Micro and Nanofluid Convection with Magnetic Field Effects for Heat and Mass Transfer Applications using MATLAB®

321 Pages·2022·18.342 MB·English

by  Chakravarthula Raju, Ilyas Khan, Suresh Kumar Raju, Mamatha S. Upadhya

Micro and Nanofluid
Convection with Magnetic
Field Effects for Heat and
Mass Transfer Applications
s
Using MATLAB
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Micro and Nanofluid
Convection with Magnetic
Field Effects for Heat and
Mass Transfer Applications
s
Using MATLAB
Edited by
CHAKRAVARTHULA S.K. RAJU
Departmentof Mathematics, GITAM University, Visakhapatnam, India
ILYAS KHAN
Basic Engineering Sciences Department, Collegeof Engineering
MajmaahUniversity, Al Majma'ah,Saudi Arabia
SURESH KUMAR RAJU S.
Departmentof Mathematics and Statistics, King Faisal University,
Hofuf, Saudi Arabia
MAMATHA S. UPADHYA
Departmentof Mathematics, KristuJayanti College (Autonomous),
Bangalore, India
Elsevier
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Contents
Listofcontributors ix
Abouttheeditors xi
Preface xiii
1. Backgroundto micro- and nanofluids 1
MamathaS.UpadhyaandC.S.K.Raju
References 5
2. Mathematical modeling ofequations of couple stress fluid in
respective coordinates 7
C.S.K.Raju,MamathaS.UpadhyaandIlyasKhan
2.1 Basicflowequations 7
2.2 Equationsofmotion 8
2.3 Equationsofmotionbystresstensor 9
2.3.1 IntheCartesiancoordinatessystem 9
2.3.2 Inthecylindricalcoordinatessystem 13
2.3.3 Inthesphericalcoordinatessystem 16
2.4 Equationsofmotionbyvectorcalculus 21
2.4.1 IntheCartesiancoordinatessystem 21
2.4.2 Inthecylindricalcoordinatessystem 24
2.4.3 Inthesphericalcoordinatessystem 26
References 30
3. Mathematical model ofsteady incompressible nanofluid for
heat transfer applications using MATLABs 31
SathySureshandS.R.Shanthi
3.1 Introduction 31
3.2 Problemdescription 33
3.3 Methodofsolution 36
3.4 AlgorithmandimplementationofMATLABs 38
3.5 Resultsanddiscussion 41
3.6 Conclusion 57
References 58
v
vi Contents
4. Mathematical model for an incompressible unsteady nanofluid flow with
heat transfer application 59
S.Rajamani,G.Venkatesan,A.SubramanyamReddy,A.K.Shukla,K.Jagadeshkumar
andS.Srinivas
4.1 Introduction 59
4.2 Formulationoftheproblem 61
4.3 Resultsanddiscussion 64
4.4 Conclusion 72
References 73
5. Mathematical model for incompressible unsteadynanofluid fluid flow with
heat and mass transfer application 75
G.P.Ashwinkumar
Nomenclature 75
5.1 Introduction 76
5.2 Mathematicalformulation 78
5.3 Resultsanddiscussion 80
5.4 Conclusions 89
References 89
6. Stefan blowing effect on nanofluid flow over a stretching sheet
in the presenceof a magneticdipole 91
R.NaveenKumar,R.J.PunithGowda,B.C.PrasannakumaraandC.S.K.Raju
Nomenclature 91
6.1 Introduction 92
6.2 Mathematicalformulation 94
6.2.1 Conditionsandassumptionsofthemodel 95
6.2.2 Geometryoffluidflow 95
6.2.3 Modelequations 95
6.2.4 Nonuniformheatsource/sink 96
6.2.5 Magneticdipole 96
6.3 Thesolutiontotheproblem 97
6.3.1 Expressionofparameters 98
6.3.2 Physicalquantitiesofinterest 98
6.4 Numericalmethod 98
6.4.1 Convergenceanderrortolerance 100
6.5 Resultsanddiscussion 100
6.5.1 Velocityandthermalprofile 100
Contents vii
6.5.2 Concentrationprofile 104
6.5.3 Physicalquantitiesofpracticalinterest 106
6.6 Conclusions 109
References 109
7. Nonlinear unsteadyconvection onmicro and nanofluidswith
Cattaneo-Christov heat flux 113
MamathaS.UpadhyaandC.S.K.Raju
Nomenclature 113
7.1 Introduction 114
7.2 Problemdevelopments 116
