Index
A
Absolute viscosity, effective, 5
Adaptive grid refinement procedure, 448
Advection-diffusion equation, 56
Al2O3-water nanofluid
MHD free convection, 195–203
active parameters, effect of, 199–203
Hartmann number, 200–202
Lorenz force, 199
radiation parameter, 200–202
viscous dissipation parameter, 200–202
average Nusselt number
radiation parameter, 203
Rayleigh number, 203
viscous dissipation parameter, 203
Boussinesq approximation, 195
enhancement ratio
Hartmann number, 204
radiation parameter, 204
Rayleigh number, 204
viscous dissipation parameter, 204
geometry conditions, 196
Koo-Kleinstreuer-Li (KKL) model, 197
local Nusselt number, 198
Prandtl number, 198
problem definition, 195–199
Rosseland approximation, 195
sample triangular element and corresponding control volume, 196
Stefan-Boltzmann constant, 195
Average Nusselt number, effect of
Hartmann number, 157
magnetic number, 157
Reynolds number, 157
B
Berman’s similarity transformation, 494
Blood plasma, thermophysical properties, 397
Boltzmann constant, 3
Boltzmann equation, 279
kinetic, 102
for velocity, 492
Boundary layer approximations, 477
Brinkman model x-momentum equation, 475
Brownian diffusion, 2
coefficient, 3
Brownian forces, 2
Buongiorno model, 369
mathematical, 15
Buoyancy, 123
species-induced, 337
thermal, 337
C
Cartesian coordinate system, 340
Charge distribution models, 239
conductivity model, 239
mobility model, 239
Codes for flex PDE, 589
melting, 591
MHD natural convection heat transfer in porous media, 589
basic idea of, 56–60
electrohydrodynamic, 239–246
MHD effect on, 321
nanofluid, 243
Rayleigh numbers, 322
Convection nanofluid flow, 294
electric field, in presence of, 248
CuO-water nanofluid
coefficient values, 140
hydrothermal analysis, in complex-shaped cavity, 53–61
effects of active parameters, 60–61
problem definition and mathematical model, 53–56
Nusselt number, effect of
Eckert number, 148
Hartmann number, 177
heat source parameter, 177
nanoparticle volume fraction, 168
Reynolds number, 168
squeeze number, 177
suction parameter, 168
pressure distribution, effects of
Reynolds number, 165
suction parameter, 167
skin friction coefficient, effects of
Hartmann number, 177
nanoparticle volume fraction, 167
Reynolds number, 167
squeeze number, 177
suction parameter, 167
temperature distribution, effects of
Reynolds number, 165
suction parameter, 167
temperature profiles, effect of
Eckert number, 148
Hartmann number, 176
heat source parameter, 177
squeeze number, 175
velocity profile, effects of
Hartmann number, 176
Reynolds number, 165
squeeze number, 175
suction parameter, 167
D
Darcy model, 477
Dielectric constant, 253
Dimensionless equations, 493
Discrete velocity, 81
Discretization, 59
D3Q19 model, 348
Dynamic boundary conditions, 494
effective, 476
E
Eccentricity, 97
Einstein-Stokes’s equation, 3
Electrical charges displacement, 256
Electrical conductivity, effective, 493
Electric field, formula, 239
Electric flux density, 255
Electrohydrodynamic nanofluids, 31
Energy equation, 4
generation, 289
contribution of HTI, 292
Hartmann number, effect of, 289
mechanism, 282
for nondimensional numbers, 485
F
Fe3O4 water nanofluid, 257, See also Ferrofluid-mixed convection heat transfer
forced convection heat transfer
geometry and the boundary conditions, 128
magnetic field
intensity component, 128
strength, 128
mesh of enclosure, 128
nonuniform magnetic field, effect of, 127–137
active parameters, effects of, 132–137
problem definition, 127–132
components, of magnetic field intensity, 395
contours, of magnetic field strength, 396
density and distribution functions, 395
discrete lattice velocity, 397
discrete velocity set, of two-dimensional nine velocity, 396
effects of active parameters, 398
magnetic number, on streamlines, 399–402
geometry of vessel, 396
kinetic viscosity, 397
lattice Boltzmann methods (LBM), 395
magnetic number and Reynolds number on
average skin friction coefficient, 404
