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Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems [electronic resource] / by Gianpietro Elvio Cossali, Simona Tonini.

By: Cossali, Gianpietro Elvio [author.].
Contributor(s): Tonini, Simona [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Mathematical Engineering: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2021Edition: 1st ed. 2021.Description: XI, 399 p. 86 illus., 19 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783030492748.Subject(s): Fluid mechanics | Engineering mathematics | Mathematics—Data processing | Mathematical models | Geometry, Differential | Engineering Fluid Dynamics | Engineering Mathematics | Computational Science and Engineering | Mathematical Modeling and Industrial Mathematics | Differential GeometryAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 620.1064 Online resources: Click here to access online
Contents:
Part I: Mathematical tools -- Introduction to tensor analysis -- Elements of differential geometry of a surface -- Separability of PDE -- Orthogonal curvilinear coordinate systems -- Sturm-Liouville problems -- Part II: Mass, momentum and energy conservation equations in curvilinear coordinates -- Conservation equations. .
In: Springer Nature eBookSummary: This book describes analytical methods for modelling drop evaporation, providing the mathematical tools needed in order to generalise transport and constitutive equations and to find analytical solutions in curvilinear coordinate systems. Transport phenomena in gas mixtures are treated in considerable detail, and the basics of differential geometry are introduced in order to describe interface-related transport phenomena. One chapter is solely devoted to the description of sixteen different orthogonal curvilinear coordinate systems, reporting explicitly on the forms of their differential operators (gradient, divergent, curl, Laplacian) and transformation matrices. The book is intended to guide the reader from mathematics, to physical descriptions, and ultimately to engineering applications, in order to demonstrate the effectiveness of applied mathematics when properly adapted to the real world. Though the book primarily addresses the needs of engineering researchers, it will also benefit graduate students.
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Part I: Mathematical tools -- Introduction to tensor analysis -- Elements of differential geometry of a surface -- Separability of PDE -- Orthogonal curvilinear coordinate systems -- Sturm-Liouville problems -- Part II: Mass, momentum and energy conservation equations in curvilinear coordinates -- Conservation equations. .

This book describes analytical methods for modelling drop evaporation, providing the mathematical tools needed in order to generalise transport and constitutive equations and to find analytical solutions in curvilinear coordinate systems. Transport phenomena in gas mixtures are treated in considerable detail, and the basics of differential geometry are introduced in order to describe interface-related transport phenomena. One chapter is solely devoted to the description of sixteen different orthogonal curvilinear coordinate systems, reporting explicitly on the forms of their differential operators (gradient, divergent, curl, Laplacian) and transformation matrices. The book is intended to guide the reader from mathematics, to physical descriptions, and ultimately to engineering applications, in order to demonstrate the effectiveness of applied mathematics when properly adapted to the real world. Though the book primarily addresses the needs of engineering researchers, it will also benefit graduate students.

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