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001 978-3-319-45726-0
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008 161102s2017 sz | s |||| 0|eng d
020 _a9783319457260
_9978-3-319-45726-0
024 7 _a10.1007/978-3-319-45726-0
_2doi
050 4 _aTA329-348
050 4 _aTA345-345.5
072 7 _aTBJ
_2bicssc
072 7 _aTEC009000
_2bisacsh
072 7 _aTBJ
_2thema
082 0 4 _a620
_223
100 1 _aZohuri, Bahman.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_960529
245 1 0 _aDimensional Analysis Beyond the Pi Theorem
_h[electronic resource] /
_cby Bahman Zohuri.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXIX, 266 p. 78 illus., 36 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPrinciples of the Dimensional Analysis -- Dimensional Analysis: Similarity and Self-Similarity -- Shock Wave and High Pressure Phenomena -- Similarity Methods for Nonlinear Problems -- Appendix A: Simple Harmonic Motion -- Appendix B: Pendulum Problem -- Appendix C: Similarity Solutions Methods for Partial Differential Equations (PDEs) -- Index.
520 _aDimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First and Second kind. Such solutions are not newly discovered; they have been identified and named by Zel’dovich, a famous Russian Mathematician in 1956. They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials. Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation. It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar. Variables can be specifically chosen for the calculations.
650 0 _aEngineering mathematics.
_93254
650 0 _aEngineering—Data processing.
_931556
650 0 _aThermodynamics.
_93554
650 0 _aHeat engineering.
_95144
650 0 _aHeat transfer.
_932329
650 0 _aMass transfer.
_94272
650 0 _aFluid mechanics.
_92810
650 1 4 _aMathematical and Computational Engineering Applications.
_931559
650 2 4 _aEngineering Thermodynamics, Heat and Mass Transfer.
_932330
650 2 4 _aEngineering Fluid Dynamics.
_960530
710 2 _aSpringerLink (Online service)
_960531
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319457253
776 0 8 _iPrinted edition:
_z9783319457277
776 0 8 _iPrinted edition:
_z9783319833590
856 4 0 _uhttps://doi.org/10.1007/978-3-319-45726-0
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c80567
_d80567