We study the problem of heat transport by fluid flows with prescribed veloc
ity fields. The advection-diffusion equation in two dimensions is solved fo
r two velocity fields: (i) a circulation and (ii) a shear flow. These two f
lows focus separately on the two dominant features of the mean large-scale
flow observed in turbulent convection experiments. We find that the Nusselt
number, which measures the heat transport, scales respectively for the two
velocity fields.