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Shear flows of a new class of power-law fluids

Christiaan Le Roux, Kumbakonam R. Rajagopal (2013)

Applications of Mathematics

We consider the flow of a class of incompressible fluids which are constitutively defined by the symmetric part of the velocity gradient being a function, which can be non-monotone, of the deviator of the stress tensor. These models are generalizations of the stress power-law models introduced and studied by J. Málek, V. Průša, K. R. Rajagopal: Generalizations of the Navier-Stokes fluid from a new perspective. Int. J. Eng. Sci. 48 (2010), 1907–1924. We discuss a potential application of the new...

Start-up of channel-flow of a Bingham fluid initially at rest

Irene Daprà, Giambattista Scarpi (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We present an analytical solution of plane motion for a Bingham fluid initially at rest subjected to a suddenly applied constant pressure gradient. Using the Laplace transform we obtain expressions which allow a direct easy calculation of the velocity, of the plug thickness and of the rate of flow as function of time.

Steady-state buoyancy-driven viscous flow with measure data

Tomáš Roubíček (2001)

Mathematica Bohemica

Steady-state system of equations for incompressible, possibly non-Newtonean of the p -power type, viscous flow coupled with the heat equation is considered in a smooth bounded domain Ω ⊂ ℝ n , n = 2 or 3, with heat sources allowed to have a natural L 1 -structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if p > 3 / 2 (for n = 2 ) or if p > 9 / 5 (for n = 3 ).

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