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 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.
|Journal||Electronic Journal of Differential Equations|
|Publication status||Published - 2001|
- Decay estimates
- Heat transfer
- Power-law flow
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