Mathematical modeling of melting and freezing processes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington u.a.
Hemisphere Publ. Corp.
1993
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 323 S. graph. Darst. |
| ISBN: | 1560321253 |
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Record in the Search Index
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| adam_text | MATHEMATICAL MODELING OF MELTING AND FREEZING PROCESSES VASILIOS
ALEXIADES THE UNIVERSITY OF TENNESSEE AND OAK RIDGE NATIONAL LABORATORY
ALAN D. SOLOMON CONSULTANT FORMERLY AT OAK RIDGE NATIONAL LABORATORY
OHEMISPHERE PUBLISHING CORPORATION A MEMBER OF THE TAYLOR & FRANCIS
GROUP WASHINGTON PHILADELPHIA LONDON CONTENTS PREFACE XI 1. PROBLEM
FORMULATION 1 1.1 AN OVERVIEW OF THE PHENOMENA INVOLVED IN A PHASE
CHANGE 2 PROBLEMS 5 1.2. FORMULATION OF THE STEFAN PROBLEM 6 1.2.A
INTRODUCTION 6 1.2.B ASSUMPTIONS 6 1.2.C HEAT CONDUCTION 8 1.2.D
BOUNDARY CONDITIONS 17 1.2.E INTERFACE CONDITIONS 19 1.2.F THE STEFAN
PROBLEM 22 PROBLEMS 26 1.3. GENERAL MELTING AND SOLIDIFICATION PROCESSES
29 PROBLEMS 32 2. PROBLEMS WITH EXPLICIT SOLUTIONS 33 2.1. THE ONE-PHASE
STEFAN PROBLEM 34 2.1.A INTRODUCTION 34 2.1.B THE NEUMANN SOLUTION 36
2.1.C DIMENSIONLESS FORM 37 2.1.D THE ROOT X VS THE STEFAN NUMBER 38
2.1.E EXAMPLE: MELTING A SLAB OF ICE 40 2.1.F THE CASE OF SMALL STEFAN
NUMBER 43 PROBLEMS 44 2.2. THE TWO-PHASE PROBLEM ON A SEMI-INFINITE SLAB
46 2.2.A PROBLEM STATEMENT AND SOLUTION 46 2.2.B DIMENSIONLESS FORM 48
2.2.C APPROXIMATIONS TO THE ROOT X 49 2.2.D APPROXIMATING THE FINITE
SLAB CASE 50 2.2.E ENERGY CONTENT AND STEFAN NUMBERS 51 2.2.F SHAPE OF
MELTING AND COOLING CURVES 52 2.2.G AN EXAMPLE 55 PROBLEMS 56 V 2.3. THE
EFFECT OF DENSITY CHANGE 59 2.3.A PHYSICAL EFFECTS 59 2.3.B EXPANSION
WITH BULK MOVEMENT DUE TO P L P S 61 2.3.C APPLICATION TO CRYOSURGERY
64 2.3.D VOID FORMATION 68 2.3.E CONSERVATION LAWS AND INTERFACE
CONDITIONS 72 PROBLEMS 77 2.4. SOLIDIFICATION OF A SUPERCOOLED MELT 79
2.4.A HOW SUPERCOOLING ARISES 79 2.4.B ONE-PHASE SUPERCOOLED
SOLIDIFICATION : 82 2.4.C TWO-PHASE SUPERCOOLED SOLIDIFICATION 84 2.4.D
SUPERCOOLED SOLIDIFICATION WITH DENSITY CHANGE 87 2.4.E STEADY-STATE OF
A FINITE SLAB 87 2.4.F PHASE EQUILIBRIUM AND THE GIBBS-THOMSON EFFECT 88
2.4.G MULLINS-SEKERKA MORPHOLOGICAL STABILITY ANALYSIS 94 PROBLEMS 96
2.5. CHANGE OF PHASE IN A BINARY ALLOY 98 2.5.A INTRODUCTION 98 2.5.B
THE PHASE DIAGRAM 99 2.5.C INTERDIFFUSION 102 2.5.D A SIMPLE BINARY
ALLOY SOLIDIFICATION MODEL 104 2.5.E THE RUBINSTEIN SIMILARITY SOLUTION
106 2.5.F SHORTCOMINGS OF THE SIMPLE MODEL 107 2.5.G UNCOUPLED MODELS OF
ALLOY SOLIDIFICATION 109 2.5.H THE TIEN-GEIGER MODEL FOR FREEZING OVER
AN EXTENDED RANGE 110 2.5.1 RAPID FREEZING OF A FINITE SLAB WITH STINING
