Heat transfer in toroidal pipes when the Prandtl number is large

We discuss the temperature distribution in a toroidal pipe in the limit case $\Pr\to\infty$. The temperature is constant along the streamlines of the secondary flow. The temperature distribution on the streamlines is governed by an equation which is derived from the primary equation $(\Pr\ne\infty)$ by integration along closed streamlines. The boundary condition for this equation follows from the existence of the closed boundary layer near the wall and the symmetry plane of the pipe.