local skin friction coefficient, 404
velocity profile, 403
Ferrofluid-mixed convection heat transfer, 422
comparison, of streamlines between nanofluid and pure fluid, 426
contours of magnetic field strength, and magnetic field intensity, 422
effects of active parameters, 426–428
geometry and boundary conditions, 422
heat transfer and fluid flow, 423
isotherms and streamlines contours, for different values
of Richardson number and magnetic number, 427
magnetic field-dependent (MFD) viscosity, 423
magnetic field intensity on ferrofluid
of inside inner pipe of heat exchanger, 430
magnetic source, 422
mesh of enclosure, 422
three-dimensional sinusoidal double-tube heat exchanger
with magnetic field carrying wire, 430
adaptive grid refinement procedure, 448
adding copper particles, effect of, 453
comparison between solidification front, 448
conduction-dominated solidification process, 445
effect of adding Y-shaped fins, 448
effect of fin branch angle, on temperature and solid fraction contours, 450
fin length temperature and solid fraction contours, 452
full solidification time, for different values of fin geometry parameters, 449
geometry parameters of Y-shaped fins, 449
during solidification process, 448
solidification rate, 449
effect of nanoparticles volume fraction on
full solidification time and improvement, 453
solidification front position, 454
enhancement of process rate, 454
Galerkin integral, 447
nanoparticles and Y-shaped fins, comparison between, 454
solid fraction during discharging process, 455
total energy released, during discharging process, 455
physical properties of water, 446
thermal conductivity of NEPCM, 447
problem, 106
in a semiannulus under influence of a variable magnetic field, 148
Fortran code
for CVFEM, 564
2D advection diffusion, 570
2D pure diffusion, 564
for LBM, 577
lid-driven cavity, 577
natural convection in a cavity, 582
Free stream velocity, 500
G
Galerkin equations, 447
Gauss-Seidel method, 59
Gravity forces, 492
H
Hartmann number, 25, 130, 132, 281, 284, 294, 388, 493, 497 See also Active parameters, effect of under specific nanofluids
heat transfer, effect on, 336
when Reynolds number 10, 100, 1000
streamlines contours, 133–135
Heated permeable stretching surface, 500
in a porous medium using nanofluid, 500
effects of active parameters, 503–507
suction or injection parameter (γ) and nanoparticle volume fraction, 505
temperature distribution for different types of nanofluids, 508
thermal conductivity parameter and nanoparticle volume fraction, 504
problem definition, 500–503
figure of geometer, 500
boundary conditions, 478
distribution, 477
Heat transfer, 69
definition, 390
inclination angle, 311
magnetic number, 158
ratio, See Heat transfer
fluids, 1
irreversibility (HTI), 479
mechanism, 93
Homogeneous-heterogeneous reactions, 7
Homogenous porous medium, 475
application of, 482–485
Homotopy perturbation method, 480
Hydrodynamic boundary
conditions, 476
layer thickness scales, 477
Hydrodynamic displacement ratio, 255
I
comparison of isotherms and streamlines contours, 67
contours between nanofluid, 61
Cu-water case, 94
nanoparticles on, effect of, 284
supplied voltage on, effect of, 267
upward, 284
volume fraction of nanoparticle, effect of, 342
J
K
correlation for simulation of nanofluid flow, 515
heat transfer in a permeable channel, 515
effects of active parameters, 520–524
expansion ratio on, 522
numerical method, 520
power law index, 523
problem definition, 515–519
Reynolds number, expansion ratio, and power law index on, 524
on temperature profile/Nusselt number, 523
on velocity profiles, 521
volume fraction of nanofluid on temperature profile, 522
effective viscosity, Brownian motion, effect of, 144
Nusselt number, effect of
nanoparticle volume fraction, 145
rotation parameter, 147
skin friction coefficient, effect of
magnetic parameter, 145–147
nanoparticle volume fraction, 145
Reynolds number, 146
rotation parameter, 147
