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Sustainable Nanocellulose and Nanohydrogels from Natural Sources
explores the use of biopolymers in specific application areas such
as electronics, energy, consumer goods, packaging materials,
therapeutics, water treatment and engineering, and what makes the
particular polymer to engage it in these applications. This is an
important reference source for those who would like to learn more
about how biopolymeric nanocomposites are used in sustainability
and environmental protection. Biopolymers, including plant and
sea-based polymers, play an important role in the formation and
maintaining the stability of industrial nanocomposites; their
common functions being the surface modification and protection for
the highly oxidative-unstable cores, as stable base for holding
multiple targets, and as a shield for the inorganic and highly
toxic metals. These biopolymer-based nanocomposites are being used
for applications in the electronics, automobile, construction and
biomedical sectors.
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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