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Alexiades V. - Mathematical Modeling of Melting and Freezing Processes
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Название: Mathematical Modeling of Melting and Freezing ProcessesАвтор: Alexiades V. Язык: Рубрика: Разное /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1992Количество страниц: 323Добавлена в каталог: 09.04.2008Операции: Положить на полку |
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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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