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.
Product Identifiers
Publisher
Lap Lambert Academic Publishing
ISBN-13
9783847321057
eBay Product ID (ePID)
113869944
Product Key Features
Author
Fouad Ibrahim, Mohamed Mansour, Mohammad Hamad
Publication Name
Lie-Group Analysis of Newtonian/Non-Newtonian Fluids Flow
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
2012
Type
Textbook
Number of Pages
260 Pages
Dimensions
Item Height
229mm
Item Width
152mm
Item Weight
386g
Additional Product Features
Title_Author
Mohamed Mansour, Fouad Ibrahim, Mohammad Hamad
Country/Region of Manufacture
Germany
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