References* - rd.springer.com978-1-4757-2175-1/1.pdf · References* Aidun, C. K. 1987 Stability of...

References*

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Index

A

Acceleration coefficient tensor, 9 Acceleration, 7-9 Agar-agar, 4 Alternating hot and cold spots, 243,

244 Analogy between layering and

anisotropy, 181-183 Anisotropy, 23, 25, 40, 178-180,

186, 192, 229-231, 240, 284, 285

Annulus, 194, 196, 227, 232-234, 250, 256, 270, 272

Arrhenius relationship, 34 Attic-shaped enclosure, 236, 237 Augmentation of heat transfer, 57 Averaging theorem, 37 Axisymmetric cavities, 237 Axisymmetric surface, 118-120, 267,

303, 342, 343

B

Beads: see Spheres Beavers-Joseph condition, 15-17,

205, 207 Bifurcation, 161, 175, 187-191, 196,

256 Biot number, 147 Blowing at the surface: see Suction

or blowing at the surface Body of revolution, 119, 303 Boiling, 334-343 Boundary between two porous media,

17 Boundary conditions, 14-18, 27, 198

Boundary friction, 66-74, 91-97, 104, 135, 249, 250, 256, 263, 267, 273, 326, 343

Boundary imperfections, 226 Boundary layer regime, 216-221 Boundary layers, 47, 48, 50, 51,

58-60, 82, 85, 90, 91, 138, 214, 259, 312, 325, 326, 351

Boundary topography, 355 Boussinesq approximation:

see Oberbeck-Boussinesq approximation

Brick, 4 Brinkman boundary friction:

see Boundary friction Brinkman model, or equation, 11-14,

16, 66, 73, 92, 97, 134, 156-158, 175, 201, 208, 209, 226, 249, 250, 268, 272, 285, 286, 343

Brinkman term, 156 Brinkman-Forchheimer:

see Forchheimer-Brinkman Buoyancy ratio, 277, 289, 292, 293

source, 297, 301 Buoyant wake, 99 Buried pipes, 137

c

Capillary pressure, 42 Carman-Kozeny relationship, 6, 7, 9,

156 Catalyst, 4 Catalytic reaction, 35 Centrosymmetry, 217 Channel, 56, 71, 188-193, 267-274

402 Index

Channelling, 16, 18, 25, 73, 161, 263, 356

Chemical reaction, 34, 35, 286, 351 Chemical reactors, 73 Cigarette, 4 Circular plate, 137 Coal, 4 Combined heat and mass transfer, 33,

34, 275-304 Compressibility effect, 159 Concentrated heat and mass sources:

see Sources Concentration expansion coefficient,

33, 276 Concrete, 4 Condensation, 343, 344 Conduction, 142, 215 Conduction and convection 135, 320 Conductivity variation, 263 Cone, 115-119, 342, 343 Configurations, other, 135-137, 267,

330 Confined (enclosed) flow, 56-58,

70-74, 141-258, 290-296, 305-334

Conjugate boundary layers, 88-90 Conjugate conduction and convection:

see Conduction and convection Conservation of energy:

see Energy equation Conservation of mass:

see Mass conservation Conservation of momentum:

see Momentum equations Continuity equation, 5 Convection with change of phase,

305-344 Copper powder, 4 Core flow, 221, 226, 315, 317 Corey formulas, 45 Cork board, 4 Comer, 136, 137 Correlation formulas, 108, 164-168,

210, 233, 234, 236, 254-256, 269, 270, 273, 326

Critical point, stability, 153 Critical point, thermodynamics, 356 Critical Rayleigh number, 145, 147,

158, 159, 161, 163, 170, 172, 174, 177, 178, 184, 189, 194, 205-207, 237, 257, 278, 285, 286, 297, 336, 350, 353

Critical wavenumber, 145, 147, 207, 257, 297

Cross-diffusion, 34, 282 Crystallization, 351 Curvature effects, 118 Cylinder embedded in box, 137 Cylinder, 51-54, 64, 71, 106-110,

119, 193-195, 231-234 241 264-267 "

Cylindrical enclosure, 231-234

D

Dalton's law, 30 Darcy flow, 5-7, 13, 14, 16, 44, 79,

120, 141, 211-226, 338 Darcy number, 105, 144, 156, 250 Darcy's law: see Darcy flow Darcy, permeability unit, 6 Darcy-Forchheimer intermediate range,

