CONTENT
of the Fourth Volume
Berezovsky B.M.  MATHEMATICAL MODELS of ARC WELDING, 547 pages, 2006
The subtitle: Fundamentals of heat transfer in the workpieces

CONTENT 3
INTRODUCTION 7
Chapter 15 THE MAIN PURPOSES and TECHNOLOGICAL TASKS of THERMAL PHYSICS of the WELDING PROCESSES and RELATED TECHNOLOGIES 12
15.1 Major development trends of welding technological thermal physics 17
15.1.1. Heat checking of manufacturing processes 17
15.1.2. Optimization of temperature fields during heat treatment 19
15.1.3. Urgency of mathematical modeling of heat transfer at welding and related processes 22
15.1.4. Creation the software for problem solving for welding technological thermal physics 27
15.1.5. Computer Aided Systems for simulation of thermal processes 38
15.1.6. Stresses and strains at welding and their links with temperature fields and different problems of welding production 46
15.2. Main principles of mathematical models design for processes of heat trans-fer in the workpieces to be welded 51
15.3. Features and areas of usage of thermal physics of welding processes 55
15.3.1. Areas of application of thermal mathematical modeling of welding technologies 56
15.3.2. Practical using of computational technological thermal physics 57
15.4. Development of thermal fundamentals of welding: the milestones 65
Chapter 16 TEMPERATURE FIELDS AT WELDING, its PROPERTIES and METHODS of mathematical MODELING 69
16.1. The types of heat transfer at welding and related manufacturing processes 69
16.2. Basic characteristics of a temperature field 78
16.3. The gradient of temperature and the heat flow 78
16.4. Fourier's Law of thermal conductivity 82
16.5. Performance of a temperature field. The Vector Stream and the Divergence 84
16.6. The heat conduction differential equation 87
16.7. The special conditions of heat transfer 93
16.8. Classification of different types of heat conductivity differential equations 96
16.9. Differential equations, related equation thermal conductivities 100
16.10. Conditions of uniqueness and mathematical posing of boundary value problems of a transient heat conduction. Boundary and initial conditions 104
16.11. Surface heat transfer, its aspects and main calculate proportions 109
16.12. Dependence of materials thermal properties of on temperatures 113
16.13. Taking into account the phase changes for mathematical modeling of temperature fields 120
16.14. Solution methods for the differential heat conduction equation 126
16.14.1. Methods of calculus variations for mathematical modeling of heat transfer 140
16.14.2. Variables separation method for restricted regions with heat sources 154
16.14.3. Method of variables separation for unlimited regions. The fundamental solutions of the equation of thermal conductivity 161
16.14.3.1. Temperature smoothing in the rod of finite length 175
16.14.3.2. Transient temperature field in the rectangular plate 178
16.14.3.3. Applying separation variables method for temperature fields with moving heat sources 186
16.14.3.4. Method of variables separation, its generalizing and further development 191
16.15. The power sources for fusion welding and their performance 194
16.16. Features of mathematical modeling of heat processes and principles of choice for the calculate schemes 198
16.17. Idealization of calculate schemes of welding heat sources and bodies to be heated 204
16.17.1. Idealization of bodies to be heated during fusion welding 204
16.17.2. Idealization of heat sources applied at fusion welding 210
Chapter 17 SOLUTION METHODS of the DIFFERENTIAL HEAT CONDUCTION EQUATION FOR MATHEMATICAL MODELING of WELDING TECHNOLOGICAL SYSTEMS 214
17.1. The method of sources and its main possibilities for a solution of the differential heat conduction equation 214
17.1.1. Applying the principle of superposition for moving concentrated and spatially distributed heat sources 222
17.1.2. Heating the semi-infinite body by moving point heat source 231
17.1.3. Heating the semi-infinite body by a moving linear heat source of finite width 239
17.1.4. Heating the semi-infinite body by the moving ring-type heat source 246
17.1.5. Applying the method of sources for mathematical modeling of heating the semi-infinite body by surface distributed heat sources 250
17.1.6. Heating a semi-infinite body by a source with an uniform distribution of heat flow on a rectangular area 251
17.2. The method of integral transforms and its applying for a solution of a dif-ferential heat conductivity equation 261
17.2.1. Basic stages of integral transforms for solution of the differential heat conductivity equation 264
17.2.2. Delta-function of Dirac and its usage at problem solving of thermal conductivity by the method of integral transforms 273
17.2.3. Fixed temperature field in a unlimited band with a concentrated heat source 286
17.2.4. Problems solving of thermal conductivity for transient temperature fields 289
17.3. The method of Greene functions for problem solving of thermal conductivity 300
17.4. Methods of physical and analogue simulation of temperature fields 326
17.4.1. Common analogies between the physical fields 328
17.4.2. The electric analogies of the physical fields 332
17.4.3. The modeling circuits (grid electrical models) 347
17.4.4. Applying the electric simulation of temperature fields at arc welding and building-up 356
17.5. Applying methods of the similarity theory of and the dimensional analysis 379
17.5.1. Theory of similarity and dimensional analysis in a technological thermal physics 381
17.5.2 Main criteria of the theory of similarity in heat transfer and thermal technique 388
Chapter 18 Effect of OPERATING PERIODICITY of WELDING HEAT SOURCE on TYPE and FEATURES of a thermal FIELD in workpieces to be welded 403
18.1. Temperature fields of sources moving on curvilinear pathways 404
18.1.1. Affecting oscillations of a welding heat source on the temperature field of a welded workpiece 418
18.1.2. Temperature field at welding with electrode oscillations for workpieces with large thickness of  metal 454
18.2. Influencing an alternation of power of welding heat source on the temperature field 459
18.2.1. Calculation of temperature fields at pulse arc welding 454
18.3. Mathematical models of temperature fields at welding by heat sources with changing power 481
THE BIBLIOGRAPHIC LIST 508
Addendum 1 List of the abbreviations 544
Addendum 2 Lists of main conventional nomenclatures 545

This monograph is written in Russian language 

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