An analytical study is performed to determine the threshold value of the Peclet number below which conventional Nusselt number relations are invalidated by the effect of streamwise heat conduction. The investigation encompasses the Prandtl number range of liquid metals. Consideration is given to pure forced-convection boundary layer flow on a flat plate and to the forced-convection boundary layer on a vertical plate with superposed free convection. If Pex, Rex, and Grx, respectively, denote the Peclet, Reynolds, and Grashof numbers, all based on the streamwise coordinate x, then the threshold value of Pex is found to range from 12 to 7 as Grx/Rex2 ranges from 0 (pure forced convection) to 1.0. The present analysis does not provide Nusselt number results for very low Peclet numbers, where streamwise conduction effects play a decisive role.