Abstract:
In this work, we compare a parabolic equation with an elliptic
equation both of which are used in modeling temperature profile of a powerlaw
polymer
ow in a semi-infinite straight pipe with circular cross section.
We show that both models are well-posed and we derive exponential rates of
convergence of the two solutions to the same steady state solution away from
the entrance. We also show estimates for difference between the two solutions
in terms of physical data.