248 Density differences, large, 130 Density inversion, 347 Density variation, 196 Departure from Darcy flow:

see Non-Darcy effects Deterministic models, 6, 7 Diagenetic processes, 351-353 Diffusion, 31 Diffusive flux, 31, 33 Disc, 137 Dispersion tensor, 24, 284 Dispersion, 24-26, 28, 64-66, 69-74,

91-97, 130, 156-158, 175, 180, 261-264, 267, 280, 284, 285

Distinct boundary layers, 214 Double diffusion, 33, 104, 267,

275-303, 333, 350, 356 Double walls, 224 Duct, 56, 71, 196 Dufour effect, 34, 282 Dupuit-Forchheimer relationship, 5,

7, 33

E

Eccentricity, 234 Effective Prandtl number, 68, 69, 165 Effective thermal conductivity, 43,

73, 164 Effective viscosity, 12, 13 Elastic porous matrix, 160

Elliptic cross-section, 54 Enclosures: see Confined (enclosed)

flow Energy equation, 21-26, 40-43 Energy method, 350 Equation of state, 26, 346 Ergun's equation, 10, 19 Experimental investigations, 28, 70,

73, 97-99, 104, 122, 124, 151, 152, 162-169, 174, 177, 178, 181, 194, 201, 208, 209, 226, 230, 233, 234, 236, 250, 251, 253-256, 264, 266, 269, 270, 272, 273, 280, 281, 303, 332-334, 336

External flow, 47-56, 259-267 External natural convection, 79-139

F

Fiberglass, 4 Fick's law, 32 Film boiling, 338-343 Film condensation, 343, 344 Fingering, 280, 281, 303, 350 Finite-amplitude convection,

160-162, 280, 281 Fins, 75, 135, 136, 267 Fissures, 284 Floquet theory, 177 Fluctuating convection regime, 160,

164, 254 Fluid adjacent to porous medium, 14,

201-209, 250, 251 Fluid mechanics, 1-19 Folded porous layer, 352 Forced convection, 47-77, 343 Forchheimer coefficient, 156 Forchheimer drag, 8, 69 Forchheimer flow limit, 167 Forchheimer model, or equation, 9-11,

93, 95, 109, 122-124, 156, 165, 246, 247, 328

Forchheimer parameter, 96 Forchheimer-Brinkman model,

or equation, 13, 19, 73, 99, 161, 201, 329, 333

Form drag coefficient, 9, 10 Fourier number, 307 Fourier's law, 21 Freezing, 330-334 Frustum of cone, 116

Index 403

G

Galerkin method, 174, 177, 257 General two-dimensional body:

see Two-dimensional body Geophysical aspects, 345-356 Geothermal reservoirs, 345, 355, 356 Geothermal system, 179 Grashof number, 98, 99 Gravitational instability, 334, 336

H

Hair, 4, 74-77, 137-139 Heat capacity ratio, 143 Heat flux distribution, 353 Heat flux unit, 353 Heat transfer coefficient, 23, 24, 139 Heat transfer, 21-28 Heat-generating porous medium:

see Internal heating Hele-Shaw cell analogy, 27, 28, 162,

181, 280, 355 Helicoidal cells, 254, 347, 348 Hexagons, 152, 160, 162, 168, 175,

347 High Rayleigh number, 106-108,

110-112, 120-124, 127-130, 215, 216, 282-284

Higher-order boundary layer theory, 90, 91, 104, 121, 263

Higher-order transitions, 160-162 Homogenization method, 7 Horizontal cylinder, 106-11 0, 112,

139, 194, 195, 266, 267, 342 Horizontal heat and mass transfer,

286-297 Horizontal layer: see Horton-Rogers

Lapwood problem Horizontal layer, melting, 322-325 Horizontal layer, mixed convection,

268-271 Horizontal line source, 120-127, 267 Horizontal plate, 99-103, 106, 137,

264 Horton-Rogers-Lapwood problem,

141, 142, 256, 275-279, 346 Hot springs, 355 Hydrodynamic boundary conditions,

14-18

404 Index

I J

Ice front, 347 Ice melting, 330 Ideal gas, 159 Images, method of, 126 Inclined cylinders, concentric, 256 Inclined plate, 104, 105, 136,

