Results are reported of calculations of the Nusselt number for steady two‐dimensional laminar convection in a thin fluid layer between parallel conducting plates. An iterative numerical technique is used to calculate the Nusselt number and the structure of the roll for Rayleigh numbers between 2000 and 22 000 and for Prandtl numbers of 0.5, 1, 2, 6.8, and 200. Comparison with results at Prandtl numbers of 6.8 and ∞ obtained by other investigators using different techniques show good agreement. Discussion is included of the factors affecting accuracy: (1) the zone size in a finite‐difference mesh, (2) the number of iteration cycles, and (3) extrapolation from a sequence of meshes to zero zone size. The conclusion is that extrapolation from a pair of grids using 20 and 30 zones per length scale can yield 1% accuracy over the ranges of parameters considered.