In this work, we compare a parabolic equation with an elliptic equation both of which are used in modeling temperature profile of a power-law polymer flow 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.
Electronic Journal of Differential Equations
Wei, Dongming [Wei,Dongming1] (1-NORL); Zhang, Zhenbu (1-TULN) Decay estimates of heat transfer to Melton polymer flowin pipes with viscous dissipation. (English summary) Electron. J. Differential Equations 2001, No. 39, 14 pp.