Electron. J. Diff. Eqns., Vol. 2001(2001), No. 39, pp. 1-14.

Decay estimates of heat transfer to melton polymer flow in pipes with viscous dissipation

Dongming Wei & Zhengbu Zhang

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.

Submitted March 3, 2001. Published May 29, 2001.
Math Subject Classifications: 35B45, 76D03, 80A20.
Key Words: Heat transfer, decay estimates, pipes, power-law flow.

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Dongming Wei
Department of Mathematics
University of New Orleans
New Orleans, Louisiana 70148 USA
e-mail: dwei@math.uno.edu
Zhenbu Zhang
Department of Mathematics
Tulane University
New Orleans, Louisiana 70118 USA
e-mail: zzhang@tulane.edu

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