temperature profiles, effect of
magnetic parameter, 145
Reynolds number, 146
rotation parameter, 147
velocity, effect of
magnetic parameter, 145
Reynolds number, 146
rotation parameter, 147
L
Laminar nanofluid flow, 73
Laminar two-dimensional stationary nanofluid flow, 491
Latent heat thermal energy storage system (LHTESS), 445
addition, of nanoparticles, 453
comparison between nanoparticles and Y-shaped fins, 454
effect of fin branch angle, on solidification process, 453
fin branches efficiency, 460
full solidification time, for different values of fin geometry parameters, 449
phase change front, 457
Snowflake-shaped fin, for expediting discharging process in, 455
Y-shaped fins addition, effect of, 448
Lattice Boltzmann equation (LBE), 80
simulation of nanofluid in, 83–84
advantages, 395
algorithm flowchart of, 92
buoyancy forces and magnetic forces in, 397
skin friction coefficient, 398
studies on nanofluid, 39
Lattice fluid density, 280
Lattice relaxation, 280
Lattice time, 280
Lattice velocity, 280
Lewis number, 25
Linear velocity distribution, 475
Local Nusselt number See also Active parameters, effect of under specific nanofluids
along cold wall, effect of
Hartmann number, 190
magnetic number, 190
Reynolds number, 190
along hot wall, effect of
Hartmann number, 157
magnetic number, 157
Reynolds number, 157
Hartmann number, effect of, 136
Reynolds number, effect of, 136
on forced convection nanofluid flow over, 177
Hartmann number, effect of, 308
interacts with buoyancy force, 353
make thermal boundary layer thickness, 381
simulation of MHD CuO-water nanofluid flow and, 340
variation of, 286
M
Magnetic drug targeting, 38
Magnetic field, 38
Magnetic nanofluid forced convective heat transfer, 401
contours of magnetic field strength, and magnetic field intensity, 405
effects of active parameters, 407–410
geometry and boundary conditions, 405
magnetic field strength, 401
magnetic source, 401
Nusselt number of, 407
stream function and vorticity, 406
Magnetic nanofluid in double-sided, lid-driven cavity with wavy wall
forced convective heat transfer, 185–191
active parameters, effect of, 185–191
constant coefficient, 191
Hartmann number
heat transfer enhancement
Hartmann number, effect of, 191
magnetic number, effect of, 191
Reynolds number, effect of, 191
magnetic field intensity component, 186
magnetic field strength, 186
magnetic number
problem definition, 185
streamlines, nanofluid vs. pure fluid, 187
Magnetic nanofluid, influence of magnetic field on heat transfer, 428
continuity equation, 431
effect of geometric
form factor, on average Nusselt, 440
of magnetic field, in dimensionless temperature, 440
effect of magnetic field
in nondimensional temperature in along the axis of heat exchanger, 442
effects of active parameters, 433
energy equation, 431
friction factor in Reynolds number, effect of, 438
Kelvin force, 431
Langevin parameter, 432
magnetization, 432
momentum equation, 431
Navier-Stokes equations, 431
nondimensional temperature
contour, in six sinusiodal wave sections, 441
nonuniform crossover magnetic field
on nondimensional axial velocity distribution, effect, 439
Nusselt number, effect of, 434
ratio of average Nusselt number of ferrofluid, 442
three-dimensional sinusoidal double-tube heat exchanger
with magnetic field carrying wire, 430
two-dimensional sinusoidal double-tube heat exchanger
without magnetic field carrying wire, 430
effect on on local Nusselt number, 224
isotherms and streamlines contours for different values of, 392
Magnetite thermophysical properties, 397
effects of active parameters, 497–499
Hartmann numbers on, 498
Reynolds numbers (Re) on, 499
and heat transfer
active parameters
Brownian parameter, 213
fourth-order Runge-Kutta method, 213
magnetic parameter, 213
radiation parameter, 213
Reynolds number, 213
rotation parameter, 213
Schmidt number, 213
thermophoretic parameter, 213
Prandtl number, 213
Rosseland approximation, 210