259-263, 264 Inclined porous layer or enclosure,

251-256, 347, 353 Inclined temperature gradient,

256-258 Inertia, 7-9, 64-66, 69-74, 86, 91-97,

104, 120, 165, 246-249, 261, 263, 267, 326, 328

Inhomogeneity, 180-187, 229-231, 285, 296

Injection, 261, 264, 355 Instability (see also Stability, Linear

stability analysis, Nonlinear stability analysis), 28, 280

attic-shaped enclosure, 237 gravitational, 334 oscillatory, 275, 280, 281 phase-change, 335 sinuous, 153 subcritical, 149 varicose, 153 vortex, 104-106, 264

Instantaneous point source, 133 Integral method, 84-86 Interface between porous medium and

impermeable wall, 16 Intermediate Rayleigh number,

108-110, 113, 134, 135 Internal flow, 56-58, 267-274 Internal heating, 172-175, 178, 193,

195, 196, 209, 251 Internal natural convection:

heating from below, 141-210, 330, 334-338

heating from the side, 211-258, 305-332

Internal partitions: see Partitions Internal Rayleigh number, 174 Intrinsic average, 5 Intrinsic phase average, 36 Intrusion layer, horizontal, 322-325 Irmay-Ergun equation, 19 Isothermal side walls, 211

Jakob number, 341, 344, 351 Jets, 214 Karman-Pohlhausen integral method:

see Integral method Kozeny's equation, 10

L

Large-Reynolds-number limit: Rayleigh number, 94, 247

Lateral mass flux, 83, 84, 135, 263, 343, 344

Lateral penetration, 238-240 Lateral thermal dispersion, 169 Layered double-diffusive convection,

280 Layered porous media, 181, 229-231 Leather, 4 Lewis number, 277, 283, 300 Lienhard's swept length, 53 Limestone, 4 Line source, 54-56, 120-127 Linear stability analysis, 142-147,

152, 169, 188-191, 225, 252, 257, 276, 335

Liquid-dominated system, 334, 335 Local nonsimilarity method, 118,

264, 266 Local similarity, 105, 137, 267 Local thermal equilibrium, 21, 42,

141, 154, 333 Localized heating, 197-201, 268-274 Low Rayleigh number, 108-110, 112,

113, 124-127, 130-134

M

Macroscopic quantities, Magma bodies, 356 Magma chambers, 350, 351 Magma production, 350, 351 Malkus hypothesis, 151 Mammals, body lengths and hair

sizes, 77 Mass conservation, 31-33, 37-39 Mass flow, net, 169-171, 258

Mass fraction, 30 Mass transfer, 29-46, 103 Matched boundary layer analysis,

217, 226 Materials, porous, 2, 4 Maximum density effects, 103, 104,

171, 209, 210, 235, 236, 330 Melting rate, 319 Melting, 305-330 Merged-layer regime, 225 Mixed convection, 259-274 Modified averaging theorem, 37 Molar mass, 29 Mole fraction, 30 Mole, 29 Momentum equation, 5-7, 39, 40 Multicomponent flow, 29-31 Multiphase flow, 35-45

N

Natural convection: internal, heating from below,

141-210, 330, 334-338 internal, heating from the side,

211-258, 305-332 external, 79-139

Net mass flow, 169-171 Neumann solution, 311, 312, 319 Neutral stability curve, 154, 208,

277, 338 Non-Boussinesq effects, 158-160, 231 Non-Darcy effects, 98, 106, 118,

135, 136, 156-158, 161, 246-250

Non-equilibrium, thermal, 23, 74, 137, 154-156

Non-Newtonian fluid, 99, 103, 108, 112

Non-similarity results, 96 Non-uniform porosity:

see Porosity variation Nonlinear initial profiles, 172-178,

258, 279-281 Nonlinear neutral curves, 153 Nonlinear stability analysis, 171,

175, 225, 281, 350 Nonuniform heating, 187, 188 Nusselt number:

conduction referenced, 149, 222 local, 49, 50, 52, 82, 85, 95,

Index 405

100, 101, 105, 107, 117, 148, 261, 263, 341

o

overall, 49, 50, 53, 57, 69, 83, 87, 88, 101, 110, 113, 157, 214, 283, 287, 310, 323

