Steady temperature fields in second order fluids

It was shown earlier that if a viscometric flow of an incompressible simple fluid takes place between two surfaces held at constant but differing temperatures, and if the temperature gradient exists in the direction of the velocity gradient only, two conductivity coefficients determine the heat flow and the temperature field. In this article, after the zeroth, first and second order asymptotic expansions for the heat flux vector are developed under a fading memory assumption, the temperature fields in a few viscometric flows are determined und the above condition on the temperature gradient. It is found that a reduction in heat transfer can occur under these conditions, which suggests that the present theory may be used to explain the observations in turbulent flows of polymer additives in water.