Stefan-Boltzmann constant, 210
temperature profile, effect of
Reynolds number, 215
rotation parameter, 215
two-phase model, means of
active parameters, 213–214
problem definition, 210–213
thermal radiation, effects of, 210–214
velocity profiles, effect of
magnetic parameter, 214
Reynolds number, 214
rotation parameter, 214
problem geometry, 138
problem definition, 491–494
semi analytical method, 494
application of OHAM, 496–497
basic idea of OHAM, 494–496
Maple codes for semianalytical methods, 527
ADM, 530
AGM, 561
DTM, 540
HAM, 549
HPM, 535
OHAM, 543
Runge-Kutta method, 528
MAPLE package, 511
Mean velocity, 492
Momentum, 502
N
Nanofluid-filled enclosure
heat flux boundary condition, in presence of magnetic field, 309–320
active parameters, effects of, 315–320
problem definition, 309–315
Nanofluid flow, 256
electric field effect on, 270
fourth-order Runge-Kutta method, role of, 142
velocity vs. temperature profiles, 142
Nanofluid heat transfer, 475
enhancement and entropy generation, 102–114
active parameters, effects of, 107–114
problem definition and governing equations, 102–107
Nanofluid natural convection heat transfer, 53
in nanofluid filled inclined L-shaped enclosure, 61–70
active parameters, effects of, 66–70
problem definition, 61–66
along cold circular wall, local Nusselt number, 153
along hot wall, local Nusselt number, 153
magnetohydrodynamic free convection of, considering thermophoresis and brownian motion effects, 329–339
conservation equations, 2–5
single-phase model, 2
two-phase model, 2
simulation of MHD, flow and convective heat transfer considering lorentz forces, 340–343
active parameters, effects of, 341–343
problem definition, 340
MHD on flow, effect of, 301–308
active parameters, effects of, 302–308
problem definition, 301–302
dynamic viscosity, 130
effective electrical conductivity, 151
electrical conductivity, 292
electrohydrodynamic, 253–262
flow and forced convective heat transfer, 253–262
active parameters, effect of, 257–262
problem definition, 253–257
force convective heat transfer, 270–274
active parameters, effect of, 270–274
problem definition, 270
free convection heat transfer, 239–246
active parameters, effect of, 243–246
nonuniform electric field, effect of, 243
problem definition, 239–243
hydrothermal treatment, 263–269
active parameters, effect of, 266–269
problem definition, 263
entropy generation, in presence of magnetic field using LBM, 279–289
active parameters, effects of, 284–289
Hartmann number, 284
Prandtl number, 284
Rayleigh number, 284
volume fraction of nanoparticle, 284
problem definition, 279–284
Fe3O4-ethylene glycol, 242
electric field-dependent viscosity of, 242
flow and heat transfer, 1
simulation methods, 7–39
control volume-based finite element method, 25–32
finite difference method, 14–20
lattice Boltzmann method, 38–39
runge-kutta method, 9–15
semianalytical methods, 7–10
fluid flow equation, 291
free convection of magnetic, considering MFD viscosity effect, 373–381
active parameters, effects of, 379–381
Hartmann number, 379
Rayleigh number, 379
viscosity parameter, 379
problem definition, 373–379
heat transfer
enhancement, 132
equation, 291
hydrothermal behavior
active parameters, 251–252
problem definition, 248–250
Reynolds number, effect of, 257
supplied voltages, effect of, 257
comparison of isotherms, streamlines, isoconcentration, and heatline contours for, 417–420
contours of magnetic field strength and magnetic field intensity, 413
effects of active parameters, 416–420
effects of Hartmann number, Rayleigh number, buoyancy ratio number, and Lewis number on, 421
in existence of electric field, 239
geometry and boundary conditions, 412
laminar and steady-state natural convection, 414
local Nusselt number of, 416
effects of Hartmann number, Rayleigh number and, 421
mesh of enclosure, 412
nanofluid’s density, 413
nonuniform magnetic field effect on, 412
role of convection, in heat transfer, 416
