We have examined the styles of steady-state convective heat transfer for two kinds of mantle thermal conductivity models in an aspect-ratio one box. We have employed the phonon portion of the thermal conductivity model of Hofmeister (1999) and varied the radiative component in this model. We have also considered a second model which emphasizes radiative heat transfer and has a high contribution in the lower mantle. We have conducted constant viscosity calculations out to a surface Ra of 1010. Variable conductivity enhances in most cases the surface heat flow. The smallest deviation from the constant conductivity model comes from the phonon model with the parameters associated with oxides. Larger heat flow is obtained with silicates and increasing radiative contributions associated with the values of Shankland et al.(1979). The highest heat flow values are obtained for the radiatively dominated model, where the thermal conductivity in the deep mantle can be a factor of 50 greater than the surface conductivity value. ¿ 2001 American Geophysical Union