OF MELT 112 PROBLEMS 116 2.6. SIMILARITY SOLUTIONS IN CYLINDRICAL AND
SPHERICAL GEOMETRIES 117 2.6.A SIMILARITY SOLUTIONS 117 2.6.B
AXIALLY-SYMETRIC MELTING DUE TO A LINE SOURCE 118 2.6.C FREEZING OF
SUPERCOOLED LIQUID 119 PROBLEMS 120 2.7. BENCHMARK SOLUTIONS OF
MULTIDIMENSIONAL PROBLEMS FOR SIMULATION VERIFICATION 121 2.7.A
NECESSITY OF BENCHMARK SOLUTIONS 121 2.7.B PHASE-CHANGE IN A BOX 121
2.7.C SUMMARY OF THE METHOD 123 PROBLEMS 123 3. ANALYTICAL
APPROXIMATIONS 125 3.1. THE QUASISTATIONARY APPROXIMATION 126 3.1.A
INTRODUCTION 126 3.1.B ONE-PHASE STEFAN PROBLEM WITH IMPOSED TEMPERATURE
127 3.1.C ONE-PHASE STEFAN PROBLEM WITH IMPOSED LLUX 134 3.1.D THE CASE
OF CONVECTIVE BOUNDARY CONDITION 137 3.1.E VOLUMETRIC HEATING 140
PROBLEMS 141 3.2. QUASISTATIONARY APPROXIMATION OF AXIALLY OR RADIALLY
SYMMETRIC PROCESSES 144 3.2.A INTRODUCTION 144 3.2.B OUTWARD MELTING OF
A HOLLOW CYLINDER 144 3.2.C INWARD MELTING OF A CYLINDER 147 3.2.D
INWARD MELTING OF A SPHERE 148 3.2.E SIMPLE APPROXIMATIONS OF A HEAT
STORAGE PROCESS 149 PROBLEMS 152 3.3. PERTURBATION METHODS FOR ONE-PHASE
PROBLEMS .... 154 3.3.A INTRODUCTION 154 3.3.B LANDAU TRANSFORMATION 155
3.3.C FRONT LOCATION AS INDEPENDENT VARIABLE 157 3.3.D RAPID FREEZING OF
DILUTE ALLOYS 160 PROBLEMS 161 3.4. THE MEGERLIN AND
HEAT-BALANCE-INTEGRAL METHODS 162 3.4.A INTRODUCTION 162 3.4.B THE
MEGERLIN METHOD 162 3.4.C THE HEAT-BALANCE-INTEGRAL METHOD 165 PROBLEMS
167 3.5. SOME MELTING TIME RELATIONS 168 3.5.A INTRODUCTION 168 3.5.B
MELT-TIME FOR A SIMPLE PCM BODY WITH IMPOSED TEMPERATURE 168 3.5.C
MELT-TIME FOR A SIMPLE PCM BODY WITH CONVECTIVE BOUNDARY CONDITION 171
3.5.D MELT-TIME FOR A RECTANGULAR BODY UNDER IMPOSED TEMPERATURE 173
3.5.E FREEZING OF A PCM CYLINDER ARRAY 174 PROBLEMS 178 4. NUMERICAL
METHODS - THE ENTHALPY FORMULATION 180 4.1. NUMERICAL HEAT TRANSFER 181
VLLL CONTENTS 4.1.A INTRODUCTION 181 4.1.B CONTROL VOLUME DISCRETIZATION
OF THE CONSERVATION LAW 184 4.1.C DISCRETIZATION OF BOUNDARY CONDITIONS
191 4.1.D THE DISCRETE PROBLEM 192 4.1.E EXPLICIT TIME UPDATING 194
4.1.F IMPLICIT TIME UPDATING 197 4.1.G HEAT CONDUCTION IN 2 OR 3
DIMENSIONS 199 4.1.H INTERNAL HEAT SOURCE 202 4.1.1 SOME PROGRAMMING
SUGGESTIONS 203 PROBLEMS 205 4.2. BRIEF OVERVIEW OF NUMERICAL METHODS
FOR PHASE CHANGE PROBLEMS 210 4.3. THE ENTHALPY METHOD IN ONE SPACE
DIMENSION 212 4.3.A INTRODUCTION 212 4.3.B THE ENTHALPY METHOD 212 4.3.C
A TIME-EXPLICIT SCHEME 217 4.3.D PERFORMANCE OF THE EXPLICIT SCHEME ON A
ONE-PHASE PROBLEM 218 4.3.E IMPLICIT SCHEMES 224 4.3.F IMPLICIT SCHEME
BY NEWTON ITERATION 229 4.3.G PERFORMANCE OF THE SCHEMES ON THE
TWO-PHASE STEFAN PROBLEM 231 4.3.H PERFORMANCE ON PROBLEMS WITH UNEQUAL
PROPERTIES 236 4.3.1 IMPLICIT VERSUS EXPLICIT SCHEMES 238 4.3 J USE OF
THE ENTHALPY METHOD FOR A MULTI-LAYERED SLAB 239 PROBLEMS 241 4.4.