7.3 Graphicaloutcomesanddiscussion 120
7.4 Conclusions 129
References 130
8. Comparison of steady incompressible micropolar andnanofluid flow
with heat and mass transfer applications 133
SathySuresh,S.R.ShanthiandMamathaS.Upadhya
8.1 Introduction 133
8.2 Formulation 135
8.3 Entropygeneration 139
8.4 Numericalprocedure 140
8.5 Resultsanddiscussion 141
8.6 Concludingremarks 149
References 149
9. Comparison of unsteadyincompressible micropolarandnanofluid
flowwith heat transferapplications 153
D.Rajkumar,K.Govindarajulu,T.Thamizharasan,A.SubramanyamReddy,
K.Jagadeshkumar,S.SrinivasandA.K.Shukla
9.1 Introduction 153
9.2 Formulationoftheproblem 156
9.3 Resultsanddiscussion 160
9.3.1 Velocitydistribution 161
9.3.2 Angularmomentumdistribution 163
9.3.3 Temperaturedistribution 164
9.3.4 Nusseltdistribution 164
9.4 Conclusion 166
References 166
viii Contents
10. Implementation of boundary value problems in using MATLABs 169
MamathaS.UpadhyaandC.S.K.Raju
10.1 IntroductiontoMATLABs 169
10.1.1 Plottingofcurvesandsurfaces 169
10.2 Vectorfieldandgradient 176
10.2.1 Aim 176
10.3 Limitsandcontinuity 180
10.3.1 Aim 180
10.4 Definiteintegralsandtheirapplications 185
10.4.1 Aim 185
10.5 Localmaximaandlocalminima 189
10.5.1 Aim 189
10.6 Lagrange’smultipliersmethod 194
10.6.1 Aim 194
10.7 Multipleintegrals 199
10.7.1 Aim 199
10.7.2 Volumeofasolidregion 199
10.7.3 Changeofvariables:polarcoordinates 199
10.8 Applicationsofderivatives 205
10.8.1 Aim 205
10.8.2 Maximumandminimumforasinglevariable 207
10.9 Casestudy 212
10.9.1 Introduction 212
10.9.2 Methodology 213
10.9.3 MATLABs implementation 214
10.9.4 Resultsanddiscussion 216
10.9.5 Conclusion 220
10.10 Navier(cid:1)StokesequationsolvingusinganODEsolver 221
10.11 Solvingtheinitialvalueproblem 223
10.12 Solvingtwocouplednonlinearequations 224
10.13 Interpretingtheresults 228
Furtherreading 237
Appendix1 239
Index 299
List of contributors
G.P. Ashwinkumar
Departmentof Mathematics, Vijayanagara Sri Krishnadevaraya University,Bellary, Karnataka,
India
K. Govindarajulu
Departmentof Mathematics, School of Advanced Sciences, Vellore Institute of Technology,
Vellore, Tamil Nadu, India
K. Jagadeshkumar
Departmentof Mathematics, School of Advanced Sciences, Vellore Institute of Technology,
Vellore, Tamil Nadu, India
Ilyas Khan
Departmentof Mathematics, MajmaahUniversity, Al Majma'ah, MajmaahCity,Saudi Arabia
R.Naveen Kumar
Departmentof Studies and Research inMathematics, Davangere University, Davangere,
Karnataka, India
B.C. Prasannakumara
Departmentof Studies and Research inMathematics, Davangere University, Davangere,
Karnataka, India
R.J. Punith Gowda
Departmentof Studies and Research inMathematics, Davangere University, Davangere,
Karnataka, India
S.Rajamani
Departmentof Mathematics, School of Advanced Sciences, Vellore Institute of Technology,
Vellore, Tamil Nadu, India
D.Rajkumar
Departmentof Mathematics, School of Advanced Sciences, Vellore Institute of Technology,
Vellore, Tamil Nadu, India
C.S.K. Raju
Departmentof Mathematics, GITAM School of Science, GITAM Deemedto be University,
Bengaluru, Karnataka,India
A. Subramanyam Reddy
Departmentof Mathematics, School of Advanced Sciences, Vellore Institute of Technology,
Vellore, Tamil Nadu, India
S.R. Shanthi
Departmentof Mathematics, Cambridge Instituteof Technology, Bengaluru, Karnataka, India
A.K. Shukla
Departmentof Mathematics, School of Advanced Sciences and Languages,VIT-Bhopal
University, Bhopal,MadhyaPradesh,India
ix