shape of inner cylinder profile, 412
stream function and vorticity, 414
isotherms vs. streamlines, 154
magnetic field effect on natural convection of, three-dimensional mesoscopic simulation of, 347–355
active parameters, effects of, 351–355
Hartmann number, 351
Rayleigh number, 351
volume fraction of nanoparticle, 351
problem definition, 347–351
magnetic field effect on unsteady flow and heat transfer using buongiorno model, 364–372
model description, 2
models for viscosity of nanofluids, used in simulation, 7
volume fraction, effect of, 175
skin friction coefficient
volume fraction, effect of, 175
technology, 1
thermal
distribution, 163
expansion coefficient of, 291
physical properties, 8
two-dimensional flow of, 365
two-phase simulation of flow and heat transfer, in presence of axial magnetic field, 355–364
velocity profile, 163
continuity, 4
Nusselt number, 143
skin friction coefficient, 143
temperature profiles, 143
of water and, 242
velocity profiles, 143
volume fraction
on local Nusselt number, effects of, 64
on Nusselt number, effect of, 114
in nanofluid, filled concentric annulus between outer square cylinder and inner circular cylinder, 79–89
active parameters, effects of, 84–89
Rayleigh numbers and aspect ratio, effects of, 89
Rayleigh numbers, effects of, 90
lattice Boltzmann method, 80–83
problem definition and mathematical model, 79–84
in nanofluid, filled concentric annulus with inner elliptic cylinder using LBM, 91–96
active parameters, effects of, 91–96
Rayleigh numbers, effects of, 94
Rayleigh numbers on average Nusselt number, effects of, 96
problem definition, 91
in nanofluid, filled enclosure with elliptic inner cylinder, 70–78
active parameters, effects of, 75–78
adding nanoparticles, effects of, 75
inclination angle and Rayleigh number on ratio of heat transfer, effects of, 79
problem definition, 70–75
in nanofluid, filled square cavity with curve boundaries, 97–102
active parameters, effects of, 91–96
problem definition, 91
Rayleigh number and inclination angle on enhancement heat transfer, effects of, 102
Newton-Raphson iteration process, 447
Nield model, 477
Non-Darcian regime, 477
Nondimensional quantities, 511
Nonlinear differential equation, 480
active parameter, effect of, 372
Al2O3-water vs. CuO-water, 174
buoyancy ratio number, effect of, 339
Hartmann number
relationship between, 308
magnetic parameter, effects of, 184
nanoparticles, effects of, 164
polynomial representations for, 392
profile, 132
ratio, effect of
active parameters, 288
Hartmann number, 288
nanoparticle volume fraction, 288
Rayleigh number, 288
thermophoresis parameter, effect on, 361
velocity ratio parameter, effects of, 184
O
P
Parallel plates, nanofluid flow and heat transfer
differential transformation method (DTM), using, 166–176
active parameters, effect of, 174–176
problem definition, 166–171
semianalytical method, 171–173
Particle draft velocity, 5
Perturbation techniques, 283
Poisson equation, 253
Porous surface, 478
Power-law heat flux, 479
definition, 140
Pure fluid isotherms vs. streamlines, 154
R
isotherms and streamlines contours for different values of, 392
on ratio of enhancement of heat transfer, effects of, 97
Coulomb forces in, 262
electric density distribution, 258
rate of heat transfer, relationship between, 270
Richardson number, 31
S
Sedimentation, 2
active parameters, effects of, 485
nanoparticle volume fraction, 490
Reynolds number, and wall injection/suction on skin friction coefficient, 488
Reynolds number, wall injection/suction parameter, and power of temperature/heat flux distribution on Nusselt number, 488
temperature distribution, 486
velocity profiles, 486
temperature profiles, power-law temperature and power-law heat flux for different types of nanofluids, 487
velocity for nanofluids, 487
application of HAM, 482–485
basic idea of HAM, 480–482
Semiannulus enclosure
ferrofluid flow and heat transfer
average Nusselt number
