Weakly compressible Poiseuille flows of a HerschelBulkley fluid
Date
2009Source
Journal of NonNewtonian Fluid MechanicsVolume
158Issue
13Pages
162169Google Scholar check
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In this work, we derive approximate semianalytical solutions of the steady, creeping, weakly compressible plane and axisymmetric Poiseuille flows of a HerschelBulkley fluid. Since the flow is weakly compressible, the radial velocity component is assumed to be zero and the derivatives of the axial velocity with respect to the axial direction are assumed to be much smaller than those with respect to the radial direction. The axial velocity is then given by an expression similar to that holding for the incompressible flow, the only difference being that the pressuregradient is a function of the axial coordinate and satisfies a nonlinear equation involving the density of the fluid. In the present work, a linear as well as an exponential equation of state, relating the density of the fluid to the pressure, are considered. The pressure distribution along the flow direction is calculated by means of numerical integration and the twodimensional axial velocity can then be constructed. The effects of compressibility, the equation of state, the Bingham number and the powerlaw exponent on the solutions are investigated. © 2008 Elsevier B.V. All rights reserved.
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