Editor: S. G. Ahmed

Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application

eBook: US $89 Special Offer (PDF + Printed Copy): US $142
Printed Copy: US $98
Library License: US $356
ISBN: 978-981-5040-89-0 (Print)
ISBN: 978-981-5040-88-3 (Online)
Year of Publication: 2022
DOI: 10.2174/97898150408831220101


The mathematical modelling of free and moving boundary problems are an important topic in engineering, industry, technology and theoretical sciences. These models allow us to make calculations involved in phase change transitions of materials due to heat transfer. Boundary layer applications are widespread in research and industry.

Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application equips the reader with information about heat transfer problems occurring during phase changes. The book covers several boundary element methods, including methods for phase changes, fixed and moving domains and new approaches. The contents are rounded off with chapters on numerical results and industrial applications.

Key features:

  • - Simple, didactic presentation of boundary layer problems for heat transfer problems
  • - Covers a wide range of boundary element methods
  • - Includes methods for fixed and moving domains
  • - Explains industrial applications of the methods
  • - Includes solutions to numerical problems

The book serves as a textbook for students of advanced mathematics and engineering. It is also a handbook for researchers working on numerical analysis, who require a focused volume on boundary element methods for heat transfer applications.

Audience: Students of advanced mathematics and engineering. Researchers working on numerical analysis, who require a focused volume on boundary element methods for heat transfer applications.


Free and moving boundaries are among the problems of the world of engineering, industry, technology, and even theoretical sciences. These applications are widespread, and the phase change problems are among the most important types of these problems. In modern science, discussing phase transition problems receives a lot of attention, and as technology advances, we discover that interest in the topic is growing, with a wide range of applications. If we want to know the initial emergence of this science, we find it emerged from a very simple thing, which is how to look at an ice cube and how it takes the form of melting until the ice cube reaches a liquid state, and this is what the scientist Stefan started with, through which this science developed and took multiple applied fields among them, for example, are not limited to, and in engineering fields, we mention only some of them:

Industrial and engineering applications:
  • - Diffusion problems
  • - Solidification problems
  • - Freezing Problems
  • - Groundwater proliferation problems
  • - Road paving problems
  • - Problems of the food industry

In the medical fields:
  • - The diffusion of oxygen in the cell
  • - The spread of cancer in the body
  • - In the field of epidemics

In the fields of the environment:
  • - In the field of wastewater treatment
  • - In the desalination of sea water
  • - In the field of groundwater dispersal, tracking, and utilization

In the nuclear field:
  • - Laser industry
  • - In nuclear reactors in many stages of the nuclear bomb
  • - In the stages of generating the hydrogen bomb

The current book, in fact, consists of two parts, and each part is comprises more than 500 pages. It is a theoretical and practical study of one type of application of free and moving boundary problems, namely Phase change problems with different methods of dealing with these applications through an advanced numerical method, namely, the Boundary Element Methods. The first part is divided into eight chapters and four appendices and can be classified as follows:

  • Chapter One: it is a theoretical study of phase change issues in terms of the theoretical framework, historical overview, and various mathematical models.
  • Chapter Two: An analytical study of the limit element methods and their application to positional issues.
  • Chapter Three: Application of boundary element methods to phase change issues in general.
  • Chapter Four : Application of boundary element methods to fixed-band prop- agation problems.
  • Chapter Five: Application of boundary element methods to mobile-band propagation problems.
  • Chapter Six: A new proposal and a vision for methods of borderline elements.
  • Chapter Seven: Numerical studies and analysis of results.
  • Chapter Eight: An extensive study of one of the applications of free phase change problems.

The appendix consists of four sub-appendices.

The current work is the result of more than 35 years of academic research in this field, and we pray for God's blessing.


The authors declare no conflict of interest.



S. G. Ahmed
Faculty of Engineering
Zagazig University