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E-raamat: Modeling and Analysis of Modern Fluid Problems

(University of Science and Technology, Beijing, China), (University of Science and Technology, Beijing, China)
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Modeling and Analysis of Modern Fluid ProblemsSuurem pilt
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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 Padé 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.

Muu info

Combines abstract and applied modern methods for solving nonlinear applied partial differential equations in modern multi-dimensional fluid and heat transfer problems
Preface xi
1 Introduction
1(38)
1.1 Basic Ideals of Analytical Methods
1(8)
1.1.1 Analytical Methods
1(3)
1.1.2 Pade Approximation
4(5)
1.2 Review of Analytical Methods
9(11)
1.2.1 Perturbation Method
9(4)
1.2.2 Adomian Decomposition Method
13(2)
1.2.3 Homotopy Analysis Method
15(1)
1.2.4 Differential Transformation Method
16(3)
1.2.5 Variational Iteration Method and Homotopy Perturbation Method
19(1)
1.3 Fractal Theory and Fractional Viscoelastic Fluid
20(6)
1.3.1 The Concept of Fractals
20(1)
1.3.2 Fractional Order Calculus
21(2)
1.3.3 Fractional Integral Transformations and Their Properties
23(2)
1.3.4 Fractional Viscoelastic Fluid
25(1)
1.4 Numerical Methods
26(1)
1.5 Modeling and Analysis for Modern Fluid Problems
27(1)
1.6 Outline
27(12)
References
29(10)
2 Embedding-Parameters Perturbation Method
39(40)
2.1 Basics of Perturbation Theory
39(2)
2.1.1 Perturbation Theory
40(1)
2.1.2 Asymptotic Expansion of Solutions
40(1)
2.1.3 Regular Perturbation and Singular Perturbation
41(1)
2.2 Embedding-Parameter Perturbation
41(5)
2.2.1 Approximate Solution to Blasius Flow
42(2)
2.2.2 Approximate Solutions to Sakidias Flow
44(2)
2.3 Marangoni Convection
46(1)
2.4 Marangoni Convection in a Power Law Non-Newtonian Fluid
47(10)
2.4.1 Marangoni Convection Caused by Temperature Gradient
48(1)
2.4.2 Mathematical Formulation
49(1)
2.4.3 Embedding-Parameters Perturbation Method Solutions
50(3)
2.4.4 Results and Discussion
53(4)
2.5 Marangoni Convection in Finite Thickness
57(17)
2.5.1 Background to the Problem
57(1)
2.5.2 Mathematical Model for Three Types of Conditions
58(2)
2.5.3 Embedding-Parameters Perturbation Method Solutions and Discussion
60(14)
2.6 Summary
74(5)
References
75(4)
3 Adomian Decomposition Method
79(36)
3.1 Introduction
79(1)
3.2 Nonlinear Boundary Layer of Power Law Fluid
80(10)
3.2.1 Physical Background
80(1)
3.2.2 Mathematical Formulation
81(1)
3.2.3 Similarity Transformation
82(1)
3.2.4 Crocco Variable Transformation
83(1)
3.2.5 Adomian Decomposition Method Solutions
84(1)
3.2.6 Results and Discussion
85(5)
3.3 Power Law Magnetohydrodynamic Fluid Flow Over a Power Law Velocity Wall
90(8)
3.3.1 Physical Background
90(2)
3.3.2 Basic Governing Equations
92(1)
3.3.3 Lie Croup of Transformation
92(2)
3.3.4 Generalized Crocco Variables Transformation
94(1)
3.3.5 Adomian Decomposition Method Solutions
95(1)
3.3.6 Results and Discussion
96(2)
3.4 Marangoni Convection Over a Vapor--Liquid Surface
98(12)
3.4.1 Boundary Layer Governing Equations
99(1)
3.4.2 Adomian Decomposition Method Solutions
100(3)
3.4.3 Results and Discussion
103(7)
3.5 Summary
110(5)
References
111(4)
4 Homotopy Analytical Method
115(64)
4.1 Introduction
115(1)
4.2 Flow and Radiative Heat Transfer of Magnetohydrodynamic Fluid Over a Stretching Surface
116(14)
4.2.1 Description of the Problem
116(1)
4.2.2 Mathematical Formulation
117(2)
4.2.3 Homotopy Analysis Method Solutions
119(5)
4.2.4 Results and Discussion
