Front Cover

WEIGHTED RESIDUAL METHODS

WEIGHTED RESIDUAL METHODS: Principles, Modifications and Applications

Copyright

Dedication

CONTENTS

PREFACE

1 - Introduction to Analytical Methods

1.1 INTRODUCTION

1.2 ADOMIAN DECOMPOSITION METHOD

1.3 VARIATIONAL ITERATION METHOD

1.4 DIFFERENTIAL TRANSFORMATION METHOD

1.5 HOMOTOPY PERTURBATION METHOD

1.6 HOMOTOPY ANALYSIS METHOD

1.7 WEIGHTED RESIDUAL METHODS

1.7.1 Galerkin Method (GM)

1.7.2 Collocation Method (CM)

1.7.3 Rayleigh-Ritz Method (RRM)

1.7.4 Least Square Method (LSM)

1.8 DIFFERENTIAL QUADRATURE METHOD

1.9 OPTIMAL HOMOTOPY ASYMPTOTIC METHOD

REFERENCES

2 - Weighted Residual Methods Principles and Modifications

2.1 INTRODUCTION

2.2 WEIGHTED RESIDUAL METHODS PRINCIPLES

2.2.1 Collocation Method

2.2.2 Least Square Method

2.2.3 Galerkin Method

2.2.4 Rayleigh-Ritz Method (RRM)

2.3 WRMS FOR COUPLED EQUATIONS

2.4 OPTIMAL WRMS FOR INFINITE BOUNDARY CONDITIONS

2.5 COMBINED WRMS WITH OTHER ANALYTICAL METHODS

2.6 MODIFIED WRMS FOR COMBINED BOUNDARY CONDITIONS

2.7 HYBRID WRMS FOR PARTIAL DIFFERENTIAL EQUATIONS

2.8 MULTISTEP POLYNOMIAL WRMS FOR FRACTIONAL ORDER DIFFERENTIAL EQUATIONS

2.9 PADE APPROXIMATION AND OTHER ANALYTICAL METHODS

REFERENCES

3 - Weighted Residual Methods in Fluid Mechanic Applications

3.1 INTRODUCTION

3.2 NANOFLUID FLOW IN A POROUS CHANNEL

3.2.1 Application of Least Square Method (LSM)

3.2.2 Application of GM

3.3 NANOFLUID FLOW BETWEEN PARALLEL DISKS

3.4 JEFFERY-HAMEL FLOW

3.5 CONDENSATION FLOW OVER INCLINED DISKS

3.6 ELECTROHYDRODYNAMIC (EHD) FLOW

3.7 MAGNETOHYDRODYNAMIC (MHD) FLOW IN DIVERGENT/CONVERGENT CHANNELS

3.8 NANOFLUID FLOW IN A MICROCHANNEL HEAT SINK

3.9 NANOFLUID FLOW IN EXPANDING AND CONTRACTING GAPS

REFERENCES

4 - Weighted Residual Methods in Heat Transfer and Energy Conversion Applications

4.1 INTRODUCTION

4.2 HEAT TRANSFER OF LONGITUDINAL, CONVECTIVE-RADIATIVE, POROUS FINS

4.3 HEAT TRANSFER OF CIRCULAR, CONVECTIVE-RADIATIVE, POROUS FINS

4.4 HEAT TRANSFER OF CONVECTIVE-RADIATIVE, SEMISPHERICAL FINS

4.5 REFRIGERATION OF FULLY WET, CIRCULAR, POROUS FINS

4.6 REFRIGERATION OF FULLY WET, SEMISPHERICAL, POROUS FINS

4.7 NANOFLUIDS CONDENSATION AND HEAT TRANSFER

4.8 NANOFLUID HEAT TRANSFER IN CIRCULAR, CONCENTRIC HEAT PIPES

4.9 NANOFLUID HEAT TRANSFER IN A MICROCHANNEL HEAT SINK

REFERENCES

5 - WRMs in Nanoengineering Applications

5.1 INTRODUCTION

5.2 NATURAL CONVECTION OF NON-NEWTONIAN NANOFLUID

5.3 MHD JEFFERY-HAMEL NANOFLUID FLOW

5.4 MHD NANOFLUIDS OVER A CYLINDRICAL TUBE

5.5 FORCED CONVECTION FOR MHD NANOFLUID FLOW OVER A POROUS PLATE

5.6 NON-NEWTONIAN NANOFLUID IN POROUS MEDIA BETWEEN TWO COAXIAL CYLINDERS

5.7 MHD NANOFLUID FLOW IN A SEMIPOROUS CHANNEL

5.8 NANOFLUID IN MICROCHANNEL HEAT SINK (MCHS) COOLING

5.9 CARBON NANOTUBE (CNT)-WATER BETWEEN ROTATING DISKS

REFERENCES

INDEX

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

R

S

T

V

W

Z

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