The purpose of this research was to investigate the extent to which the thermal conductivity of non-Newtonian fluids is affected by fluid motion, and then the effect of this shear-rate-dependent thermal conductivity, measured in Lee [1995], on the heat transfer for a typical convective system. Such information would have important implications in the design and analysis of non-Newtonian thermal systems such as are found in food processing operations, polymer processing, paint manufacturing, biological systems and many others. A simple parallel plate flow model with temperature-independent properties gave increases in heat transfer on the order of 30-80% compared to the heat transfer with shear-rate-independent thermal conductivity in Newtonian fluid flow over the entire temperature range (20-50℃) of CMC solutions depending on the inlet average velocity due to the effect of the shear-rate-dependent thermal conductivity.