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The purpose of this research was to investigate the extent to which the thermal conductivity of non-Newtonian fluids is affected by fluid motion under conditions in which it is known that the viscous properties undergo significant changes, and then the effect of these shear rate dependent thermal conductivity measured in Lee [1995], on the heat transfer for a typical convective system. A coaxial cylinder apparatus with a rotating outer cylinder was used for the determination of the thermal conductivity of non-Newtonian liquids in a shear field. A simple parallel plate flow model with temperature independent properties gave increases in heat transfer of the order of 30--80% over the entire temperature range (20°C--50°C) of CMC solutions depending on the inlet average velocity due to the effect of the shear dependent thermal conductivity.