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Lie-Group Analysis of Newtonian/Non-Newtonian Fluids Flow (Paperback)
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Lie-Group Analysis of Newtonian/Non-Newtonian Fluids Flow (Paperback)
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In this book, group methods are presented for finding the
similarity solutions for some systems of partial differential
equations, which govern the problems of convective flow in the
boundary layer of Newtonian and non-Newtonian fluid. We will use
three methods for finding the similarity representations (i)
Scaling transformations, (ii) Infinitesimal Lie group analysis and
(iii) Suitable similarity transformations. Lie groups, and hence
their infinitesimal generators, can be naturally extended or
"prolonged" to act on the space of independent variables, dependent
variables and derivatives of the dependent variables up to any
finite order. As a consequence, the seemingly intractable nonlinear
conditions of group invariance of a given system of differential
equations reduce to linear homogeneous equations determining the
infinitesimal generators of the group. Since these determining
equations form an over determined system of linear homogeneous
partial differential equations. If a system of partial differential
equations is invariant under a Lie group of point transformations,
one can find, constructively, special solutions, called similarity
solutions or invariant solutions.
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