Application of lie group analysis and computational methods to the analysis of the flow of a thin non-Newtonian fluid
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Date
2009-09-16T08:23:33Z
Authors
Neossi Nguetchue, S.N.
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Abstract
This thesis is primarily concerned with the application of Lie group analysis and
numerical methods to the analysis of the flow of a thin non-Newtonian fluid. In fact
due to the increasing importance of non-Newtonian fluids in industry and technological
applications during the last decades, researchers have written many papers and
developed methods to solve the equations resulting from the modelling of the flow
of such fluids. It is worth noting here that these equations are highly nonlinear due
to the nonlinear dependence of the fluid’s viscosity on the velocity gradient, adding
more complexity/nonlinearity to the nonlinear Navier-Stokes equations.
We show the importance of combining Lie group analysis and computational
methods to describe the flow of a thin non-Newtonian fluid. Lie group analysis
provides a systematic way, when well handled, to find exact solutions to certain
classes of nonlinear differential equations. When it is impossible to obtain exact
solutions, we can therefore make use of approximate methods and numerical schemes.
For the case of the axisymmetric spreading of a power-fluid over a horizontal plane, we use the method of separation of variables combined with the linearization
criterion given by Lie to find new exact solutions. We also extend the study of Newtonian
fluids to power-law fluids by applying the Lie group method. We determine
group-invariant solutions that generalize those of Newtonian fluids and take into
account the effects of shear-thinning and shear-thickening. Finally the homotopy
analysis method is applied to solve the flow of a generalized second-grade fluid on a
moving belt.