Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems

ISBN-13: 9783030492731 / Angielski / Twarda / 2020 / 399 str.

Gianpietro Elvio Cossali; Simona Tonini

Spis treści

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.  

Blurb

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.