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| Alexiades V. — Mathematical Modeling of Melting and Freezing Processes |
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| Предметный указатель |
Ablation 25
Alloy see also “Binary alloy”
Alloy, dilute 114 160
Alloy, solidification 104 109
Alloy, solidification, of eutectic 110
Alloy, solidification, with complete mixing of liquid 112
Amorphous phase 2 80 102
Approximation to root of transcendental equation to two-phase case 40 50
Axisymmetric problems 118 144
Binary alloy, definition 98
Binary alloy, similarity solution 106 111
Binary alloy, uncoupled models of solidification 109
Biot number 137—139
boundary conditions 13 17
Boundary conditions, discretization of 191
CFL stabUity condition 183 195 218 285
Charging time 29 300
Clapeyron relation 90—91
Classical formulation 24 250 261
Concentration in binary alloy 98 100
Conduction 2 12 183
Conductivity, thermal 18
Conservation law 12 72—73 103 183
Conservation law, discrete 185
Constitutional supercooling 112
Contrived solution of multidimensional problem 121
Control volume 184
Convection 2 61
Convergence 193 260
Cryosurgery 64—68
Curvature 81
Density, effect of change upon phase change 59
Diffusion equation 103 (see also “Heat equation”)
Dilute alloy 114
Dimensionless form 37 48
Dirac  245
Directional solidification 115
Discharging time 29—30 297
Distribution or generalized function 245
Distribution, coefficient, of binary alloy 114 160
Elliptic equation 14
Energy balance, global 21 185 212
Energy conservation 12 72
Enthalpy 8 72
Enthalpy, method 211 212
Enthalpy, method, convergence, of 263—264
Equation of state 6 74 212
Equilibrium melt temperature 79 91
Error function 16 36 39—40 58
Error, computing 121 194 232 273
Explicit scheme 187 218 260
Fick’s law 103
Flux, discrete 187
Flux, heat 8 73
Flux, mass 103
Fourier number 37
Fourier’s law 10—11
Front capturing schemes 210
Front tracking schemes 210
Gauss — Seidel iteration 199 225
Gibbs — Thomson relation 4 80 92—93
Gibbs, free energy 90
Gibbs, phase rule 100
Glauber’s salt 55 172
Goodman’s method 165
Grashof number 281
Heat 2 8—17
Heat, balance integral method 165
Heat, balance, discrete 190
Heat, capacity see “Specific heat”
Heat, conduction 8
Heat, equation 12—13
Heat, flow rate 11
Heat, of fusion 9 74 90
Heat, storage 55 149
Heat, transfer coefficient 18 174 290
Heat, transfer, modes of 2
Heat, transfer, numerical 181
Hyperbolic equation 15
Hypercooling 3 85
Implicit scheme 187 224—231
Instability, of interface 80 102
Interdiffusion 102
Interdiffusion, coefficient 103
INTERFACE 3 20 80
Interface, condition 19 72—73 80
Jump condition across an interface 20 73 81 247
Kirchoff temperature 216 252
Laplace equation 13
Laplace — Young relation 89
Latent heat 2 6 9 81
Latent heat, thermal energy storage 29 274 284 293
Lever rule 100 115
Liquid fraction 100 213
Liquidus curve 100 114—115
Lithium fluoride 71 294
Marangoni convection 5 60
Mass conservation 72
| Megerlin method 162
Melt time approximations, convective boundary condition 171
Melt time approximations, cylinder array 174
Melt time approximations, rectangular body 173
Melt time approximations, simple body 168
Miscibility gap in phase diagram 100
Mole fraction 98
Moving boundary problem 6 24
Mushy region 9 100 102 140 301
Neumann similarity solution 36—37 47 50
Newton iteration scheme 229
Newton’s Law of Cooling 18
One-phase problem 25 34 82 114 127 134 140 144 155 157 160 163—167
Parabolic equation 15
PCM 6 276 284 290—303
Perturbation method 154
Phase, diagram 99 114
Phase, equilibrium 88—93
Prandtl number 152 281
Pressure 73—75 89—92
Quasistationary approximation 44 126
Quasistationary approximation for 2-phase problems 133
Quasistationary approximation for cylindrical geometry 144 147
Quasistationary approximation for slab geomerty 127 134 137
Quasistationary approximation for spherical geometry 148
Quasistationary approximation, flaw for large Biot number 137
Quasistationary approximation, internal heating case 140
Radiation 2 18
Reynolds number 152
Scheilrule 115
Segregation 112
Sensible heat 9 51 113
Sensitivity 9
Similarity solution 36 47 63
Similarity solution, to alloy solidification 106 111
Similarity solution, to axisymmetric problems 118—119
Similarity solution, to one-phase Stefan problem 34—35
Similarity solution, to spherically symmetric problems 117
Similarity solution, to supercooling 84—85
Similarity solution, to two-phase Stefan problem 46
Similarity solution, to void growth scenario 68
Sobolev space 247
Solidus curve 100 114 115
Solute 98
Solvent 98
Specific heat 8 9
Spherically symmetric problems 117 148
Stability, morphological 81 94—96
Stability, numerical 183 195 218
Steady state 79 87
Stefan condition 21—22 47 255
Stefan number 38 46 293
Stefan number, case of small value 43 126
Stefan number, interpretation as ratio of energies 52
Stefan Problem, 1-phase see “One-phase problem”
Stefan Problem, 2-phase 23 46 62 70 84 105 111
Stefan Problem, classical 6 34 46 250 261
Stefan Problem, weak formulation 248 262
Subcooling, initial 52 168
Supercooling 3 79—82
Supercooling, constitutional 102 108
Supercooling, freezing of supercooled melt 82 84 119
Superheating 3
Temperature 2—5 8
Temperature of phase-change (or melt) 2 79 84 91
Temperature-time curve, shape of 52
Thermal diffusivity 13
Thermal energy 2 52 276 293
Thermodynamics, first law of 12
Thermodynamics, second law of 89
Thermophysical properties of Calcium Cloride Hexahydrate 277
Thermophysical properties, copper 38
Thermophysical properties, Glauber’s salt 55 172
Thermophysical properties, ice 8 38 45 65 86
Thermophysical properties, LiF 71 294
Thermophysical properties, parafin wax 39 169
Thermophysical properties, silicon dioxide 39
Thermophysical properties, water 8 38 41 65 86
Transcendental equation for binary alloy solidification 104
Transcendental equation for Neumann solution 36—37 47
Transcendental equation for problem with density change 59
Transcendental equation for problem with void formation 68
Transcendental equation for supercooled solidification 85
Transcendental equation, approximation to root of 49
Trombe wall 276 279—290
Two-phase problem 46—58
Void due to shrinkage, formation 68—71 76
Void due to shrinkage, heat transfer across 69
Void due to shrinkage, problem with explicit solution 68
Wave equation 14
Weak derivative 244
Weak formulation 248 253 262
Weak solution 250 263
Weak solution, uniqueness of 257 263
Weight fraction of solute 98—99
Well posedness 12 260
Zero latent heat 51—52
Zone refining 112 115
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