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Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems

  • Book
  • © 2021

Overview

Authors:
  1. Gianpietro Elvio Cossali

    1. Department of Engineering and Applied Sciences, University of Bergamo, Dalmine, Italy

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    You can also search for this author in PubMed   Google Scholar

  2. Simona Tonini

    1. Department of Engineering and Applied Sciences, University of Bergamo, Dalmine, Italy

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    You can also search for this author in PubMed   Google Scholar

  • Provides both rigorous treatments of the theory and real-world examples
  • Includes solutions to Laplace and Helmholtz in explicit form and several coordinate systems
  • Addresses the needs of engineering researchers in academia and industry

Part of the book series: Mathematical Engineering (MATHENGIN)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xi
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  2. Mathematical Tools

    1. Front Matter

      Pages 1-1
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    2. Introduction to Tensor Analysis

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 3-40

    3. Elements of Differential Geometry of a Surface

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 41-71

    4. Separability of PDE

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 73-88

    5. Orthogonal Curvilinear Coordinate Systems

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 89-148

    6. Sturm–Liouville Problems

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 149-181

  3. Mass, Momentum and Energy Conservation Equations in Curvilinear Coordinates

    1. Front Matter

      Pages 183-183
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    2. Conservation Equations

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 185-206

    3. Introduction to Constitutive Equations

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 207-224

    4. Conservation and Constitutive Equations in Curvilinear Coordinates

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 225-233

    5. Modelling Heat and Mass Transfer from an Evaporating Drop

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 235-249

  4. Analytical Modelling of Drop Heating and Evaporation

    1. Front Matter

      Pages 251-251
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    2. One-Dimensional Modelling of Drop Heating and Evaporation Under Steady Conditions

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 253-295

    3. Two- and Three-Dimensional Modelling of Heating and Evaporation Under Steady Conditions

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 297-328

    4. Drop Evaporation Under Unsteady Conditions

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 329-356

    5. Multi-component Drop Evaporation

      • Gianpietro Elvio Cossali, Simona Tonini
      Pages 357-370

  5. Back Matter

    Pages 371-399
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Keywords

About this book

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 alsobenefit graduate students.

Authors and Affiliations

  • Department of Engineering and Applied Sciences, University of Bergamo, Dalmine, Italy

    Gianpietro Elvio Cossali, Simona Tonini

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