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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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