http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Modeling and analysis of modern fluid problems
1 online resource (xii, 467 pages) : illustrations
Modeling and Analysis of Modern Fluids helps researchers solve physical problems observed in fluid dynamics and related fields, such as heat and mass transfer, boundary layer phenomena, and numerical heat transfer. These problems are characterized by nonlinearity and large system dimensionality, and 'exact' solutions are impossible to provide using the conventional mixture of theoretical and analytical analysis with purely numerical methods. To solve these complex problems, this work provides a toolkit of established and novel methods drawn from the literature across nonlinear approximation theory. It covers PadïÅ½ approximation theory, embedded-parameters perturbation, Adomian decomposition, homotopy analysis, modified differential transformation, fractal theory, fractional calculus, fractional differential equations, as well as classical numerical techniques for solving nonlinear partial differential equations. In addition, 3D modeling and analysis are also covered in-depth.
Front Cover ; Mathematics in Science and Engineering; Mathematics in Science and Engineering; Copyright; Contents; Preface; 1 -- Introduction; 1.1 BASIC IDEALS OF ANALYTICAL METHODS; 1.1.1 Analytical Methods; 1.1.1.1 Taylor Series; 1.1.1.2 Fourier Series; 1.1.2 Padé Approximation; 1.1.2.1 Weierstrass Approximation Theorem; 1.1.2.2 Definition of Padé Approximants; 1.1.2.3 Uniqueness Theorem of Padé Approximants; 1.1.2.4 Table of Padé Approximants; 1.2 REVIEW OF ANALYTICAL METHODS; 1.2.1 Perturbation Method; 1.2.1.1 Regular Perturbation and Singular Perturbation
1.2.1.2 Asymptotic Matching Method1.2.1.3 Poincare-Lighthill-Kuo Method; 1.2.1.4 Average Method; 1.2.1.5 Multiple Scales Method; 1.2.2 Adomian Decomposition Method; 1.2.3 Homotopy Analysis Method; 1.2.4 Differential Transformation Method; 1.2.5 Variational Iteration Method and Homotopy Perturbation Method; 1.3 FRACTAL THEORY AND FRACTIONAL VISCOELASTIC FLUID; 1.3.1 The Concept of Fractals; 1.3.2 Fractional Order Calculus; 1.3.2.1 Definition of Fractional Order Derivatives; 1.3.3 Fractional Integral Transformations and Their Properties; 1.3.3.1 Fourier Transformation
1.3.3.2 Laplace Transformation1.3.3.3 Mellin Transformation; 1.3.4 Fractional Viscoelastic Fluid; 1.4 NUMERICAL METHODS; 1.5 MODELING AND ANALYSIS FOR MODERN FLUID PROBLEMS; 1.6 OUTLINE; REFERENCES; 2 -- Embedding-Parameters Perturbation Method; 2.1 BASICS OF PERTURBATION THEORY; 2.1.1 Perturbation Theory; 2.1.2 Asymptotic Expansion of Solutions; 2.1.3 Regular Perturbation and Singular Perturbation; 2.2 EMBEDDING-PARAMETER PERTURBATION; 2.2.1 Approximate Solution to Blasius Flow; 2.2.2 Approximate Solutions to Sakidias Flow; 2.3 MARANGONI CONVECTION
2.4 MARANGONI CONVECTION IN A POWER LAW NON-NEWTONIAN FLUID2.4.1 Marangoni Convection Caused by Temperature Gradient; 2.4.2 Mathematical Formulation; 2.4.3 Embedding-Parameters Perturbation Method Solutions; 2.4.4 Results and Discussion; 2.5 MARANGONI CONVECTION IN FINITE THICKNESS; 2.5.1 Background to the Problem; 2.5.2 Mathematical Model for Three Types of Conditions; 2.5.3 Embedding-Parameters Perturbation Method Solutions and Discussion; 2.5.3.1 Solutions for Cases I and II; 2.6 SUMMARY; REFERENCES; 3 -- Adomian Decomposition Method; 3.1 INTRODUCTION
3.2 NONLINEAR BOUNDARY LAYER OF POWER LAW FLUID3.2.1 Physical Background; 3.2.2 Mathematical Formulation; 3.2.3 Similarity Transformation; 3.2.4 Crocco Variable Transformation; 3.2.5 Adomian Decomposition Method Solutions; 3.2.6 Results and Discussion; 3.2.6.1 Analysis of Velocity Field; 3.2.6.2 Analysis of Temperature Field; 3.3 POWER LAW MAGNETOHYDRODYNAMIC FLUID FLOW OVER A POWER LAW VELOCITY WALL; 3.3.1 Physical Background; 3.3.2 Basic Governing Equations; 3.3.3 Lie Group of Transformation; 3.3.4 Generalized Crocco Variables Transformation; 3.3.5 Adomian Decomposition Method Solutions
Includes bibliographical references and index.