The Application of the Chebyshev-Spectral Method in Transport Phenomena, 1st Edition

  • Published By:
  • ISBN-10: 3642340881
  • ISBN-13: 9783642340888
  • DDC: 512.89
  • Grade Level Range: College Freshman - College Senior
  • 229 Pages | eBook
  • Original Copyright 2012 | Published/Released May 2014
  • This publication's content originally published in print form: 2012

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Transport phenomena problems that occur in engineering and physics are often multi-dimensional and multi-phase in character.  When taking recourse to numerical methods the spectral method is particularly useful and efficient. The book is meant principally to train students and non-specialists  to use the spectral method for solving problems that model fluid flow in closed geometries with heat or mass transfer.  To this aim the reader should bring a working knowledge of fluid mechanics and heat transfer and should be readily conversant with simple concepts of linear algebra including spectral decomposition of matrices as well as solvability conditions for inhomogeneous problems.  The book is neither meant to supply a ready-to-use program that is all-purpose nor to go through all manners of mathematical proofs.  The focus in this tutorial is on the use of the spectral methods for space discretization, because this is where most of the difficulty lies. While time dependent problems are also of great interest, time marching procedures are dealt with by briefly introducing and providing a simple, direct, and efficient method. Many examples are provided in the text as well as numerous exercises for each chapter. Several of the examples are attended by subtle points which the reader will face while working them out. Some of these points are deliberated upon in endnotes to the various chapters, others are touched upon in the book itself.

Table of Contents

Front Cover.
Half Title Page.
Other Front Matter.
Title Page.
Copyright Page.
1: An Introduction to the Book and a Road Map.
2: An Introduction to the Spectral Method.
3: Steady One-Dimensional (1D) Heat Conduction Problems.
4: Unsteady 1D Heat Conduction Problems.
5: Steady Two-Dimensional (2D) Heat Conduction Problems.
6: 2D Closed Flow Problems: The Driven Cavity.
7: Applications to Transport Instabilities.
8: Exercises for the Reader.