124(6)
4.3 Flow and Heat Transfer of Nanofluids Over a Rotating Disk
130(13)
4.3.1 Background of the Problem
130(1)
4.3.2 Formulation of the Problem
131(2)
4.3.3 Von Karman's Transformation
133(1)
4.3.4 Homotopy Analysis Method Solutions
134(3)
4.3.5 Results and Discussion
137(6)
4.4 Mixed Convection in Power Law Fluids Over Moving Conveyor
143(16)
4.4.1 Physical Background of the Problem
143(1)
4.4.2 Mathematical Formulation
144(2)
4.4.3 Nonlinear Boundary Value Problems
146(2)
4.4.4 Homotopy Analysis Method Solutions
148(2)
4.4.5 Results and Discussion
150(9)
4.5 Magnetohydrodynamic Thermosolutal Marangoni Convection in Power Law Fluid
159(15)
4.5.1 Background of the Problem
159(1)
4.5.2 Mathematical Formulation
160(4)
4.5.3 Homotopy Analysis Method Solutions
164(3)
4.5.4 Results and Discussion
167(7)
4.6 Summary
174(5)
References
174(5)
5 Differential Transform Method
179(74)
5.1 Introduction
179(5)
5.1.1 Ideas of Differential Transform---Pade and Differential Transform---Basic Function
180(1)
5.1.2 Definition of Differential Transformation Method and Formula
181(2)
5.1.3 Magnetohydrodynamic Boundary Layer Problem
183(1)
5.2 Magnetohydrodynamics Falkner---Skan Boundary Layer Flow Over Permeable Wall
184(8)
5.2.1 Mathematical Physical Description
184(1)
5.2.2 Differential Transformation Method---Pade Solutions
185(2)
5.2.3 Results and Discussion
187(5)
5.3 Unsteady Magnetohydrodynamics Mixed Flow and Heat Transfer Along a Vertical Sheet
192(16)
5.3.1 Mathematical Physical Description
192(3)
5.3.2 Differential Transformation Method---Basic Function Solutions
195(5)
5.3.3 Results and Discussion
200(8)
5.4 Magnetohydrodynamics Mixed Convective Heat Transfer With Thermal Radiation and Ohmic Heating
208(18)
5.4.1 Mathematical and Physical Description
208(1)
5.4.2 Formulation of the Problem
209(3)
5.4.3 Differential Transformation Method---Basic Function Solutions
212(4)
5.4.4 Numerical Solutions
216(1)
5.4.5 Results and Discussion
217(9)
5.5 Magnetohydrodynamic Nanofluid Radiation Heat Transfer With Variable Heat Flux and Chemical Reaction
226(21)
5.5.1 Mathematical and Physical Description
226(1)
5.5.2 Formulation of the Problem
227(4)
5.5.3 Differential Transformation Method---Basic Function Solutions
231(5)
5.5.4 Numerical Solutions
236(1)
5.5.5 Results and Discussion
237(10)
5.6 Summary
247(6)
References
248(5)
6 Variational Iteration Method and Homotopy Perturbation Method
253(26)
6.1 Review of Variational Iteration Method
253(5)
6.2 Fractional Diffusion Problem
258(1)
6.3 Fractional Advection-Diffusion Equation
258(8)
6.3.1 Formulation of the Problem
258(1)
6.3.2 Variational Iteration Method Solutions
259(1)
6.3.3 Examples
260(6)
6.4 Review of Homotopy Perturbation Method
266(1)
6.5 Unsteady Flow and Heat Transfer of a Power Law Fluid Over a Stretching Surface
267(8)
6.5.1 Boundary Layer Governing Equations
267(2)
6.5.2 Modified Homotopy Perturbation Method Solutions
269(3)
6.5.3 Results and Discussion
272(3)
6.6 Summary
275(4)
References
276(3)
7 Exact Analytical Solutions for Fractional Viscoelastic Fluids
279(82)
7.1 Introduction
279(3)
7.1.1 The Viscoelastic Non-Newtonian Fluids
279(2)
7.1.2 The Fractional Calculus
281(1)
7.2 Fractional Maxwell Fluid Flow Due to Accelerating Plate
282(13)
7.2.1 Governing Equations
282(1)
7.2.2 Statement of the Problem
282(1)
7.2.3 Calculation of the Velocity Field
283(3)
7.2.4 Calculation of the Shear Stress
286(3)
7.2.5 Limiting Cases
289(2)
7.2.6 Analysis and Discussion
291(4)
7.3 Helical Flows of Fractional Oldroyd-B Fluid in Porous Medium
295(19)
7.3.1 Formulation of the Problem
295(2)