Oberbeck -Boussinesq approximation, 26, 27, 79, 141, 212, 338, 356

Oceanic crust, 353-355 Optimal hair strand diameter, 76, 138 Oscillating wall temperature, 99 Oscillations, tidal, 130 Oscillatory convection, 137, 157,

160-162, 194, 198, 267, 269, 270, 284, 335, 355

Oscillatory instability, 275, 280, 282 Oseen linearization method, 88, 216,

226, 247 Overall thermal conductivity, 22, 23

p

Packed bed, 73 spheres, 3, 4

Packed column, 74 Parabolic density model, 236 Paraboloid, 119, 267 Partial melt problem, 350 Partial pressure, 30 Partitions, 224, 227-229, 250 Pattern selection, 191 Patterned ground, 347, 348 Penetrative convection, 237-243 Permeability, 4-6, 12, 76, 77, 139,

263, 264 intrinsic, specific, 6 relative, 40, 43-45

Perturbations, 142 Pec1et number, 25, 48, 50, 53, 55,

62, 170, 262, 268 Phase average, 36 Phase change, 305-345 Phase-change instability, 335 Pipes, buried, 137 Plane wall, 47, 50, 60, 63-70,

79-104, 259-263 Plate fin, 267 Plate: see Plane wall

406 Index

Point source, 54-56, 127-135 Polyhedral cells, 160, 253, 334 Pore Reynolds number, 26, 67, 249 Pore scale, 1 Porosity, 3, 4

effective, 3 hair, 75, 138 non-uniform, 67, 96, 263 surface, 3, 21, 33 variation, 13, 18, 19, 23, 66-74,

103, 161, 168, 250, 263, 267, 343

values, 4 Porous materials, 2, 4 Porous medium, 1 Porous medium Prandtl number, 165 Power series solution, 126, 131, 146,

150, 151 Power-law wall temperature, 81, 136,

264 Prandtl number, 67, 68, 73

effective, 68, 69, 165 porous medium, 165

Pressure changes, 23, 24, 356 Properties, 4 Property variations, 152, 159, 196,

198, 231, 348

Q

Quadratic drag, 9-11, 64, 66, 86, 94, 122, 135, 157, 158, 165, 196, 249, 250, 262-264, 267, 273, 343

Quartz, 352

R

Rayleigh number, 81, 97, 102, 107, 117, 121, 123, 125, 129, 131, 138, 139, 178, 184, 213, 233, 234, 236, 262, 277, 307, 331, 344

based on heat flux, 226, 293 based on source strength, 297, 302 critical: see Critical Rayleigh

number high, 106-108, 110-112, 120-124,

127-130, 215, 216, 282-284, 302

horizontal, 257

intermediate, 108-110, 113, 134, 135

internal, 174 large Reynolds number limit, 94,

247 low, 108-110, 112, 113, 124-127,

130-134, 300, 301 two-phase region, 335, 340

Rayleigh-Darcy number: see Rayleigh number

Recharge, 355 Rectangular box or cavity, 188-193,

195, 250, 251, 256, 314, 323 Regimes, 211-216, 287, 313, 323 Regions bounded by two planes, 136,

137 Representative elementary volume, 1,

3 Reynolds number, 9, 75 Rock, granular, 4 Rolls, 150, 152, 153, 160, 168, 169,

175, 178, 187, 254, 347, 348

s

Salinity gradients, 349 Salt domes, 356 Salt fingering: see Fingering Sand, sandstone, 4, 352 Saturation, 38 Scale analysis, 48, 58-60, 103, 137,

165-168, 211-216, 234, 235, 238-240, 245-247, 287, 290, 311-314

Seepage velocity, 5 Semi-infinite region, 109, 135, 243 Shale, 352 Shallow layers, 215, 216, 221-225,