MATHEMATICAL FRAMEWORK OF THE ENTHALPY FORMULATION 242 4.4.A
INTRODUCTION 242 4.4.B WEAK DERIVATIVES 244 4.4.C EXAMPLES OF WEAK
FORMULATION OF PROBLEMS 248 4.4.D CLASSICAL FORMULATION OF STEFAN
PROBLEMS IN 3-DIMENSIONS 250 4.4.E WEAK FORMULATION OF THE STEFAN
PROBLEM 253 PROBLEMS 260 4.5. CONVERGENCE OF THE ENTHALPY SCHEME AND
EXISTENCE OF THE WEAK SOLUTION 260 4.5.A INTRODUCTION 260 4.5.B
STRUCTURE OF THE PROOF 261 4.5.C PROOF OF CLAIM 1 264 4.5.D PROOF OF
CLAIM 2 269 4.5.E PROOF OF CLAIM 3 272 4.5.F NOTE ON ERROR ESTIMATES 273
PROBLEMS 273 CONTENTS IX 5. APPLYING THE TECHNIQUES OF MODELING 27 4
5.1. LATENT HEAT STORAGE AND PHASE CHANGE MATERIALS 276 5.1.A
INTRODUCTION 276 5.1.B A SIMPLE HEAT STORAGE EXAMPLE 277 5.1.C TROMBE
WALL 279 PROBLEMS 283 5.2. NUMERICAL SIMULATION OF A LATENT HEAT TROMBE
WALL 284 PROBLEMS 290 5.3. DEVELOPMENT OF A SIMULATION CODE FOR A LHTES
SYSTEM IN A SPACE STATION 290 5.3.A INTRODUCTION 290 5.3.B THE SYSTEM OF
INTEREST 291 5.3.C ROUGH SIZING OF THE STORAGE SYSTEM VIA THE
QUASISTATIONARY APPROXIMATION 296 5.3.D NUMERICAL SIMULATION 298 5.3.E
SOME SIMULATION RESULTS 299 PROBLEMS 304 BIBLIOGRAPHY 305 INDEX 321
|
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| language | English |
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| physical | XIII, 323 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
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| spelling | Alexiades, Vasilios Verfasser aut Mathematical modeling of melting and freezing processes Vasilios Alexiades ; Alan D. Solomon Washington u.a. Hemisphere Publ. Corp. 1993 XIII, 323 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fisica geral larpcal Fusion, Points de - Modèles mathématiques ram Solidifications - Modèles mathématiques ram Transitions de phases - Modèles mathématiques ram Mathematisches Modell Fusion Mathematical models Phase transformations (Statistical physics) Mathematical models Solidification Mathematical models Schmelzen (DE-588)4179780-2 gnd rswk-swf Erstarrung (DE-588)4140191-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Schmelzen (DE-588)4179780-2 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Erstarrung (DE-588)4140191-8 s Solomon, Alan D. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005024573&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alexiades, Vasilios Solomon, Alan D. Mathematical modeling of melting and freezing processes Fisica geral larpcal Fusion, Points de - Modèles mathématiques ram Solidifications - Modèles mathématiques ram Transitions de phases - Modèles mathématiques ram Mathematisches Modell Fusion Mathematical models Phase transformations (Statistical physics) Mathematical models Solidification Mathematical models Schmelzen (DE-588)4179780-2 gnd Erstarrung (DE-588)4140191-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4179780-2 (DE-588)4140191-8 (DE-588)4114528-8 |
| title | Mathematical modeling of melting and freezing processes |
| title_auth | Mathematical modeling of melting and freezing processes |
| title_exact_search | Mathematical modeling of melting and freezing processes |
| title_full | Mathematical modeling of melting and freezing processes Vasilios Alexiades ; Alan D. Solomon |
| title_fullStr | Mathematical modeling of melting and freezing processes Vasilios Alexiades ; Alan D. Solomon |
| title_full_unstemmed | Mathematical modeling of melting and freezing processes Vasilios Alexiades ; Alan D. Solomon |
| title_short | Mathematical modeling of melting and freezing processes |
| title_sort | mathematical modeling of melting and freezing processes |
| topic | Fisica geral larpcal Fusion, Points de - Modèles mathématiques ram Solidifications - Modèles mathématiques ram Transitions de phases - Modèles mathématiques ram Mathematisches Modell Fusion Mathematical models Phase transformations (Statistical physics) Mathematical models Solidification Mathematical models Schmelzen (DE-588)4179780-2 gnd Erstarrung (DE-588)4140191-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Fisica geral Fusion, Points de - Modèles mathématiques Solidifications - Modèles mathématiques Transitions de phases - Modèles mathématiques Mathematisches Modell Fusion Mathematical models Phase transformations (Statistical physics) Mathematical models Solidification Mathematical models Schmelzen Erstarrung |
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