Hartmann number, effect of, 229
magnetic number, effect of, 229
nanoparticle volume fraction, effect of, 229
radiation parameter, effect of, 229
average Nusselt number along hot wall
Hartmann number, effect of, 229
Rayleigh number, effect of, 229
Boussinesq approximation, 218
concentration profile
Brownian parameter, effect of, 216
radiation parameter, effect of, 216
Reynolds number, effect of, 216
Schmidt number, effect of, 216
thermophoretic parameter, effect of, 216
geometry and boundary conditions, 218
isotherm and streamlines
Hartmann number, effect of, 225
local Nusselt number along hot wall, 223
Hartmann number, effect of, 228
magnetic number, effect of, 228
radiation parameter, effect of, 228
Rayleigh number, effect of, 228
magnetic field intensity component, 219
magnetic field strength, 219
magnetic source, presence of, 215–224
active parameters, effect of, 223–224
problem definition, 215–223
mesh of enclosure, 218
nanofluid vs. pure fluid
isotherm and streamlines, 224
Nusselt number
Brownian parameter, effect of, 218
magnetic parameter, effect of, 217
radiation parameter, effect of, 217–218
Reynolds number, effect of, 217
rotation parameter, effect of, 217
Schmidt number, effect of, 218
thermophoretic parameter, effect of, 217
Rayleigh number, Hartmann number, and magnetic number
Semiannulus forced convection heat transfer
geometry and the boundary conditions, 149
magnetic field intensity component, 150
magnetic field strength, 150
mesh of enclosure, 149
variable magnetic field, effect of, 148–154
active parameters, 153–154
problem definition, 148–153
Shear stress, 478
Shooting technique, 162
Silver, 506
Similarity function, 478
Single-phase model, See also Two phase modeling of nanofluid
physical properties of nanofluids for, 5–7
density, 5
dynamic viscosity, 6
electrical conductivity, 6
specific heat capacity, 5
thermal conductivity, 7
thermal expansion coefficient, 6
Al2O3-water vs. CuO-water, 174
magnetic parameter, effects of, 184
nanoparticles, effects of, 163
velocity ratio parameter, effects of, 184
Slip velocity, 4
Snowflake shaped fin-assisted LHTESS, 455
convection effect, on solidification process of, 458
enhancement techniques, comparison, 472
full solidification time, for different values of geometry parameters, 461
optimization of configuration, 467
effect on solidification rate
bigger branch direction, 467
bigger branch distance, from cold wall, 468
smaller branch direction, 468
smaller branch distance from cold wall, 468
time surfaces, for different geometry parameters, 469
average temperature variations over
computational domain, 466
solution domain, 472
total energy released during, 473
phase change front, 457
snowflake crystal structure, 460
solid fraction-temperature contour plots, 458
solidification rate
branches direction effect on, 462
effect of changing distance, between branches, 463
solution domain and geometry parameters, 456
three-dimensional view of, 456
Snowflake-shaped fin structure, geometry parameters, 457
Standard Galerkin finite element method, 447
Stefan-Boltzmann constant, 179
Stokes’ flow, 71
definition, 390
isotherms contours, comparison, 61
nanoparticles on, 284
Reynolds number, influence of, 266
volume fraction of nanoparticle, 342
Stretched surface
forced convection nanofluid flow
figure of geometery, 178
geometry and boundary conditions, 185
Lorentz forces, effect of, 177–183
active parameters, effects of, 181–183
numerical method, 180–181
problem definition, 177–180
mesh of enclosure, 185
Nusselt number, effect of
radiation parameter, 184
temperature index parameter, 184
temperature profile, effect of
magnetic parameter, 182
radiation parameter, 184
temperature index parameter, 184
velocity ratio parameter, 183
velocity, effect of
magnetic parameter, 182
velocity ratio parameter, 183
Stretching porous cylinder
nanofluid flow and heat transfer, 229–233
active parameters, effects of, 233
boundary conditions, 230
