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Publication 17-CNA-005

The Couette-Poiseuille flow of a suspension modeled as a modified third-grade fluid

Mehrdad Massoudi
Center for Nonlinear Analysis
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
and
National Energy Technology Laboratory (NETL)
U.S. Department of Energy
626 Cochrans Mill Road, P.O. Box 10940
Pittsburgh, PA 15236
massoudi@netl.doe.gov

Phuoc X. Tran
National Energy Technology Laboratory (NETL)
U.S. Department of Energy
626 Cochrans Mill Road, P.O. Box 10940
Pittsburgh, PA 15236

Abstract: In this paper, we modify the thermodynamically compatible third-grade fluid model by introducing a shear-rate- and volume-fraction-dependent viscosity into the equation.With this new model, it is possible to predict not only the normal stress differences, but also the variable viscosity observed in many suspensions.We study the Couette-Poiseuille flow of such a fluid between two horizontal flat plates. The steady fully developed flow equations are made dimensionless and are solved numerically; the effects of different dimensionless numbers are discussed.

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