Lie Group Analysis of Creeping Flow
of a Second-Grade Fluid .
Due to the small scale of the calculation model, the pore size is less than 0.1 mm, and the Reynolds number is far less than 1; thus the creeping flow
(Stokes Flow) interface was utilized to solve the flow problem instead of the Laminar Flow (N-S equation) interface in this paper.
, based on this concept was developed, inducing perfectly axisymetric creeping flow
, showing high distributive and dispersive capabilities without generating excessive pressure drops as shown by Bouquey et al.
pattern was observed at low Re (Re=1) for all step height as per Fig.
Among the topics are a boundary element solution of thermal creeping flow
in a nanometer single mixer, evaluating interface cracks, rotational symmetry applied to boundary element computation for nuclear fusion plasma, fundamental solutions for inverse obstacle acoustic scattering, the volume integral equation method for analyzing scattered waves in an elastic half space, and analyzing layered soil problems with an alternative multi-region boundary element method technique and a new infinite boundary element formulation.
For very low Reynolds numbers (Re<0.1), the so-called "creeping flow
" conditions apply and the drag coefficient for a sphere takes a simple form, first derived by Stokes:
For Re > 35, upward deviation of f values from the linear relation is observed indicating transition from the creeping flow
. The additional pressure losses are due to contributions from the creeping flow
as well as the boundary layer flow with in the transition region.
The equations of conservation of mass, momentum and energy for steady, creeping flow
(very low Reynolds Number, inertialess) must be solved.
This approach has been used to study the creeping flow
of power law fluids (Bruschke and Advani, 1993; Chen and Wung, 1989; Spelt et al., 2005a) and finite Reynolds number flow has been considered by Spelt et al.
However, no attempt so far has been made to extend this method for quasi-hyperbolic constitutive equations in the limit of creeping flow
To further reduce the difficulty of the problem, creeping flow
It is now well known that the so-called Stokes paradox does not exist for the creeping flow
of shear-thinning (n < 1) fluids past an unconfined circular cylinder (Tanner, 1993; Marusic-Paloka, 2001) and reliable results are now available for the creeping flow
of power law fluids (Tanner, 1993; Whitney and Rodin, 2001; Ferreira and Chhabra, 2004).