geometry of problem, 230
numerical method, 232–233
Runge-Kutta integration scheme, 232
Nusselt number, effect of
nanoparticle volume fraction, 236
radiation parameter, 236
Reynolds number, 236
suction parameter, 236
pressure distribution, effect of
Reynolds number, 235
suction parameter, 235
problem definition, 229–232
skin friction coefficient, effect of
nanoparticle volume fraction, 234
Reynolds number, 234
suction parameter, 234
temperature profile, effect of
nanoparticle volume fraction, 235
radiation parameter, 235
Reynolds number, 235
suction parameter, 235
velocity profile, effect of
nanoparticle volume fraction, 234
Reynolds number, 234
suction parameter, 234
Stretching velocity, 500
T
Taylor series expansion, 481
Temperature dependence, 71
Temperature distribution
nanoparticles volume fraction, effects of, 164
Thermal boundary conditions, 476
Thermal boundary layer thickness
Hartmann number, effect of, 132
effective, 501
low, 1
Maxwell-Garnetts (MG) model, 130
models, nanofluids used in simulation, 8
models of nanofluids, used in simulation, 8
ratio, 521
Thermal energy equation, 478
Thermal equilibrium, 2
Thermal expansion coefficient, 71
Thermal interfacial resistance, 72
Thermodynamics, second law of, 477
Thermophoresis, 4
diffusion coefficient, 3
effects, 412
parameter, 14
Titanium oxide, 506
Transformations, 492
Transport properties, 475
in a rotating system with permeable sheet, 508
effects of active parameters, 511–515
Brownian parameter and thermophoretic parameter on, 515
injection parameter and Reynolds number on Nusselt number, 513
injection parameter on velocity profiles, temperature profile, and, 512
Reynolds number on velocity profiles, temperature profile, and, 513
rotation parameter on velocity profile, 514
Schmidt number on concentration profile and Nusselt number, 514
problem definition, 508–511
Two phase simulation of nanofluid flow, and heat transfer, using heatline analysis, 114–123
active parameters, effects of, 118–123
thermal Rayleigh number, buoyancy ratio number, and Lewis number, effects of, 122
geometry and boundary conditions, 115
problem definition, 114–117
U
Unsteady nanofluid flow, and heat transfer
active parameters, effect of
Runge-Kutta method, 207
Schmidt number, 207
squeeze number, 208
thermophoretic parameter, 207
concentration profiles
Schmidt number, effect of, 209
thermophoretic parameter, effect of, 209
magnetic field, presence of, 204–209
active parameters, effects of, 207–209
Brownian motion parameter, 206
geometry of problem, 205
Prandtl number, 206
problem definition, 204–207
Rosseland approximation, 205
Schmidt number, 206
Stefan-Boltzmann constant, 205
Nusselt number, effect of
Eckert number, 210
radiation parameter, 210
squeeze parameter, 210
temperature and concentration profiles
Eckert number, effect of, 208
radiation parameter, effect of, 209
velocity, temperature, and concentration profiles
squeeze number, effect of, 208
V
Velocity
profile
nanoparticles volume fraction, effects of, 164
ratio parameter, 506
u-velocity, 477
Viscosity
Volumetric entropy generation rate, 281
definition, 390
formulas, 250
W
Wall shear stress, 478
Water
and nanoparticles, thermo physical properties of, 55
Water nanofluid, free convection of Fe3O4, 385
Boussinesq approximation, 387
comparison, of isotherms and streamlines between pure fluid and, 391
components, of magnetic force, 387
dynamic viscosity of, 388
elliptic function, 385
geometry and boundary conditions, 386
heat capacitance of, 388
heat transfer enhancement, 390
magnetic field
magnetocaloric effect, 387
mesh of enclosure, 386
Nusselt number, 390
role of convection in heat transfer, 391
stream function and vorticity, 390
thermal diffusivity of, 388
thermal expansion coefficient of, 388
thermophysical properties of, 390
Working nanofluid, mixture of ethylene glycol and Fe3O4, 243
Z
Zeroth-order deformation equation, 481
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