312 Sherwood number, 281, 283, 284,

287, 290-296 Silica, 4 Similarity solution, 49, 55, 81, 86,

95, 100, 101, 121, 123, 129, 259, 288, 289, 326, 340

Single-phase flow, 1 Sinks

line, 355, 356 vertical plane, 355, 356

Slate powder, 4 Sloping: see Inclined Slot, 192

Slug flow, 56 Snow, 345-347 Soil, 4 Solid-fluid heat transfer, 23, 24,

154-156, 164 Soret and Dufour effects:

see Cross-diffusion Soret effect, 34, 281, 282, 303 Sources, 297-302

horizontal line, 301, 302 point, 297-301

Spatial approach, 1 Sphere, 51-54, 107, 110-114, 139,

234, 235, 264-267, 302, 342 Spheres, 3 Spherical enclosure, 234, 235 Stability analysis, 142-147, 152,

153, 350 Stability balloon, 154, 158 Stability (see also Instability, Linear

stability analysis, Nonlinear stability analysis), 177, 181, 186, 225, 226, 297

Stably heated comer, 136 Starting temperature difference, 88 Statistical approach, 1, 7 Stefan number (see also Jakob

number), 307, 351 Stefan problem (see also Neumann

problem), 349 Stone patterns, 347 Stratification, 86-88, 120, 201, 226 Subcooled forced convection film

boiling, 343 Subcooling, solid, 325 Suction or blowing at the surface,

115, 137, 259, 260, 261, 263, 289

Superconvection, 356 Superheating, liquid, 314-322, 325,

326 Superposition of sources, 133 Surface covered with hair: see Hair Surface per unit volume, 4 Surface porosity, 3, 21, 33 Surface tension, 344

T

Tall layers, 215 Thawing frozen soil, 348

Index 407

Thawing subsea permafrost, 349, 350 Thermal boundary conditions, 27 Thermal boundary layer, 48, 58-60,

82, 85, 138 Thermal diffusivity tensor, 26 Thermal dispersion conductivity

tensor, 26 Thermal dispersion: see Dispersion Thermal expansion coefficient, 23,

33, 276 Thermal wakes, 54-56 Thermohaline, 33, 275 Thin box, 192 Third diffusing component, 286 Three-dimensional disturbances, 28,

152, 153 Throughflow, 170, 171, 175, 258 Tidal oscillations, 130 Time-dependent boundary cooling,

178 Time-dependent boundary heating,

176-178 Topographical forcing, 353-355 Tortuosity, 12 Transient effects, 8, 58-64, 66,

84-86, 103, 115, 127, 130, 131, 135, 175-178, 243-246, 267, 269, 288, 296, 297, 303, 333, 343

Transitions, 160-162, 233, 247, 254, 312, 330

Transport of water vapor, 345 Transport theorem, 37 Truncated cone, 118 Turbulent flow, 8, 249 Two-dimensional bodies, 108, 111,

118-120, 267, 303, 342, 343 Two-dimensional cavities, 237 Two-phase flow, 1, 36 Two-phase 'region, 334 Two-temperatures porous medium

model, 23, 24, 74-77, 137, 154-156, 355

Two-zone model, melt region, 323

u

Uniform acceleration, 267 Unsaturated porous media, 45, 46 Unsteady: see Transient effects

408 Index

v

Vapor-dominated system, 334-338 Vertical cone: see Cone Vertical cylinder, 64, 114, 115, 193,

194, 196, 266, 267, 303 Vertical cylindrical annulus, 227 Vertical cylindrical fin, 135 Vertical layer, mixed convection,

271, 272 Vertical melting front, 325, 326, 330 Vertical penetration, 240-244 Vertical plate, 79-99, 118, 135, 136,

259-263, 326, 343 Vertical side walls:

isothermal, 211 uniform flux, 226, 256

Vertical symmetry, 356 Viscosity variation, 159, 161, 171,

196, 263, 281, 343 effective, 12, 13

Viscous dissipation, 23, 120 Visualization, 162, 168 Volumetric heating:

see Internal heating Vortex instability, 104-106, 264 Vortex, expanding, 126-134, 300

w Wall thickness parameter, 88 Water, 159, 209, 210, 235-236, 254,

330, 336, 345-347, 351 Wavenumber, 144, 337 Weakly nonlinear theory, 147-154,

187, 193 Wedge, 121, 136, 342, 343 Wire crimps, 4 Withdrawal, 264, 355

References* - rd.springer.com978-1-4757-2175-1/1.pdf · References* Aidun, C. K. 1987 Stability of...

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