7.3.2 Helical Flow Between Coaxial Cylinders
297(1)
7.3.3 Calculation of the Velocity Field
298(3)
7.3.4 Calculation of the Shear Stress
301(2)
7.3.5 The Solution of Heat Transfer Equation
303(1)
7.3.6 Results and Discussion
304(10)
7.4 Magnetohydrodynamic Flow and Heat Transfer of Generalized Burgers' Fluid
314(12)
7.4.1 Governing Equations
315(2)
7.4.2 Formulation of the Problem
317(1)
7.4.3 The Solution of Velocity Fields
318(2)
7.4.4 The Solution of Temperature Fields
320(2)
7.4.5 Results and Discussion
322(4)
7.5 Slip Effects on Magnetohydrodynamic Flow of Fractional Oldroyd-B Fluid
326(17)
7.5.1 Governing Equations
326(1)
7.5.2 Formulation of the Problem
327(1)
7.5.3 Exact Solutions
328(4)
7.5.4 Special Cases
332(1)
7.5.5 Results and Discussion
333(10)
7.6 The 3D Flow of Generalized Oldroyd-B Fluid
343(12)
7.6.1 Governing Equation
343(1)
7.6.2 Formulation of the Problem
344(1)
7.6.3 Calculation of the Velocity Field
345(2)
7.6.4 Calculation of the Shear Stress
347(1)
7.6.5 Special Cases
348(2)
7.6.6 Results and Discussion
350(5)
7.7 Summary
355(6)
References
356(5)
8 Numerical Methods
361(96)
8.1 Review of Numerical Methods
361(7)
8.1.1 Numerical Methods for Linear System of Equations
361(2)
8.1.2 Numerical Methods for Ordinary/Partial Differential Equations
363(4)
8.1.3 Numerical Methods for Fractional Differential Equations
367(1)
8.2 Heat Transfer of Power Law Fluid in a Tube With Different Flux Models
368(18)
8.2.1 Background of the Problem
368(1)
8.2.2 Formulation of the Problems and Numerical Algorithms
369(6)
8.2.3 Results and Discussion
375(11)
8.3 Heat Transfer of the Power Law Fluid Over a Rotating Disk
386(17)
8.3.1 Background of the Problem
386(1)
8.3.2 Formulation of the Problem and Governing Equations
387(1)
8.3.3 Generalized Karman Transformation
388(2)
8.3.4 Multiple Shooting Method
390(1)
8.3.5 Results and Discussion
391(12)
8.4 Maxwell Fluid With Modified Fractional Fourier's Law and Darcy's Law
403(17)
8.4.1 Background of the Problem
403(1)
8.4.2 Mathematical Formulation and Governing Equations
404(3)
8.4.3 Numerical Algorithms
407(2)
8.4.4 Results and Discussion
409(11)
8.5 Unsteady Natural Convection Heat Transfer of Fractional Maxwell Fluid
420(13)
8.5.1 Background of the Problem
420(1)
8.5.2 Mathematical Formulation
420(2)
8.5.3 Numerical Algorithms
422(6)
8.5.4 Results and Discussion
428(5)
8.6 Fractional Convection Diffusion With Cattaneo---Christov Flux
433(16)
8.6.1 Fractional Anomalous Diffusion
434(2)
8.6.2 Mathematical Formulation
436(1)
8.6.3 Numerical Algorithms
437(4)
8.6.4 Comparison of Numerical and Analytical Solutions
441(1)
8.6.5 Results and Discussion
441(8)
8.7 Summary
449(8)
References
449(8)
Index 457
Liancun Zheng (University of Science and Technology, Beijing), is a Professor in Applied mathematics with interest in partial/ordinary differential equations, fractional differential equations, non-Newtonian fluids, viscoelastic fluids, micropolar fluids, nanofluids, heat and mass transfer, radioactive heat transfer, nonlinear boundary value problems, and numerical heat transfer. He has published more than 260 papers in international journals and 5 books (in Chinese) and has served as Editor or Guest Editor of International Journals on 10 occasions. Xinxin Zhang is a Professor in the School of Engergy and Environmental Enginerring at the University of Science and Technology, Bejing.He is interested in thermal physical properties and thermal physics, mathematical modelling, system optimization and computer control, the numerical analysis of fluid flow, and heat transfer.
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