The present study investigates the effect of the shear rate-dependent thermal conductivity of non-newtonian fluids on the heat transfer enhancement in a 2:1 rectangular duct flow. An axially-constant heat flux and a peripherally-constant temperature boundary conditions(H1) was adopted for a top-wall-heated configuration. The present numerical results of Nusselt numbers for SRDC(Separan) show heat transfer enhancement over those of SRIC. The Nusselt numbers increased linearly as Reynolds numbers increased. The heat transfer enhancement is due to an increased thermal conductivity near the wall, which is attributed to the shear rate-dependence.