotic limit of large Rayleigh numberR, assuming a very viscous fluid with the Prandtl number effectively infinite. The method here is applied to cellular convection between isothermal horizontal planes (Bénard convection). The result for the dimensionless heat flux, or Nusselt number, iswherecis ⅓ for free-surface convection and ⅕ for fixed surface convection. The constantbis found numerically, as a function of the cell aspect ratio.