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Analytical solutions for transport processes. Fluid mechanics, heat and mass transfer. (English) Zbl 1382.35003

Mathematical Engineering. Berlin: Springer (ISBN 978-3-662-51421-4/hbk; 978-3-662-51423-8/ebook). xv, 300 p. (2017).
The book provides analytical solutions to a number of classical problems in transport processes in fluid mechanics, heat and mass transfer. In its nine chapters and an appendix, it covers a variety of topics of both fundamental and practical applications and develops a bench mark solutions which may be used for the comparison and the physical interpretations of the computer solutions of the complex problems.
Chapter 1 discusses the theoretical basis of the fluid dynamic equations especially to incompressible fluid continua with negligible effects of dissipative heating.
Chapter 2 presents the equations for the stream function for two dimensional flow problems in Cartesian, cylindrical and spherical coordinates. The presentation is structured according to linearity, time dependence and dependence of pressure on the spatial coordinates.
Chapter 3 presents laminar two dimensional flow through structures with solid walls and constant flow cross section; and flows outside the surfaces of solid bodies in motion, allowing the formation of two dimensional velocity fields. Onset of flow between two concentric spherical shells, particularly the cerebrospinal fluid between human brain and the skull is of special interest.
Chapter 4 presents the lubrication approximation in analyzing flow fields characterized by very different geometrical length scales in the flow directions and transverse to it. The problem of technical importance like plane solid bearing, cylindrical bearing, wire coatings etc. is discussed.
Chapter 5 presents boundary layer flows. Laminar flows along a flat plate, flow along a slender body of revolution, plane submerged free jet axisymmetric submerged free jet, plane free shear layer, and wake behind a flat plate are discussed in a lucid manner.
Chapter 6 presents the flows with interfaces. These flows and their instability are elementary to the formation of the disperse phase in many gas-liquid two phase flows, such as sprays and bubbly flows. For transport processes across the interface, oscillations of drops and bubbles are studied. Capillary flows find a special mention.
Chapter 7 presents the thermal energy equation with its special form for heat conduction, and the continuity equation for a component of a mixture in its various forms, including the purely diffusive form for equimolar processes. Various non-dimensional parameters are introduced to simplify the energy transport equations.
Chapter 8 presents the analytical solutions of the heat transfer problems of conduction and convection. The solutions of the heat conduction problems in various geometries and also cooling fins are derived. Some problems of free and forced convections are also discussed.
Chapter 9 presents the solution of mass transport problems, which involves the diffusion equations, the underlying differential equations for the spatiotemporal evolution of the species concentration. Convective mass transfer from flat surfaces and convective dryings are also discussed.
The equations of transport processes in various geometries, basic vector analytical operations and special functions are put in the Appendices A, B and C.
The book is well written and the readers may find the book easy reading. The readers interested in the solution of heat transfer problems may also find a book on the Mathematical Principles of Heat Transfer by K. N. Shukla [Mathematical principles of heat transfer. New York, NY: Begell House (2005; Zbl 1108.76001)] as a supplement to this book.
To sum, this book will serve a niche readership interested on the analytical solutions of the transport processes. It is recommended as a text book for the students of mathematics and engineering and also for libraries supporting researches on transport processes and related R&D as well as educational institutions.

MSC:

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35Q35 PDEs in connection with fluid mechanics
80-02 Research exposition (monographs, survey articles) pertaining to classical thermodynamics
35Q79 PDEs in connection with classical thermodynamics and heat transfer
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics

Citations:

Zbl 1108.76001
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