Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems

✍ Scribed by Gianpietro Elvio Cossali, Simona Tonini

• Publisher: Springer International Publishing;Springer
• Year: 2021
• Tongue: English
• Leaves: 403
• Series: Mathematical Engineering
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xi
Front Matter ....Pages 1-1
Introduction to Tensor Analysis (Gianpietro Elvio Cossali, Simona Tonini)....Pages 3-40
Elements of Differential Geometry of a Surface (Gianpietro Elvio Cossali, Simona Tonini)....Pages 41-71
Separability of PDE (Gianpietro Elvio Cossali, Simona Tonini)....Pages 73-88
Orthogonal Curvilinear Coordinate Systems (Gianpietro Elvio Cossali, Simona Tonini)....Pages 89-148
Sturm–Liouville Problems (Gianpietro Elvio Cossali, Simona Tonini)....Pages 149-181
Front Matter ....Pages 183-183
Conservation Equations (Gianpietro Elvio Cossali, Simona Tonini)....Pages 185-206
Introduction to Constitutive Equations (Gianpietro Elvio Cossali, Simona Tonini)....Pages 207-224
Conservation and Constitutive Equations in Curvilinear Coordinates (Gianpietro Elvio Cossali, Simona Tonini)....Pages 225-233
Modelling Heat and Mass Transfer from an Evaporating Drop (Gianpietro Elvio Cossali, Simona Tonini)....Pages 235-249
Front Matter ....Pages 251-251
One-Dimensional Modelling of Drop Heating and Evaporation Under Steady Conditions (Gianpietro Elvio Cossali, Simona Tonini)....Pages 253-295
Two- and Three-Dimensional Modelling of Heating and Evaporation Under Steady Conditions (Gianpietro Elvio Cossali, Simona Tonini)....Pages 297-328
Drop Evaporation Under Unsteady Conditions (Gianpietro Elvio Cossali, Simona Tonini)....Pages 329-356
Multi-component Drop Evaporation (Gianpietro Elvio Cossali, Simona Tonini)....Pages 357-370
Back Matter ....Pages 371-399

✦ Subjects

Engineering; Engineering Fluid Dynamics; Engineering Mathematics; Computational Science and Engineering; Mathematical Modeling and Industrial Mathematics; Differential Geometry